diff --git a/PTD_NORMAL_BENCHMARK.md b/PTD_NORMAL_BENCHMARK.md
new file mode 100644
index 0000000000..17913d1ef1
--- /dev/null
+++ b/PTD_NORMAL_BENCHMARK.md
@@ -0,0 +1,247 @@
+# One-off `logp_dlogp` analysis for #8376 (to be removed before merge)
+
+Requested in review: an analysis of `model.logp_dlogp_function(ravel_inputs=True)` —
+the compiled graph (`print_memory_map=True`) and a timing that confirms no
+graph/eval regression after delegating Normal's `logp`/`logcdf`/`logccdf`/`icdf`
+to [pytensor-distributions](https://github.com/pymc-devs/pytensor-distributions).
+
+Produced by `benchmark_normal_ptd.py` (repo root). Raw artifacts (dprints,
+timings, op counts, values) live in `ptd_benchmark_results/{before,after}/`.
+
+## Reproduce
+
+```bash
+python benchmark_normal_ptd.py run --label after      # on this branch
+git switch --detach $(git merge-base upstream/main HEAD)
+python benchmark_normal_ptd.py run --label before     # old implementation
+git switch normal-pytensor-distributions
+python benchmark_normal_ptd.py compare
+```
+
+## Environment
+
+| | |
+|---|---|
+| before / after commits | `3b661c7e5` (merge-base with main) / `83cb13865` (this PR) |
+| pytensor / pytensor-distributions | 3.2.2 / 0.2.0 |
+| numpy / python | 2.4.6 / 3.13.11 |
+| machine / floatX | macOS 26.5.2 arm64 (M-series) / float64 |
+
+## Benchmarks
+
+1. **`normal`** — `mu ~ Normal`, `sigma ~ HalfNormal`, `obs ~ Normal(mu, sigma)` with
+   N=1000 observed. Exercises `Normal.logp` (scalar prior + vector likelihood).
+2. **`normal_censored`** — same plus `Censored(Normal.dist(mu, sigma), -1, 1)` with
+   N=500 observed, which pulls `Normal.logcdf` **and** `Normal.logccdf` into the
+   logp graph.
+3. **`icdf`** — standalone compiled `pm.icdf(pm.Normal.dist(1.5, 2.5), q)` (not part
+   of any logp graph, but also changed by this PR).
+
+Timings: `timeit.repeat(repeat=30, number=200)`, best (min) per call.
+
+## Results
+
+| bench | graph | before min | after min | ratio | values |
+|---|---|---:|---:|---:|---|
+| `normal` logp_dlogp | **byte-identical dprint** (141 lines) | 2.14 µs | 2.17 µs | **1.02** (noise) | bit-identical |
+| `normal_censored` logp_dlogp | differs (see below) | 26.9 µs | 36.1 µs | **1.34** | logp bit-identical; dlogp[0] differs by 1 ulp |
+| `icdf` | differs by design (see below) | 7.9 µs | 8.8 µs | 1.12 | ≤ 2 ulp |
+
+### `normal`: no regression ✅
+
+The delegated `logpdf` is the same expression as the old inline formula, so after
+rewrites the compiled `logp_dlogp` graph is **byte-for-byte identical** and evaluation
+time is unchanged. This is the core code path for the vast majority of models.
+
+### `normal_censored`: graph + eval regression from `logsf` ⚠️
+
+`pytensor_distributions.normal` implements
+
+```python
+def logsf(x, mu, sigma):
+    return logcdf(-x, -mu, sigma)
+```
+
+which is mathematically identical to the old `normal_lccdf`, but graph-wise it is
+not: `-x` bakes a **negated copy of the observed data into the graph as a second
+constant** (visible in the dprint as `[-5.244064 ... 58192e-01]`, duplicating the
+censored data's memory), and the standardized value inside becomes
+`(-x - (-mu))/sigma`, which the rewriter does not recombine into `-((x - mu)/sigma)`
+— so `logcdf` and `logccdf` no longer share the `z = (x - mu)/sigma` subexpression.
+Consequences on this model:
+
+- `DimShuffle` count 8 → 12; the censored fused elemwise grows from 5 to 9
+  `reduce[add]` outputs; dprint grows 500 → 571 lines.
+- eval time 26.9 µs → 36.1 µs (**1.34×**) for N=500 censored points.
+- `dlogp` wrt `mu` differs in the last ulp (different but equivalent expression
+  arrangement); logp itself is bit-identical.
+
+The old PyMC `normal_lccdf` applies the erfcx switch directly to `z`
+(`switch(z > 1, log(erfcx(z/√2)/2) − z²/2, log1p(−erfc(−z/√2)/2))`). Writing
+`logsf` that way in pytensor-distributions would restore subexpression sharing and
+remove the duplicated constant — a small upstream fix; alternatively PyMC can keep
+its own `logccdf` until then.
+
+### `icdf`: intentional behavior difference, minor micro-overhead
+
+- Old: `check_icdf_value` wraps `−erfcinv(2q)·σ√2 + μ` in a single
+  `switch(0 ≤ q ≤ 1, ..., nan)`.
+- New: the package's `ppf` uses `erfinv(2q − 1)` inside `ppf_bounds_cont`, which
+  adds explicit branches `q<0 or q>1 → nan`, `q=0 → −inf`, `q=1 → +inf`. Same
+  results (boundary infinities previously arose from `erfcinv` itself), values
+  match to ≤ 2 ulp (`erfinv` vs `erfcinv`), and the extra scalar switches cost
+  ~0.9 µs on a 1000-point batch. Not part of logp graphs; irrelevant for sampling.
+
+## Compiled graph (`print_memory_map=True`), after — `normal` model
+
+<details><summary>ptd_benchmark_results/after/normal_logp_dlogp_dprint.txt (byte-identical to before)</summary>
+
+```text
+Composite{...}.0 [id A] d={0: [1]} 8
+ ├─ Subtensor{i} [id B] v={0: [0]} 1
+ │  ├─ joined_inputs [id C]
+ │  └─ 1 [id D]
+ ├─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.0 [id E] 6
+ │  ├─ Composite{...}.1 [id F] 5
+ │  │  └─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │     └─ Exp [id H] 3
+ │  │        └─ Subtensor{i} [id B] v={0: [0]} 1
+ │  │           └─ ···
+ │  ├─ Composite{...}.0 [id F] 5
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ obs{[ 1.320334 ... 56013e+00]} [id I]
+ │  └─ Subtensor{:stop} [id J] v={0: [0]} 0
+ │     ├─ joined_inputs [id C]
+ │     └─ 1 [id K]
+ ├─ Subtensor{i} [id L] v={0: [0]} 2
+ │  ├─ joined_inputs [id C]
+ │  └─ 0 [id M]
+ └─ Exp [id H] 3
+    └─ ···
+Join{axis=0} [id N] 12
+ ├─ Composite{...}.0 [id O] d={0: [0], 1: [1]} 11
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id P] v={0: [0]} 7
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.1 [id E] 6
+ │  │     └─ ···
+ │  ├─ Subtensor{:stop} [id J] v={0: [0]} 0
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id Q] v={0: [0]} 10
+ │  │  └─ Composite{...}.1 [id A] d={0: [1]} 8
+ │  │     └─ ···
+ │  └─ ExpandDims{axis=0} [id R] v={0: [0]} 9
+ │     └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.2 [id E] 6
+ │        └─ ···
+ └─ Composite{...}.1 [id O] d={0: [0], 1: [1]} 11
+    └─ ···
+
+Inner graphs:
+
+Composite{...} [id A] d={0: [1]}
+ ← add [id S]
+    ├─ -3.221523658174155 [id T]
+    ├─ mul [id U]
+    │  ├─ -0.5 [id V]
+    │  └─ sqr [id W]
+    │     └─ mul [id X]
+    │        ├─ 0.1 [id Y]
+    │        └─ i2 [id Z]
+    ├─ Switch [id BA]
+    │  ├─ GE [id BB]
+    │  │  ├─ i3 [id BC]
+    │  │  └─ 0.0 [id BD]
+    │  ├─ add [id BE]
+    │  │  ├─ -1.83522929514961 [id BF]
+    │  │  └─ mul [id BG]
+    │  │     ├─ -0.5 [id V]
+    │  │     └─ sqr [id BH]
+    │  │        └─ mul [id BI]
+    │  │           ├─ 0.2 [id BJ]
+    │  │           └─ i3 [id BC]
+    │  └─ -inf [id BK]
+    ├─ i0 [id BL]
+    └─ i1 [id BM]
+ ← GE [id BB]
+    └─ ···
+
+FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]} [id E]
+ ← Sum{axes=None} [id BN]
+    └─ Composite{...}.0 [id BO]
+       ├─ i0 [id BP]
+       ├─ i1 [id BQ]
+       ├─ i2 [id BR]
+       ├─ i3 [id BS]
+       └─ i4 [id BT]
+ ← Sum{axes=None} [id BU]
+    └─ Composite{...}.1 [id BO]
+       └─ ···
+ ← Sum{axes=None} [id BV]
+    └─ Composite{...}.2 [id BO]
+       └─ ···
+
+Composite{...} [id F]
+ ← log [id BW]
+    └─ i0 [id BL]
+ ← GT [id BX]
+    ├─ i0 [id BL]
+    └─ 0 [id BY]
+
+Composite{...} [id O] d={0: [0], 1: [1]}
+ ← add [id BZ]
+    ├─ mul [id CA]
+    │  ├─ -0.0100000 ... 0000000002 [id CB]
+    │  └─ i2 [id Z]
+    └─ true_div [id CC]
+       ├─ true_div [id CD]
+       │  ├─ i1 [id BM]
+       │  └─ i0 [id BL]
+       └─ i0 [id BL]
+ ← add [id CE]
+    ├─ -999.0 [id CF]
+    ├─ Switch [id CG]
+    │  ├─ i3 [id CH]
+    │  ├─ mul [id CI]
+    │  │  ├─ -0.04000000000000001 [id CJ]
+    │  │  ├─ i0 [id BL]
+    │  │  └─ i0 [id BL]
+    │  └─ 0.0 [id CK]
+    └─ mul [id CL]
+       ├─ true_div [id CM]
+       │  ├─ i4 [id CN]
+       │  └─ sqr [id CO]
+       │     └─ i0 [id BL]
+       └─ i0 [id BL]
+
+Composite{...} [id BO]
+ ← Switch [id CP]
+    ├─ i0 [id CQ]
+    ├─ sub [id CR]
+    │  ├─ add [id CS]
+    │  │  ├─ -0.9189385332046727 [id CT]
+    │  │  └─ mul [id CU]
+    │  │     ├─ -0.5 [id CV]
+    │  │     └─ sqr [id CW]
+    │  │        └─ true_div [id CX]
+    │  │           ├─ sub [id CY]
+    │  │           │  ├─ i3 [id BC]
+    │  │           │  └─ i4 [id CN]
+    │  │           └─ i2 [id Z]
+    │  └─ i1 [id BM]
+    └─ -inf [id CZ]
+ ← sub [id CY]
+    └─ ···
+ ← mul [id DA]
+    ├─ true_div [id CX]
+    │  └─ ···
+    └─ sub [id CY]
+       └─ ···
+```
+
+</details>
+
+Full dprints for all benchmarks (before and after) are committed under
+`ptd_benchmark_results/` — `diff` the `before/` and `after/` files to see the
+graph changes described above.
diff --git a/benchmark_normal_ptd.py b/benchmark_normal_ptd.py
new file mode 100644
index 0000000000..c3ae27dd32
--- /dev/null
+++ b/benchmark_normal_ptd.py
@@ -0,0 +1,221 @@
+#   Copyright 2026 - present The PyMC Developers
+#
+#   Licensed under the Apache License, Version 2.0 (the "License");
+#   you may not use this file except in compliance with the License.
+#   You may obtain a copy of the License at
+#
+#       http://www.apache.org/licenses/LICENSE-2.0
+#
+#   Unless required by applicable law or agreed to in writing, software
+#   distributed under the License is distributed on an "AS IS" BASIS,
+#   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+#   See the License for the specific language governing permissions and
+#   limitations under the License.
+"""One-off benchmark for pymc-devs/pymc#8376 (to be removed before merge).
+
+Compares the compiled ``model.logp_dlogp_function(ravel_inputs=True)`` graph and
+its evaluation time before and after delegating Normal's logp/logcdf/logccdf/icdf
+to pytensor-distributions, as requested in review.
+
+Usage (run twice, then compare)::
+
+    python benchmark_normal_ptd.py run --label after      # on the PR branch
+    git switch --detach $(git merge-base upstream/main HEAD)
+    python benchmark_normal_ptd.py run --label before     # on main (old impl)
+    git switch normal-pytensor-distributions
+    python benchmark_normal_ptd.py compare
+
+Outputs go to ``ptd_benchmark_results/<label>/``.
+"""
+# ruff: noqa: T201
+
+import argparse
+import difflib
+import json
+import platform
+import subprocess
+import timeit
+
+from collections import Counter
+from pathlib import Path
+
+import numpy as np
+import pytensor
+import pytensor.tensor as pt
+
+import pymc as pm
+
+from pymc.blocking import DictToArrayBijection
+
+RESULTS_DIR = Path(__file__).parent / "ptd_benchmark_results"
+SEED = 20260807
+TIMEIT_REPEAT = 30
+TIMEIT_NUMBER = 200
+
+
+def build_models() -> dict[str, pm.Model]:
+    """Models exercising every Normal code path that reaches a logp graph.
+
+    ``normal`` only uses Normal.logp; ``normal_censored`` additionally pulls
+    Normal.logcdf and logccdf into the logp graph, isolating regressions to
+    the specific measure function responsible.
+    """
+    rng = np.random.default_rng(SEED)
+    data = rng.normal(0.5, 1.2, size=1_000)
+    cens_data = np.clip(rng.normal(0.0, 1.0, size=500), -1.0, 1.0)
+
+    with pm.Model() as m_basic:
+        mu = pm.Normal("mu", 0.0, 10.0)  # Normal.logp (scalar prior)
+        sigma = pm.HalfNormal("sigma", 5.0)  # untouched by the PR
+        pm.Normal("obs", mu, sigma, observed=data)  # Normal.logp (vector likelihood)
+
+    with pm.Model() as m_cens:
+        mu = pm.Normal("mu", 0.0, 10.0)
+        sigma = pm.HalfNormal("sigma", 5.0)
+        pm.Normal("obs", mu, sigma, observed=data)
+        pm.Censored(  # Normal.logcdf + logccdf
+            "cens",
+            pm.Normal.dist(mu, sigma),
+            lower=-1.0,
+            upper=1.0,
+            observed=cens_data,
+        )
+    return {"normal": m_basic, "normal_censored": m_cens}
+
+
+def time_call(fn, *args) -> dict:
+    times = timeit.repeat(lambda: fn(*args), repeat=TIMEIT_REPEAT, number=TIMEIT_NUMBER)
+    per_call_us = [t / TIMEIT_NUMBER * 1e6 for t in times]
+    return {
+        "min_us": min(per_call_us),
+        "median_us": float(np.median(per_call_us)),
+        "repeat": TIMEIT_REPEAT,
+        "number": TIMEIT_NUMBER,
+    }
+
+
+def op_counts(fgraph) -> dict:
+    return dict(Counter(type(node.op).__name__ for node in fgraph.apply_nodes).most_common())
+
+
+def run(label: str) -> None:
+    out = RESULTS_DIR / label
+    out.mkdir(parents=True, exist_ok=True)
+
+    values, timings, ops = {}, {}, {}
+    for name, m in build_models().items():
+        f = m.logp_dlogp_function(ravel_inputs=True)
+        f.set_extra_values({})
+        x = DictToArrayBijection.map(m.initial_point()).data
+
+        with open(out / f"{name}_logp_dlogp_dprint.txt", "w") as fh:
+            pytensor.dprint(f._pytensor_function, print_memory_map=True, file=fh)
+
+        logp, dlogp = f(x)
+        values[name] = {"logp": repr(float(logp)), "dlogp": [repr(float(g)) for g in dlogp]}
+        timings[name] = time_call(f, x)
+        ops[name] = op_counts(f._pytensor_function.maker.fgraph)
+
+    # icdf is changed by the PR but does not appear in logp graphs; time it separately.
+    q = pt.dvector("q")
+    icdf_fn = pytensor.function([q], pm.icdf(pm.Normal.dist(1.5, 2.5), q))
+    with open(out / "icdf_dprint.txt", "w") as fh:
+        pytensor.dprint(icdf_fn, print_memory_map=True, file=fh)
+    q_vals = np.linspace(0.001, 0.999, 1_000)
+    values["icdf"] = [repr(float(v)) for v in icdf_fn(q_vals)[::100]]
+    timings["icdf"] = time_call(icdf_fn, q_vals)
+    ops["icdf"] = op_counts(icdf_fn.maker.fgraph)
+
+    commit = subprocess.run(
+        ["git", "rev-parse", "--short", "HEAD"], capture_output=True, text=True, check=True
+    ).stdout.strip()
+    try:
+        import pytensor_distributions
+
+        ptd_version = pytensor_distributions.__version__
+    except ImportError:
+        ptd_version = None
+    meta = {
+        "label": label,
+        "commit": commit,
+        "pymc": pm.__version__,
+        "pytensor": pytensor.__version__,
+        "pytensor_distributions": ptd_version,
+        "numpy": np.__version__,
+        "python": platform.python_version(),
+        "machine": platform.platform(),
+        "floatX": pytensor.config.floatX,
+    }
+
+    (out / "meta.json").write_text(json.dumps(meta, indent=2))
+    (out / "timings.json").write_text(json.dumps(timings, indent=2))
+    (out / "values.json").write_text(json.dumps(values, indent=2))
+    (out / "op_counts.json").write_text(json.dumps(ops, indent=2))
+    print(f"[{label}] commit={commit}")
+    print(json.dumps(timings, indent=2))
+
+
+def compare() -> int:
+    before, after = RESULTS_DIR / "before", RESULTS_DIR / "after"
+    status = 0
+
+    for name in (
+        "normal_logp_dlogp_dprint.txt",
+        "normal_censored_logp_dlogp_dprint.txt",
+        "icdf_dprint.txt",
+    ):
+        a, b = (before / name).read_text(), (after / name).read_text()
+        if a == b:
+            print(f"GRAPH {name}: IDENTICAL ({len(b.splitlines())} lines)")
+        else:
+            status = 1
+            diff = list(
+                difflib.unified_diff(a.splitlines(True), b.splitlines(True), "before", "after")
+            )
+            print(f"GRAPH {name}: DIFFERS ({len(diff)} diff lines, first 40 shown)")
+            print("".join(diff[:40]))
+
+    va = json.loads((before / "values.json").read_text())
+    vb = json.loads((after / "values.json").read_text())
+    if va == vb:
+        print("VALUES: logp/dlogp/icdf bit-identical across runs")
+    else:
+        status = 1
+        print(f"VALUES DIFFER:\n  before: {va}\n  after:  {vb}")
+
+    ta = json.loads((before / "timings.json").read_text())
+    tb = json.loads((after / "timings.json").read_text())
+    print(
+        f"\n{'bench':<12} {'before min':>11} {'after min':>11} {'ratio':>6}   "
+        f"{'before med':>11} {'after med':>11}"
+    )
+    for key in ta:
+        r = tb[key]["min_us"] / ta[key]["min_us"]
+        print(
+            f"{key:<12} {ta[key]['min_us']:>9.1f}us {tb[key]['min_us']:>9.1f}us {r:>6.3f}   "
+            f"{ta[key]['median_us']:>9.1f}us {tb[key]['median_us']:>9.1f}us"
+        )
+
+    oa = json.loads((before / "op_counts.json").read_text())
+    ob = json.loads((after / "op_counts.json").read_text())
+    for key in oa:
+        if oa[key] != ob[key]:
+            print(f"\nOP COUNTS {key} changed:")
+            for op in sorted(set(oa[key]) | set(ob[key])):
+                na, nb = oa[key].get(op, 0), ob[key].get(op, 0)
+                if na != nb:
+                    print(f"  {op}: {na} -> {nb}")
+    return status
+
+
+if __name__ == "__main__":
+    parser = argparse.ArgumentParser(description=__doc__)
+    sub = parser.add_subparsers(dest="cmd", required=True)
+    run_p = sub.add_parser("run")
+    run_p.add_argument("--label", choices=["before", "after"], required=True)
+    sub.add_parser("compare")
+    cli_args = parser.parse_args()
+    if cli_args.cmd == "run":
+        run(cli_args.label)
+    else:
+        raise SystemExit(compare())
diff --git a/conda-envs/environment-alternative-backends.yml b/conda-envs/environment-alternative-backends.yml
index 9b87fa7c7f..375f00d692 100644
--- a/conda-envs/environment-alternative-backends.yml
+++ b/conda-envs/environment-alternative-backends.yml
@@ -21,6 +21,7 @@ dependencies:
 - pandas>=0.24.0
 - pip
 - pytensor>=3.2.2,<3.3
+- pytensor-distributions>=0.2.0,<=0.3.0
 - python-graphviz
 - networkx
 - rich>=13.7.1
diff --git a/conda-envs/environment-dev.yml b/conda-envs/environment-dev.yml
index 158ef1bfb5..d800e247fa 100644
--- a/conda-envs/environment-dev.yml
+++ b/conda-envs/environment-dev.yml
@@ -13,6 +13,7 @@ dependencies:
 - pandas>=0.24.0
 - pip
 - pytensor>=3.2.2,<3.3
+- pytensor-distributions>=0.2.0,<=0.3.0
 - python-graphviz
 - networkx
 - scipy>=1.4.1
diff --git a/conda-envs/environment-docs.yml b/conda-envs/environment-docs.yml
index 10f8db8236..25b9484073 100644
--- a/conda-envs/environment-docs.yml
+++ b/conda-envs/environment-docs.yml
@@ -12,6 +12,7 @@ dependencies:
 - pandas>=0.24.0
 - pip
 - pytensor>=3.2.2,<3.3
+- pytensor-distributions>=0.2.0,<=0.3.0
 - python-graphviz
 - rich>=13.7.1
 - scipy>=1.4.1
diff --git a/conda-envs/environment-test.yml b/conda-envs/environment-test.yml
index 56a71ae4ca..e833ba3437 100644
--- a/conda-envs/environment-test.yml
+++ b/conda-envs/environment-test.yml
@@ -16,6 +16,7 @@ dependencies:
 - pip
 - polyagamma
 - pytensor>=3.2.2,<3.3
+- pytensor-distributions>=0.2.0,<=0.3.0
 - python-graphviz
 - networkx
 - rich>=13.7.1
diff --git a/conda-envs/windows-environment-dev.yml b/conda-envs/windows-environment-dev.yml
index e0e4d1adb3..ad6b1ef9e5 100644
--- a/conda-envs/windows-environment-dev.yml
+++ b/conda-envs/windows-environment-dev.yml
@@ -13,6 +13,7 @@ dependencies:
 - pandas>=0.24.0
 - pip
 - pytensor>=3.2.2,<3.3
+- pytensor-distributions>=0.2.0,<=0.3.0
 - python-graphviz
 - networkx
 - rich>=13.7.1
diff --git a/conda-envs/windows-environment-test.yml b/conda-envs/windows-environment-test.yml
index 221244a916..8d9b5538af 100644
--- a/conda-envs/windows-environment-test.yml
+++ b/conda-envs/windows-environment-test.yml
@@ -17,6 +17,7 @@ dependencies:
 - pip
 - polyagamma
 - pytensor>=3.2.2,<3.3
+- pytensor-distributions>=0.2.0,<=0.3.0
 - python-graphviz
 - networkx
 - rich>=13.7.1
diff --git a/ptd_benchmark_results/after/icdf_dprint.txt b/ptd_benchmark_results/after/icdf_dprint.txt
new file mode 100644
index 0000000000..34587bac9d
--- /dev/null
+++ b/ptd_benchmark_results/after/icdf_dprint.txt
@@ -0,0 +1,40 @@
+Composite{switch(or(lt(i0, 0), gt(i0, 1)), nan, switch(eq(i0, 0), -inf, switch(eq(i0, 1), inf, (1.5 + (3.5355339059327378 * i1)))))} [id A] d={0: [1]} 2
+ ├─ q [id B]
+ └─ Erfinv [id C] d={0: [0]} 1
+    └─ Composite{(-1.0 + (2.0 * i0))} [id D] 0
+       └─ q [id B]
+
+Inner graphs:
+
+Composite{switch(or(lt(i0, 0), gt(i0, 1)), nan, switch(eq(i0, 0), -inf, switch(eq(i0, 1), inf, (1.5 + (3.5355339059327378 * i1)))))} [id A] d={0: [1]}
+ ← Switch [id E]
+    ├─ OR [id F]
+    │  ├─ LT [id G]
+    │  │  ├─ i0 [id H]
+    │  │  └─ 0 [id I]
+    │  └─ GT [id J]
+    │     ├─ i0 [id H]
+    │     └─ 1 [id K]
+    ├─ nan [id L]
+    └─ Switch [id M]
+       ├─ EQ [id N]
+       │  ├─ i0 [id H]
+       │  └─ 0 [id I]
+       ├─ -inf [id O]
+       └─ Switch [id P]
+          ├─ EQ [id Q]
+          │  ├─ i0 [id H]
+          │  └─ 1 [id K]
+          ├─ inf [id R]
+          └─ add [id S]
+             ├─ 1.5 [id T]
+             └─ mul [id U]
+                ├─ 3.5355339059327378 [id V]
+                └─ i1 [id W]
+
+Composite{(-1.0 + (2.0 * i0))} [id D]
+ ← add [id X]
+    ├─ -1.0 [id Y]
+    └─ mul [id Z]
+       ├─ 2.0 [id BA]
+       └─ i0 [id H]
diff --git a/ptd_benchmark_results/after/meta.json b/ptd_benchmark_results/after/meta.json
new file mode 100644
index 0000000000..424f734c48
--- /dev/null
+++ b/ptd_benchmark_results/after/meta.json
@@ -0,0 +1,11 @@
+{
+  "label": "after",
+  "commit": "83cb13865",
+  "pymc": "0+untagged.10565.g83cb138",
+  "pytensor": "3.2.2",
+  "pytensor_distributions": "0.2.0",
+  "numpy": "2.4.6",
+  "python": "3.13.11",
+  "machine": "macOS-26.5.2-arm64-arm-64bit-Mach-O",
+  "floatX": "float64"
+}
diff --git a/ptd_benchmark_results/after/normal_censored_logp_dlogp_dprint.txt b/ptd_benchmark_results/after/normal_censored_logp_dlogp_dprint.txt
new file mode 100644
index 0000000000..f215213d07
--- /dev/null
+++ b/ptd_benchmark_results/after/normal_censored_logp_dlogp_dprint.txt
@@ -0,0 +1,571 @@
+Composite{...}.0 [id A] d={0: [1]} 16
+ ├─ Subtensor{i} [id B] v={0: [0]} 0
+ │  ├─ joined_inputs [id C]
+ │  └─ 1 [id D]
+ ├─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.0 [id E] 7
+ │  ├─ Composite{...}.2 [id F] 5
+ │  │  └─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │     └─ Exp [id H] 3
+ │  │        └─ Subtensor{i} [id B] v={0: [0]} 0
+ │  │           └─ ···
+ │  ├─ Composite{...}.1 [id F] 5
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ obs{[ 1.320334 ... 56013e+00]} [id I]
+ │  └─ Subtensor{:stop} [id J] v={0: [0]} 2
+ │     ├─ joined_inputs [id C]
+ │     └─ 1 [id K]
+ ├─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.0 [id L] 6
+ │  ├─ [False Fal ... lse False] [id M]
+ │  ├─ Composite{...}.2 [id F] 5
+ │  │  └─ ···
+ │  ├─ [False Fal ... rue False] [id N]
+ │  ├─ Composite{...}.1 [id F] 5
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ cens{[ 5.244064 ... 58192e-01]} [id O]
+ │  ├─ Subtensor{:stop} [id J] v={0: [0]} 2
+ │  │  └─ ···
+ │  ├─ [-5.244064 ... 58192e-01] [id P]
+ │  ├─ Composite{...}.0 [id F] 5
+ │  │  └─ ···
+ │  ├─ [ 0.  0. ... . -1.  0.] [id Q]
+ │  └─ [ 0.  0. ... .  0.  0.] [id R]
+ ├─ Subtensor{i} [id S] v={0: [0]} 1
+ │  ├─ joined_inputs [id C]
+ │  └─ 0 [id T]
+ └─ Exp [id H] 3
+    └─ ···
+Join{axis=0} [id U] 21
+ ├─ Composite{...}.0 [id V] d={0: [0], 1: [1]} 20
+ │  ├─ ExpandDims{axis=0} [id W] v={0: [0]} 8
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.7 [id L] 6
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id X] v={0: [0]} 18
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.1 [id E] 7
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id Y] v={0: [0]} 15
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.8 [id L] 6
+ │  │     └─ ···
+ │  ├─ Subtensor{:stop} [id J] v={0: [0]} 2
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id Z] v={0: [0]} 14
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.5 [id L] 6
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id BA] v={0: [0]} 13
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.4 [id L] 6
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id BB] v={0: [0]} 12
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.3 [id L] 6
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id BC] v={0: [0]} 11
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.2 [id L] 6
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id BD] v={0: [0]} 10
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.1 [id L] 6
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id BE] v={0: [0]} 19
+ │  │  └─ Composite{...}.1 [id A] d={0: [1]} 16
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id BF] v={0: [0]} 17
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.2 [id E] 7
+ │  │     └─ ···
+ │  ├─ Composite{...}.0 [id F] 5
+ │  │  └─ ···
+ │  └─ ExpandDims{axis=0} [id BG] v={0: [0]} 9
+ │     └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.6 [id L] 6
+ │        └─ ···
+ └─ Composite{...}.1 [id V] d={0: [0], 1: [1]} 20
+    └─ ···
+
+Inner graphs:
+
+Composite{...} [id A] d={0: [1]}
+ ← add [id BH]
+    ├─ -3.221523658174155 [id BI]
+    ├─ mul [id BJ]
+    │  ├─ -0.5 [id BK]
+    │  └─ sqr [id BL]
+    │     └─ mul [id BM]
+    │        ├─ 0.1 [id BN]
+    │        └─ i3 [id BO]
+    ├─ Switch [id BP]
+    │  ├─ GE [id BQ]
+    │  │  ├─ i4 [id BR]
+    │  │  └─ 0.0 [id BS]
+    │  ├─ add [id BT]
+    │  │  ├─ -1.83522929514961 [id BU]
+    │  │  └─ mul [id BV]
+    │  │     ├─ -0.5 [id BK]
+    │  │     └─ sqr [id BW]
+    │  │        └─ mul [id BX]
+    │  │           ├─ 0.2 [id BY]
+    │  │           └─ i4 [id BR]
+    │  └─ -inf [id BZ]
+    ├─ i0 [id CA]
+    ├─ i1 [id CB]
+    └─ i2 [id CC]
+ ← GE [id BQ]
+    └─ ···
+
+FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]} [id E]
+ ← Sum{axes=None} [id CD]
+    └─ Composite{...}.0 [id CE]
+       ├─ i0 [id CF]
+       ├─ i1 [id CG]
+       ├─ i2 [id CH]
+       ├─ i3 [id CI]
+       └─ i4 [id CJ]
+ ← Sum{axes=None} [id CK]
+    └─ Composite{...}.1 [id CE]
+       └─ ···
+ ← Sum{axes=None} [id CL]
+    └─ Composite{...}.2 [id CE]
+       └─ ···
+
+Composite{...} [id F]
+ ← sqr [id CM]
+    └─ i0 [id CA]
+ ← log [id CN]
+    └─ i0 [id CA]
+ ← GT [id CO]
+    ├─ i0 [id CA]
+    └─ 0 [id CP]
+
+FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]} [id L]
+ ← Sum{axes=None} [id CQ]
+    └─ Composite{...}.0 [id CR]
+       ├─ i0 [id CS]
+       ├─ i1 [id CT]
+       ├─ i2 [id CU]
+       ├─ i3 [id CV]
+       ├─ i4 [id CJ]
+       ├─ i5 [id CW]
+       ├─ i6 [id CX]
+       ├─ i7 [id CY]
+       ├─ i8 [id CZ]
+       ├─ i9 [id DA]
+       └─ i10 [id DB]
+ ← Sum{axes=None} [id DC]
+    └─ Composite{...}.1 [id CR]
+       └─ ···
+ ← Sum{axes=None} [id DD]
+    └─ Composite{...}.2 [id CR]
+       └─ ···
+ ← Sum{axes=None} [id DE]
+    └─ Composite{...}.3 [id CR]
+       └─ ···
+ ← Sum{axes=None} [id DF]
+    └─ Composite{...}.4 [id CR]
+       └─ ···
+ ← Sum{axes=None} [id DG]
+    └─ Composite{...}.5 [id CR]
+       └─ ···
+ ← Sum{axes=None} [id DH]
+    └─ Composite{...}.6 [id CR]
+       └─ ···
+ ← Sum{axes=None} [id DI]
+    └─ Composite{...}.7 [id CR]
+       └─ ···
+ ← Sum{axes=None} [id DJ]
+    └─ Composite{...}.8 [id CR]
+       └─ ···
+
+Composite{...} [id V] d={0: [0], 1: [1]}
+ ← add [id DK]
+    ├─ mul [id DL]
+    │  ├─ -0.0100000 ... 0000000002 [id DM]
+    │  └─ i4 [id BR]
+    ├─ true_div [id DN]
+    │  ├─ true_div [id DO]
+    │  │  ├─ i2 [id CC]
+    │  │  └─ i1 [id CB]
+    │  └─ i1 [id CB]
+    ├─ neg [id DP]
+    │  └─ i3 [id BO]
+    └─ i0 [id CA]
+ ← add [id DQ]
+    ├─ 1.0 [id DR]
+    └─ mul [id DS]
+       ├─ add [id DT]
+       │  ├─ Switch [id DU]
+       │  │  ├─ i10 [id DV]
+       │  │  ├─ mul [id DW]
+       │  │  │  ├─ -0.04000000000000001 [id DX]
+       │  │  │  └─ i1 [id CB]
+       │  │  └─ 0.0 [id DY]
+       │  ├─ true_div [id DZ]
+       │  │  ├─ i11 [id EA]
+       │  │  └─ i12 [id EB]
+       │  ├─ true_div [id EC]
+       │  │  ├─ -1342.0 [id ED]
+       │  │  └─ i1 [id CB]
+       │  ├─ true_div [id EE]
+       │  │  ├─ neg [id EF]
+       │  │  │  └─ i13 [id EG]
+       │  │  └─ i12 [id EB]
+       │  ├─ i5 [id EH]
+       │  ├─ i6 [id EI]
+       │  ├─ i7 [id EJ]
+       │  ├─ i8 [id EK]
+       │  └─ i9 [id EL]
+       └─ i1 [id CB]
+
+Composite{...} [id CE]
+ ← Switch [id EM]
+    ├─ i0 [id EN]
+    ├─ sub [id EO]
+    │  ├─ add [id EP]
+    │  │  ├─ -0.9189385332046727 [id EQ]
+    │  │  └─ mul [id ER]
+    │  │     ├─ -0.5 [id ES]
+    │  │     └─ sqr [id ET]
+    │  │        └─ true_div [id EU]
+    │  │           ├─ sub [id EV]
+    │  │           │  ├─ i3 [id BO]
+    │  │           │  └─ i4 [id BR]
+    │  │           └─ i2 [id CC]
+    │  └─ i1 [id CB]
+    └─ -inf [id EW]
+ ← sub [id EV]
+    └─ ···
+ ← mul [id EX]
+    ├─ true_div [id EU]
+    │  └─ ···
+    └─ sub [id EV]
+       └─ ···
+
+Composite{...} [id CR]
+ ← Switch [id EY]
+    ├─ i0 [id EN]
+    ├─ Switch [id EZ]
+    │  ├─ i1 [id FA]
+    │  ├─ Switch [id FB]
+    │  │  ├─ LT [id FC]
+    │  │  │  ├─ true_div [id FD]
+    │  │  │  │  ├─ sub [id FE]
+    │  │  │  │  │  ├─ i5 [id EH]
+    │  │  │  │  │  └─ i6 [id EI]
+    │  │  │  │  └─ i4 [id BR]
+    │  │  │  └─ -1.0 [id FF]
+    │  │  ├─ sub [id FG]
+    │  │  │  ├─ log [id FH]
+    │  │  │  │  └─ mul [id FI]
+    │  │  │  │     ├─ 0.5 [id FJ]
+    │  │  │  │     └─ erfcx [id FK]
+    │  │  │  │        └─ true_div [id FL]
+    │  │  │  │           ├─ mul [id FM]
+    │  │  │  │           │  ├─ -0.7071067932881648 [id FN]
+    │  │  │  │           │  └─ sub [id FE]
+    │  │  │  │           │     └─ ···
+    │  │  │  │           └─ i4 [id BR]
+    │  │  │  └─ mul [id FO]
+    │  │  │     ├─ 0.5 [id FJ]
+    │  │  │     └─ sqr [id FP]
+    │  │  │        └─ true_div [id FD]
+    │  │  │           └─ ···
+    │  │  └─ log1p [id FQ]
+    │  │     └─ mul [id FR]
+    │  │        ├─ -0.5 [id FS]
+    │  │        └─ erfc [id FT]
+    │  │           └─ true_div [id FU]
+    │  │              ├─ mul [id FV]
+    │  │              │  ├─ 0.7071067932881648 [id FW]
+    │  │              │  └─ sub [id FE]
+    │  │              │     └─ ···
+    │  │              └─ i4 [id BR]
+    │  └─ -inf [id FX]
+    └─ Switch [id FY]
+       ├─ i2 [id FZ]
+       ├─ Switch [id GA]
+       │  ├─ i1 [id FA]
+       │  ├─ Switch [id GB]
+       │  │  ├─ LT [id GC]
+       │  │  │  ├─ true_div [id GD]
+       │  │  │  │  ├─ add [id GE]
+       │  │  │  │  │  ├─ i7 [id EJ]
+       │  │  │  │  │  └─ i6 [id EI]
+       │  │  │  │  └─ i4 [id BR]
+       │  │  │  └─ -1.0 [id FF]
+       │  │  ├─ sub [id GF]
+       │  │  │  ├─ log [id GG]
+       │  │  │  │  └─ mul [id GH]
+       │  │  │  │     ├─ 0.5 [id FJ]
+       │  │  │  │     └─ erfcx [id GI]
+       │  │  │  │        └─ true_div [id GJ]
+       │  │  │  │           ├─ mul [id GK]
+       │  │  │  │           │  ├─ -0.7071067932881648 [id FN]
+       │  │  │  │           │  └─ add [id GE]
+       │  │  │  │           │     └─ ···
+       │  │  │  │           └─ i4 [id BR]
+       │  │  │  └─ mul [id GL]
+       │  │  │     ├─ 0.5 [id FJ]
+       │  │  │     └─ sqr [id GM]
+       │  │  │        └─ true_div [id GD]
+       │  │  │           └─ ···
+       │  │  └─ log1p [id GN]
+       │  │     └─ mul [id GO]
+       │  │        ├─ -0.5 [id FS]
+       │  │        └─ erfc [id GP]
+       │  │           └─ true_div [id GQ]
+       │  │              ├─ mul [id GR]
+       │  │              │  ├─ 0.7071067932881648 [id FW]
+       │  │              │  └─ add [id GE]
+       │  │              │     └─ ···
+       │  │              └─ i4 [id BR]
+       │  └─ -inf [id FX]
+       └─ Switch [id GS]
+          ├─ i1 [id FA]
+          ├─ sub [id GT]
+          │  ├─ add [id GU]
+          │  │  ├─ -0.9189385332046727 [id GV]
+          │  │  └─ mul [id GW]
+          │  │     ├─ -0.5 [id FS]
+          │  │     └─ sqr [id FP]
+          │  │        └─ ···
+          │  └─ i3 [id BO]
+          └─ -inf [id FX]
+ ← Switch [id GX]
+    ├─ LT [id GC]
+    │  └─ ···
+    ├─ 0.0 [id GY]
+    └─ Switch [id GZ]
+       ├─ i2 [id FZ]
+       ├─ Switch [id HA]
+       │  ├─ i0 [id EN]
+       │  ├─ 0.0 [id GY]
+       │  └─ true_div [id HB]
+       │     ├─ true_div [id HC]
+       │     │  ├─ mul [id HD]
+       │     │  │  ├─ -0.3989422872290391 [id HE]
+       │     │  │  ├─ exp [id HF]
+       │     │  │  │  └─ true_div [id HG]
+       │     │  │  │     ├─ mul [id HH]
+       │     │  │  │     │  ├─ -0.5000000171142714 [id HI]
+       │     │  │  │     │  ├─ add [id GE]
+       │     │  │  │     │  │  └─ ···
+       │     │  │  │     │  └─ add [id GE]
+       │     │  │  │     │     └─ ···
+       │     │  │  │     └─ i8 [id EK]
+       │     │  │  └─ add [id GE]
+       │     │  │     └─ ···
+       │     │  └─ add [id HJ]
+       │     │     ├─ 1.0 [id HK]
+       │     │     └─ mul [id GO]
+       │     │        └─ ···
+       │     └─ i8 [id EK]
+       └─ 0.0 [id GY]
+ ← Switch [id HL]
+    ├─ LT [id GC]
+    │  └─ ···
+    ├─ Switch [id HM]
+    │  ├─ i2 [id FZ]
+    │  ├─ Switch [id HN]
+    │  │  ├─ i0 [id EN]
+    │  │  ├─ 0.0 [id GY]
+    │  │  └─ true_div [id HO]
+    │  │     ├─ true_div [id HP]
+    │  │     │  ├─ mul [id HQ]
+    │  │     │  │  ├─ 0.7071067932881648 [id FW]
+    │  │     │  │  ├─ add [id HR]
+    │  │     │  │  │  ├─ true_div [id HS]
+    │  │     │  │  │  │  ├─ -1.1283791670955126 [id HT]
+    │  │     │  │  │  │  └─ erfcx [id GI]
+    │  │     │  │  │  │     └─ ···
+    │  │     │  │  │  └─ true_div [id HU]
+    │  │     │  │  │     ├─ mul [id HV]
+    │  │     │  │  │     │  ├─ -1.4142135865763297 [id HW]
+    │  │     │  │  │     │  └─ add [id GE]
+    │  │     │  │  │     │     └─ ···
+    │  │     │  │  │     └─ i4 [id BR]
+    │  │     │  │  └─ add [id GE]
+    │  │     │  │     └─ ···
+    │  │     │  └─ i4 [id BR]
+    │  │     └─ i4 [id BR]
+    │  └─ 0.0 [id GY]
+    └─ 0.0 [id GY]
+ ← Switch [id HX]
+    ├─ LT [id GC]
+    │  └─ ···
+    ├─ true_div [id HY]
+    │  ├─ neg [id HZ]
+    │  │  └─ true_div [id IA]
+    │  │     ├─ mul [id IB]
+    │  │     │  ├─ i9 [id EL]
+    │  │     │  ├─ add [id GE]
+    │  │     │  │  └─ ···
+    │  │     │  └─ add [id GE]
+    │  │     │     └─ ···
+    │  │     └─ i4 [id BR]
+    │  └─ i8 [id EK]
+    └─ 0.0 [id GY]
+ ← Switch [id IC]
+    ├─ LT [id FC]
+    │  └─ ···
+    ├─ 0.0 [id GY]
+    └─ Switch [id ID]
+       ├─ i0 [id EN]
+       ├─ true_div [id IE]
+       │  ├─ true_div [id IF]
+       │  │  ├─ mul [id IG]
+       │  │  │  ├─ -0.3989422872290391 [id HE]
+       │  │  │  ├─ exp [id IH]
+       │  │  │  │  └─ true_div [id II]
+       │  │  │  │     ├─ mul [id IJ]
+       │  │  │  │     │  ├─ -0.5000000171142714 [id HI]
+       │  │  │  │     │  ├─ sub [id FE]
+       │  │  │  │     │  │  └─ ···
+       │  │  │  │     │  └─ sub [id FE]
+       │  │  │  │     │     └─ ···
+       │  │  │  │     └─ i8 [id EK]
+       │  │  │  └─ sub [id FE]
+       │  │  │     └─ ···
+       │  │  └─ add [id IK]
+       │  │     ├─ 1.0 [id HK]
+       │  │     └─ mul [id FR]
+       │  │        └─ ···
+       │  └─ i8 [id EK]
+       └─ 0.0 [id GY]
+ ← Switch [id IL]
+    ├─ LT [id FC]
+    │  └─ ···
+    ├─ Switch [id IM]
+    │  ├─ i0 [id EN]
+    │  ├─ true_div [id IN]
+    │  │  ├─ true_div [id IO]
+    │  │  │  ├─ mul [id IP]
+    │  │  │  │  ├─ 0.7071067932881648 [id FW]
+    │  │  │  │  ├─ add [id IQ]
+    │  │  │  │  │  ├─ true_div [id IR]
+    │  │  │  │  │  │  ├─ -1.1283791670955126 [id HT]
+    │  │  │  │  │  │  └─ erfcx [id FK]
+    │  │  │  │  │  │     └─ ···
+    │  │  │  │  │  └─ true_div [id IS]
+    │  │  │  │  │     ├─ mul [id IT]
+    │  │  │  │  │     │  ├─ -1.4142135865763297 [id HW]
+    │  │  │  │  │     │  └─ sub [id FE]
+    │  │  │  │  │     │     └─ ···
+    │  │  │  │  │     └─ i4 [id BR]
+    │  │  │  │  └─ sub [id FE]
+    │  │  │  │     └─ ···
+    │  │  │  └─ i4 [id BR]
+    │  │  └─ i4 [id BR]
+    │  └─ 0.0 [id GY]
+    └─ 0.0 [id GY]
+ ← add [id IU]
+    ├─ Switch [id IV]
+    │  ├─ LT [id FC]
+    │  │  └─ ···
+    │  ├─ true_div [id IW]
+    │  │  ├─ mul [id IX]
+    │  │  │  ├─ i10 [id IY]
+    │  │  │  ├─ sub [id FE]
+    │  │  │  │  └─ ···
+    │  │  │  └─ sub [id FE]
+    │  │  │     └─ ···
+    │  │  └─ i4 [id BR]
+    │  └─ 0.0 [id GY]
+    └─ Switch [id IZ]
+       ├─ i2 [id FZ]
+       ├─ 0.0 [id GY]
+       └─ Switch [id JA]
+          ├─ i0 [id EN]
+          ├─ 0.0 [id GY]
+          └─ mul [id JB]
+             ├─ -1.0 [id JC]
+             ├─ true_div [id FD]
+             │  └─ ···
+             └─ sub [id FE]
+                └─ ···
+ ← Switch [id JD]
+    ├─ LT [id GC]
+    │  └─ ···
+    ├─ add [id JE]
+    │  ├─ true_div [id JF]
+    │  │  ├─ mul [id JG]
+    │  │  │  ├─ i9 [id EL]
+    │  │  │  └─ add [id GE]
+    │  │  │     └─ ···
+    │  │  └─ i8 [id EK]
+    │  └─ Switch [id JH]
+    │     ├─ i2 [id FZ]
+    │     ├─ Switch [id JI]
+    │     │  ├─ i0 [id EN]
+    │     │  ├─ 0.0 [id GY]
+    │     │  └─ true_div [id JJ]
+    │     │     ├─ mul [id JK]
+    │     │     │  ├─ -0.7071067932881648 [id FN]
+    │     │     │  └─ add [id HR]
+    │     │     │     └─ ···
+    │     │     └─ i4 [id BR]
+    │     └─ 0.0 [id GY]
+    └─ Switch [id JL]
+       ├─ i2 [id FZ]
+       ├─ Switch [id JM]
+       │  ├─ i0 [id EN]
+       │  ├─ 0.0 [id GY]
+       │  └─ true_div [id JN]
+       │     ├─ true_div [id JO]
+       │     │  ├─ mul [id JP]
+       │     │  │  ├─ 0.3989422872290391 [id JQ]
+       │     │  │  └─ exp [id HF]
+       │     │  │     └─ ···
+       │     │  └─ add [id HJ]
+       │     │     └─ ···
+       │     └─ i4 [id BR]
+       └─ 0.0 [id GY]
+ ← add [id JR]
+    ├─ Switch [id JS]
+    │  ├─ LT [id FC]
+    │  │  └─ ···
+    │  ├─ true_div [id JT]
+    │  │  ├─ mul [id JU]
+    │  │  │  ├─ i10 [id IY]
+    │  │  │  └─ sub [id FE]
+    │  │  │     └─ ···
+    │  │  └─ i8 [id EK]
+    │  └─ 0.0 [id GY]
+    ├─ Switch [id JV]
+    │  ├─ i2 [id FZ]
+    │  ├─ 0.0 [id GY]
+    │  └─ Switch [id JW]
+    │     ├─ i0 [id EN]
+    │     ├─ 0.0 [id GY]
+    │     └─ true_div [id JX]
+    │        ├─ neg [id JY]
+    │        │  └─ true_div [id FD]
+    │        │     └─ ···
+    │        └─ i4 [id BR]
+    ├─ Switch [id JZ]
+    │  ├─ LT [id FC]
+    │  │  └─ ···
+    │  ├─ Switch [id KA]
+    │  │  ├─ i0 [id EN]
+    │  │  ├─ true_div [id KB]
+    │  │  │  ├─ mul [id KC]
+    │  │  │  │  ├─ -0.7071067932881648 [id FN]
+    │  │  │  │  └─ add [id IQ]
+    │  │  │  │     └─ ···
+    │  │  │  └─ i4 [id BR]
+    │  │  └─ 0.0 [id GY]
+    │  └─ 0.0 [id GY]
+    └─ Switch [id KD]
+       ├─ LT [id FC]
+       │  └─ ···
+       ├─ 0.0 [id GY]
+       └─ Switch [id KE]
+          ├─ i0 [id EN]
+          ├─ true_div [id KF]
+          │  ├─ true_div [id KG]
+          │  │  ├─ mul [id KH]
+          │  │  │  ├─ 0.3989422872290391 [id JQ]
+          │  │  │  └─ exp [id IH]
+          │  │  │     └─ ···
+          │  │  └─ add [id IK]
+          │  │     └─ ···
+          │  └─ i4 [id BR]
+          └─ 0.0 [id GY]
diff --git a/ptd_benchmark_results/after/normal_logp_dlogp_dprint.txt b/ptd_benchmark_results/after/normal_logp_dlogp_dprint.txt
new file mode 100644
index 0000000000..27d3711d37
--- /dev/null
+++ b/ptd_benchmark_results/after/normal_logp_dlogp_dprint.txt
@@ -0,0 +1,141 @@
+Composite{...}.0 [id A] d={0: [1]} 8
+ ├─ Subtensor{i} [id B] v={0: [0]} 1
+ │  ├─ joined_inputs [id C]
+ │  └─ 1 [id D]
+ ├─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.0 [id E] 6
+ │  ├─ Composite{...}.1 [id F] 5
+ │  │  └─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │     └─ Exp [id H] 3
+ │  │        └─ Subtensor{i} [id B] v={0: [0]} 1
+ │  │           └─ ···
+ │  ├─ Composite{...}.0 [id F] 5
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ obs{[ 1.320334 ... 56013e+00]} [id I]
+ │  └─ Subtensor{:stop} [id J] v={0: [0]} 0
+ │     ├─ joined_inputs [id C]
+ │     └─ 1 [id K]
+ ├─ Subtensor{i} [id L] v={0: [0]} 2
+ │  ├─ joined_inputs [id C]
+ │  └─ 0 [id M]
+ └─ Exp [id H] 3
+    └─ ···
+Join{axis=0} [id N] 12
+ ├─ Composite{...}.0 [id O] d={0: [0], 1: [1]} 11
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id P] v={0: [0]} 7
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.1 [id E] 6
+ │  │     └─ ···
+ │  ├─ Subtensor{:stop} [id J] v={0: [0]} 0
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id Q] v={0: [0]} 10
+ │  │  └─ Composite{...}.1 [id A] d={0: [1]} 8
+ │  │     └─ ···
+ │  └─ ExpandDims{axis=0} [id R] v={0: [0]} 9
+ │     └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.2 [id E] 6
+ │        └─ ···
+ └─ Composite{...}.1 [id O] d={0: [0], 1: [1]} 11
+    └─ ···
+
+Inner graphs:
+
+Composite{...} [id A] d={0: [1]}
+ ← add [id S]
+    ├─ -3.221523658174155 [id T]
+    ├─ mul [id U]
+    │  ├─ -0.5 [id V]
+    │  └─ sqr [id W]
+    │     └─ mul [id X]
+    │        ├─ 0.1 [id Y]
+    │        └─ i2 [id Z]
+    ├─ Switch [id BA]
+    │  ├─ GE [id BB]
+    │  │  ├─ i3 [id BC]
+    │  │  └─ 0.0 [id BD]
+    │  ├─ add [id BE]
+    │  │  ├─ -1.83522929514961 [id BF]
+    │  │  └─ mul [id BG]
+    │  │     ├─ -0.5 [id V]
+    │  │     └─ sqr [id BH]
+    │  │        └─ mul [id BI]
+    │  │           ├─ 0.2 [id BJ]
+    │  │           └─ i3 [id BC]
+    │  └─ -inf [id BK]
+    ├─ i0 [id BL]
+    └─ i1 [id BM]
+ ← GE [id BB]
+    └─ ···
+
+FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]} [id E]
+ ← Sum{axes=None} [id BN]
+    └─ Composite{...}.0 [id BO]
+       ├─ i0 [id BP]
+       ├─ i1 [id BQ]
+       ├─ i2 [id BR]
+       ├─ i3 [id BS]
+       └─ i4 [id BT]
+ ← Sum{axes=None} [id BU]
+    └─ Composite{...}.1 [id BO]
+       └─ ···
+ ← Sum{axes=None} [id BV]
+    └─ Composite{...}.2 [id BO]
+       └─ ···
+
+Composite{...} [id F]
+ ← log [id BW]
+    └─ i0 [id BL]
+ ← GT [id BX]
+    ├─ i0 [id BL]
+    └─ 0 [id BY]
+
+Composite{...} [id O] d={0: [0], 1: [1]}
+ ← add [id BZ]
+    ├─ mul [id CA]
+    │  ├─ -0.0100000 ... 0000000002 [id CB]
+    │  └─ i2 [id Z]
+    └─ true_div [id CC]
+       ├─ true_div [id CD]
+       │  ├─ i1 [id BM]
+       │  └─ i0 [id BL]
+       └─ i0 [id BL]
+ ← add [id CE]
+    ├─ -999.0 [id CF]
+    ├─ Switch [id CG]
+    │  ├─ i3 [id CH]
+    │  ├─ mul [id CI]
+    │  │  ├─ -0.04000000000000001 [id CJ]
+    │  │  ├─ i0 [id BL]
+    │  │  └─ i0 [id BL]
+    │  └─ 0.0 [id CK]
+    └─ mul [id CL]
+       ├─ true_div [id CM]
+       │  ├─ i4 [id CN]
+       │  └─ sqr [id CO]
+       │     └─ i0 [id BL]
+       └─ i0 [id BL]
+
+Composite{...} [id BO]
+ ← Switch [id CP]
+    ├─ i0 [id CQ]
+    ├─ sub [id CR]
+    │  ├─ add [id CS]
+    │  │  ├─ -0.9189385332046727 [id CT]
+    │  │  └─ mul [id CU]
+    │  │     ├─ -0.5 [id CV]
+    │  │     └─ sqr [id CW]
+    │  │        └─ true_div [id CX]
+    │  │           ├─ sub [id CY]
+    │  │           │  ├─ i3 [id BC]
+    │  │           │  └─ i4 [id CN]
+    │  │           └─ i2 [id Z]
+    │  └─ i1 [id BM]
+    └─ -inf [id CZ]
+ ← sub [id CY]
+    └─ ···
+ ← mul [id DA]
+    ├─ true_div [id CX]
+    │  └─ ···
+    └─ sub [id CY]
+       └─ ···
diff --git a/ptd_benchmark_results/after/op_counts.json b/ptd_benchmark_results/after/op_counts.json
new file mode 100644
index 0000000000..7fab75cb9d
--- /dev/null
+++ b/ptd_benchmark_results/after/op_counts.json
@@ -0,0 +1,19 @@
+{
+  "normal": {
+    "DimShuffle": 4,
+    "Elemwise": 4,
+    "Subtensor": 3,
+    "FusedElemwise": 1,
+    "Join": 1
+  },
+  "normal_censored": {
+    "DimShuffle": 12,
+    "Elemwise": 4,
+    "Subtensor": 3,
+    "FusedElemwise": 2,
+    "Join": 1
+  },
+  "icdf": {
+    "Elemwise": 3
+  }
+}
diff --git a/ptd_benchmark_results/after/timings.json b/ptd_benchmark_results/after/timings.json
new file mode 100644
index 0000000000..282200333f
--- /dev/null
+++ b/ptd_benchmark_results/after/timings.json
@@ -0,0 +1,20 @@
+{
+  "normal": {
+    "min_us": 2.1735404152423143,
+    "median_us": 2.351772563997656,
+    "repeat": 30,
+    "number": 200
+  },
+  "normal_censored": {
+    "min_us": 36.0968749737367,
+    "median_us": 37.60218998650089,
+    "repeat": 30,
+    "number": 200
+  },
+  "icdf": {
+    "min_us": 8.832084713503718,
+    "median_us": 9.569687827024609,
+    "repeat": 30,
+    "number": 200
+  }
+}
diff --git a/ptd_benchmark_results/after/values.json b/ptd_benchmark_results/after/values.json
new file mode 100644
index 0000000000..92f929eb05
--- /dev/null
+++ b/ptd_benchmark_results/after/values.json
@@ -0,0 +1,28 @@
+{
+  "normal": {
+    "logp": "-2565.649159845185",
+    "dlogp": [
+      "19.75972105470103",
+      "-933.3492016689559"
+    ]
+  },
+  "normal_censored": {
+    "logp": "-3569.201218890812",
+    "dlogp": [
+      "20.518081388517622",
+      "-1241.858721191814"
+    ]
+  },
+  "icdf": [
+    "-6.225580765419532",
+    "-1.6911015859851155",
+    "-0.5969196055813767",
+    "0.1940270910127222",
+    "0.8705114551654745",
+    "1.5031301497393552",
+    "2.135952587027799",
+    "2.8131538074356452",
+    "3.605832423092286",
+    "4.705291106465694"
+  ]
+}
diff --git a/ptd_benchmark_results/before/icdf_dprint.txt b/ptd_benchmark_results/before/icdf_dprint.txt
new file mode 100644
index 0000000000..3dd3d87604
--- /dev/null
+++ b/ptd_benchmark_results/before/icdf_dprint.txt
@@ -0,0 +1,24 @@
+Composite{switch(and(ge(i0, 0), le(i0, 1)), (1.5 + (-3.5355339059327378 * i1)), nan)} [id A] '0 <= value <= 1' d={0: [1]} 2
+ ├─ q [id B]
+ └─ Erfcinv [id C] d={0: [0]} 1
+    └─ Mul [id D] 0
+       ├─ [2.] [id E]
+       └─ q [id B]
+
+Inner graphs:
+
+Composite{switch(and(ge(i0, 0), le(i0, 1)), (1.5 + (-3.5355339059327378 * i1)), nan)} [id A] d={0: [1]}
+ ← Switch [id F]
+    ├─ AND [id G]
+    │  ├─ GE [id H]
+    │  │  ├─ i0 [id I]
+    │  │  └─ 0 [id J]
+    │  └─ LE [id K]
+    │     ├─ i0 [id I]
+    │     └─ 1 [id L]
+    ├─ add [id M]
+    │  ├─ 1.5 [id N]
+    │  └─ mul [id O]
+    │     ├─ -3.5355339059327378 [id P]
+    │     └─ i1 [id Q]
+    └─ nan [id R]
diff --git a/ptd_benchmark_results/before/meta.json b/ptd_benchmark_results/before/meta.json
new file mode 100644
index 0000000000..9dc1a3a9c8
--- /dev/null
+++ b/ptd_benchmark_results/before/meta.json
@@ -0,0 +1,11 @@
+{
+  "label": "before",
+  "commit": "3b661c7e5",
+  "pymc": "0+untagged.10564.g3b661c7",
+  "pytensor": "3.2.2",
+  "pytensor_distributions": "0.2.0",
+  "numpy": "2.4.6",
+  "python": "3.13.11",
+  "machine": "macOS-26.5.2-arm64-arm-64bit-Mach-O",
+  "floatX": "float64"
+}
diff --git a/ptd_benchmark_results/before/normal_censored_logp_dlogp_dprint.txt b/ptd_benchmark_results/before/normal_censored_logp_dlogp_dprint.txt
new file mode 100644
index 0000000000..56da6665eb
--- /dev/null
+++ b/ptd_benchmark_results/before/normal_censored_logp_dlogp_dprint.txt
@@ -0,0 +1,500 @@
+Composite{...}.0 [id A] d={0: [1]} 10
+ ├─ Subtensor{i} [id B] v={0: [0]} 1
+ │  ├─ joined_inputs [id C]
+ │  └─ 1 [id D]
+ ├─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.0 [id E] 6
+ │  ├─ Composite{...}.2 [id F] 5
+ │  │  └─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │     └─ Exp [id H] 3
+ │  │        └─ Subtensor{i} [id B] v={0: [0]} 1
+ │  │           └─ ···
+ │  ├─ Composite{...}.1 [id F] 5
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ obs{[ 1.320334 ... 56013e+00]} [id I]
+ │  └─ Subtensor{:stop} [id J] v={0: [0]} 0
+ │     ├─ joined_inputs [id C]
+ │     └─ 1 [id K]
+ ├─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.0 [id L] 7
+ │  ├─ [False Fal ... lse False] [id M]
+ │  ├─ Composite{...}.2 [id F] 5
+ │  │  └─ ···
+ │  ├─ [False Fal ... rue False] [id N]
+ │  ├─ Composite{...}.1 [id F] 5
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ cens{[ 5.244064 ... 58192e-01]} [id O]
+ │  ├─ Subtensor{:stop} [id J] v={0: [0]} 0
+ │  │  └─ ···
+ │  ├─ Composite{...}.0 [id F] 5
+ │  │  └─ ···
+ │  ├─ [ 0.  0. ... . -1.  0.] [id P]
+ │  └─ [ 0.  0. ... .  0.  0.] [id Q]
+ ├─ Subtensor{i} [id R] v={0: [0]} 2
+ │  ├─ joined_inputs [id C]
+ │  └─ 0 [id S]
+ └─ Exp [id H] 3
+    └─ ···
+Join{axis=0} [id T] 17
+ ├─ Composite{...}.0 [id U] d={0: [0], 1: [1]} 16
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id V] v={0: [0]} 8
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.1 [id E] 6
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id W] v={0: [0]} 14
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.4 [id L] 7
+ │  │     └─ ···
+ │  ├─ Subtensor{:stop} [id J] v={0: [0]} 0
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id X] v={0: [0]} 15
+ │  │  └─ Composite{...}.1 [id A] d={0: [1]} 10
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id Y] v={0: [0]} 9
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.2 [id E] 6
+ │  │     └─ ···
+ │  ├─ Composite{...}.0 [id F] 5
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id Z] v={0: [0]} 13
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.3 [id L] 7
+ │  │     └─ ···
+ │  ├─ ExpandDims{axis=0} [id BA] v={0: [0]} 12
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.2 [id L] 7
+ │  │     └─ ···
+ │  └─ ExpandDims{axis=0} [id BB] v={0: [0]} 11
+ │     └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]}.1 [id L] 7
+ │        └─ ···
+ └─ Composite{...}.1 [id U] d={0: [0], 1: [1]} 16
+    └─ ···
+
+Inner graphs:
+
+Composite{...} [id A] d={0: [1]}
+ ← add [id BC]
+    ├─ -3.221523658174155 [id BD]
+    ├─ mul [id BE]
+    │  ├─ -0.5 [id BF]
+    │  └─ sqr [id BG]
+    │     └─ mul [id BH]
+    │        ├─ 0.1 [id BI]
+    │        └─ i3 [id BJ]
+    ├─ Switch [id BK]
+    │  ├─ GE [id BL]
+    │  │  ├─ i4 [id BM]
+    │  │  └─ 0.0 [id BN]
+    │  ├─ add [id BO]
+    │  │  ├─ -1.83522929514961 [id BP]
+    │  │  └─ mul [id BQ]
+    │  │     ├─ -0.5 [id BF]
+    │  │     └─ sqr [id BR]
+    │  │        └─ mul [id BS]
+    │  │           ├─ 0.2 [id BT]
+    │  │           └─ i4 [id BM]
+    │  └─ -inf [id BU]
+    ├─ i0 [id BV]
+    ├─ i1 [id BW]
+    └─ i2 [id BX]
+ ← GE [id BL]
+    └─ ···
+
+FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]} [id E]
+ ← Sum{axes=None} [id BY]
+    └─ Composite{...}.0 [id BZ]
+       ├─ i0 [id CA]
+       ├─ i1 [id CB]
+       ├─ i2 [id CC]
+       ├─ i3 [id CD]
+       └─ i4 [id CE]
+ ← Sum{axes=None} [id CF]
+    └─ Composite{...}.1 [id BZ]
+       └─ ···
+ ← Sum{axes=None} [id CG]
+    └─ Composite{...}.2 [id BZ]
+       └─ ···
+
+Composite{...} [id F]
+ ← sqr [id CH]
+    └─ i0 [id BV]
+ ← log [id CI]
+    └─ i0 [id BV]
+ ← GT [id CJ]
+    ├─ i0 [id BV]
+    └─ 0 [id CK]
+
+FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,), add@(0,), add@(0,)]} [id L]
+ ← Sum{axes=None} [id CL]
+    └─ Composite{...}.0 [id CM]
+       ├─ i0 [id CN]
+       ├─ i1 [id CO]
+       ├─ i2 [id CP]
+       ├─ i3 [id CQ]
+       ├─ i4 [id CE]
+       ├─ i5 [id CR]
+       ├─ i6 [id CS]
+       ├─ i7 [id CT]
+       ├─ i8 [id CU]
+       └─ i9 [id CV]
+ ← Sum{axes=None} [id CW]
+    └─ Composite{...}.1 [id CM]
+       └─ ···
+ ← Sum{axes=None} [id CX]
+    └─ Composite{...}.2 [id CM]
+       └─ ···
+ ← Sum{axes=None} [id CY]
+    └─ Composite{...}.3 [id CM]
+       └─ ···
+ ← Sum{axes=None} [id CZ]
+    └─ Composite{...}.4 [id CM]
+       └─ ···
+
+Composite{...} [id U] d={0: [0], 1: [1]}
+ ← add [id DA]
+    ├─ mul [id DB]
+    │  ├─ -0.0100000 ... 0000000002 [id DC]
+    │  └─ i3 [id BJ]
+    ├─ true_div [id DD]
+    │  ├─ true_div [id DE]
+    │  │  ├─ i1 [id BW]
+    │  │  └─ i0 [id BV]
+    │  └─ i0 [id BV]
+    └─ neg [id DF]
+       └─ i2 [id BX]
+ ← add [id DG]
+    ├─ 1.0 [id DH]
+    └─ mul [id DI]
+       ├─ add [id DJ]
+       │  ├─ Switch [id DK]
+       │  │  ├─ i4 [id DL]
+       │  │  ├─ mul [id DM]
+       │  │  │  ├─ -0.04000000000000001 [id DN]
+       │  │  │  └─ i0 [id BV]
+       │  │  └─ 0.0 [id DO]
+       │  ├─ true_div [id DP]
+       │  │  ├─ i5 [id DQ]
+       │  │  └─ i6 [id DR]
+       │  ├─ true_div [id DS]
+       │  │  ├─ -1342.0 [id DT]
+       │  │  └─ i0 [id BV]
+       │  ├─ true_div [id DU]
+       │  │  ├─ neg [id DV]
+       │  │  │  └─ i7 [id DW]
+       │  │  └─ i6 [id DR]
+       │  ├─ true_div [id DX]
+       │  │  ├─ neg [id DY]
+       │  │  │  └─ i8 [id DZ]
+       │  │  └─ i6 [id DR]
+       │  └─ true_div [id EA]
+       │     ├─ neg [id EB]
+       │     │  └─ i9 [id EC]
+       │     └─ i6 [id DR]
+       └─ i0 [id BV]
+
+Composite{...} [id BZ]
+ ← Switch [id ED]
+    ├─ i0 [id EE]
+    ├─ sub [id EF]
+    │  ├─ add [id EG]
+    │  │  ├─ -0.9189385332046727 [id EH]
+    │  │  └─ mul [id EI]
+    │  │     ├─ -0.5 [id EJ]
+    │  │     └─ sqr [id EK]
+    │  │        └─ true_div [id EL]
+    │  │           ├─ sub [id EM]
+    │  │           │  ├─ i3 [id BJ]
+    │  │           │  └─ i4 [id BM]
+    │  │           └─ i2 [id BX]
+    │  └─ i1 [id BW]
+    └─ -inf [id EN]
+ ← sub [id EM]
+    └─ ···
+ ← mul [id EO]
+    ├─ true_div [id EL]
+    │  └─ ···
+    └─ sub [id EM]
+       └─ ···
+
+Composite{...} [id CM]
+ ← Switch [id EP]
+    ├─ i0 [id EE]
+    ├─ Switch [id EQ]
+    │  ├─ i1 [id ER]
+    │  ├─ Switch [id ES]
+    │  │  ├─ LT [id ET]
+    │  │  │  ├─ true_div [id EU]
+    │  │  │  │  ├─ sub [id EV]
+    │  │  │  │  │  ├─ i5 [id DQ]
+    │  │  │  │  │  └─ i6 [id DR]
+    │  │  │  │  └─ i4 [id BM]
+    │  │  │  └─ -1.0 [id EW]
+    │  │  ├─ sub [id EX]
+    │  │  │  ├─ log [id EY]
+    │  │  │  │  └─ mul [id EZ]
+    │  │  │  │     ├─ 0.5 [id FA]
+    │  │  │  │     └─ erfcx [id FB]
+    │  │  │  │        └─ true_div [id FC]
+    │  │  │  │           ├─ mul [id FD]
+    │  │  │  │           │  ├─ -0.7071067932881648 [id FE]
+    │  │  │  │           │  └─ sub [id EV]
+    │  │  │  │           │     └─ ···
+    │  │  │  │           └─ i4 [id BM]
+    │  │  │  └─ mul [id FF]
+    │  │  │     ├─ 0.5 [id FA]
+    │  │  │     └─ sqr [id FG]
+    │  │  │        └─ true_div [id EU]
+    │  │  │           └─ ···
+    │  │  └─ log1p [id FH]
+    │  │     └─ mul [id FI]
+    │  │        ├─ -0.5 [id FJ]
+    │  │        └─ erfc [id FK]
+    │  │           └─ true_div [id FL]
+    │  │              ├─ mul [id FM]
+    │  │              │  ├─ 0.7071067932881648 [id FN]
+    │  │              │  └─ sub [id EV]
+    │  │              │     └─ ···
+    │  │              └─ i4 [id BM]
+    │  └─ -inf [id FO]
+    └─ Switch [id FP]
+       ├─ i2 [id FQ]
+       ├─ Switch [id FR]
+       │  ├─ i1 [id ER]
+       │  ├─ Switch [id FS]
+       │  │  ├─ GT [id FT]
+       │  │  │  ├─ true_div [id EU]
+       │  │  │  │  └─ ···
+       │  │  │  └─ 1.0 [id FU]
+       │  │  ├─ sub [id FV]
+       │  │  │  ├─ log [id FW]
+       │  │  │  │  └─ mul [id FX]
+       │  │  │  │     ├─ 0.5 [id FA]
+       │  │  │  │     └─ erfcx [id FY]
+       │  │  │  │        └─ true_div [id FL]
+       │  │  │  │           └─ ···
+       │  │  │  └─ mul [id FF]
+       │  │  │     └─ ···
+       │  │  └─ log1p [id FZ]
+       │  │     └─ mul [id GA]
+       │  │        ├─ -0.5 [id FJ]
+       │  │        └─ erfc [id GB]
+       │  │           └─ true_div [id FC]
+       │  │              └─ ···
+       │  └─ -inf [id FO]
+       └─ Switch [id GC]
+          ├─ i1 [id ER]
+          ├─ sub [id GD]
+          │  ├─ add [id GE]
+          │  │  ├─ -0.9189385332046727 [id GF]
+          │  │  └─ mul [id GG]
+          │  │     ├─ -0.5 [id FJ]
+          │  │     └─ sqr [id FG]
+          │  │        └─ ···
+          │  └─ i3 [id BJ]
+          └─ -inf [id FO]
+ ← mul [id GH]
+    ├─ add [id GI]
+    │  ├─ Switch [id GJ]
+    │  │  ├─ LT [id ET]
+    │  │  │  └─ ···
+    │  │  ├─ 0.0 [id GK]
+    │  │  └─ Switch [id GL]
+    │  │     ├─ i0 [id EE]
+    │  │     ├─ true_div [id GM]
+    │  │     │  ├─ mul [id GN]
+    │  │     │  │  ├─ 0.3989422872290391 [id GO]
+    │  │     │  │  └─ exp [id GP]
+    │  │     │  │     └─ true_div [id GQ]
+    │  │     │  │        ├─ mul [id GR]
+    │  │     │  │        │  ├─ -0.5000000171142714 [id GS]
+    │  │     │  │        │  ├─ sub [id EV]
+    │  │     │  │        │  │  └─ ···
+    │  │     │  │        │  └─ sub [id EV]
+    │  │     │  │        │     └─ ···
+    │  │     │  │        └─ i7 [id DW]
+    │  │     │  └─ add [id GT]
+    │  │     │     ├─ 1.0 [id GU]
+    │  │     │     └─ mul [id FI]
+    │  │     │        └─ ···
+    │  │     └─ 0.0 [id GK]
+    │  └─ Switch [id GV]
+    │     ├─ GT [id FT]
+    │     │  └─ ···
+    │     ├─ Switch [id GW]
+    │     │  ├─ i2 [id FQ]
+    │     │  ├─ Switch [id GX]
+    │     │  │  ├─ i0 [id EE]
+    │     │  │  ├─ 0.0 [id GK]
+    │     │  │  └─ mul [id GY]
+    │     │  │     ├─ 0.7071067932881648 [id FN]
+    │     │  │     └─ add [id GZ]
+    │     │  │        ├─ true_div [id HA]
+    │     │  │        │  ├─ -1.1283791670955126 [id HB]
+    │     │  │        │  └─ erfcx [id FY]
+    │     │  │        │     └─ ···
+    │     │  │        └─ true_div [id HC]
+    │     │  │           ├─ mul [id HD]
+    │     │  │           │  ├─ 1.4142135865763297 [id HE]
+    │     │  │           │  └─ sub [id EV]
+    │     │  │           │     └─ ···
+    │     │  │           └─ i4 [id BM]
+    │     │  └─ 0.0 [id GK]
+    │     └─ 0.0 [id GK]
+    └─ sub [id EV]
+       └─ ···
+ ← mul [id HF]
+    ├─ add [id HG]
+    │  ├─ Switch [id HH]
+    │  │  ├─ LT [id ET]
+    │  │  │  └─ ···
+    │  │  ├─ Switch [id HI]
+    │  │  │  ├─ i0 [id EE]
+    │  │  │  ├─ mul [id HJ]
+    │  │  │  │  ├─ -0.7071067932881648 [id FE]
+    │  │  │  │  └─ add [id HK]
+    │  │  │  │     ├─ true_div [id HL]
+    │  │  │  │     │  ├─ -1.1283791670955126 [id HB]
+    │  │  │  │     │  └─ erfcx [id FB]
+    │  │  │  │     │     └─ ···
+    │  │  │  │     └─ true_div [id HM]
+    │  │  │  │        ├─ mul [id HN]
+    │  │  │  │        │  ├─ -1.4142135865763297 [id HO]
+    │  │  │  │        │  └─ sub [id EV]
+    │  │  │  │        │     └─ ···
+    │  │  │  │        └─ i4 [id BM]
+    │  │  │  └─ 0.0 [id GK]
+    │  │  └─ 0.0 [id GK]
+    │  └─ Switch [id HP]
+    │     ├─ GT [id FT]
+    │     │  └─ ···
+    │     ├─ 0.0 [id GK]
+    │     └─ Switch [id HQ]
+    │        ├─ i2 [id FQ]
+    │        ├─ Switch [id HR]
+    │        │  ├─ i0 [id EE]
+    │        │  ├─ 0.0 [id GK]
+    │        │  └─ true_div [id HS]
+    │        │     ├─ mul [id HT]
+    │        │     │  ├─ -0.3989422872290391 [id HU]
+    │        │     │  └─ exp [id GP]
+    │        │     │     └─ ···
+    │        │     └─ add [id HV]
+    │        │        ├─ 1.0 [id GU]
+    │        │        └─ mul [id GA]
+    │        │           └─ ···
+    │        └─ 0.0 [id GK]
+    └─ sub [id EV]
+       └─ ···
+ ← add [id HW]
+    ├─ true_div [id HX]
+    │  ├─ mul [id HY]
+    │  │  ├─ add [id HZ]
+    │  │  │  ├─ Switch [id IA]
+    │  │  │  │  ├─ LT [id ET]
+    │  │  │  │  │  └─ ···
+    │  │  │  │  ├─ i9 [id EC]
+    │  │  │  │  └─ 0.0 [id GK]
+    │  │  │  └─ Switch [id IB]
+    │  │  │     ├─ GT [id FT]
+    │  │  │     │  └─ ···
+    │  │  │     ├─ i8 [id DZ]
+    │  │  │     └─ 0.0 [id GK]
+    │  │  ├─ sub [id EV]
+    │  │  │  └─ ···
+    │  │  └─ sub [id EV]
+    │  │     └─ ···
+    │  └─ i4 [id BM]
+    └─ Switch [id IC]
+       ├─ i2 [id FQ]
+       ├─ 0.0 [id GK]
+       └─ Switch [id ID]
+          ├─ i0 [id EE]
+          ├─ 0.0 [id GK]
+          └─ mul [id IE]
+             ├─ -1.0 [id IF]
+             ├─ true_div [id EU]
+             │  └─ ···
+             └─ sub [id EV]
+                └─ ···
+ ← add [id IG]
+    ├─ true_div [id IH]
+    │  ├─ mul [id II]
+    │  │  ├─ add [id HZ]
+    │  │  │  └─ ···
+    │  │  └─ sub [id EV]
+    │  │     └─ ···
+    │  └─ i7 [id DW]
+    ├─ Switch [id IJ]
+    │  ├─ i2 [id FQ]
+    │  ├─ 0.0 [id GK]
+    │  └─ Switch [id IK]
+    │     ├─ i0 [id EE]
+    │     ├─ 0.0 [id GK]
+    │     └─ true_div [id IL]
+    │        ├─ neg [id IM]
+    │        │  └─ true_div [id EU]
+    │        │     └─ ···
+    │        └─ i4 [id BM]
+    ├─ mul [id IN]
+    │  ├─ -0.7071067932881648 [id FE]
+    │  └─ add [id IO]
+    │     ├─ Switch [id IP]
+    │     │  ├─ LT [id ET]
+    │     │  │  └─ ···
+    │     │  ├─ Switch [id IQ]
+    │     │  │  ├─ i0 [id EE]
+    │     │  │  ├─ true_div [id IR]
+    │     │  │  │  ├─ add [id HK]
+    │     │  │  │  │  └─ ···
+    │     │  │  │  └─ i4 [id BM]
+    │     │  │  └─ 0.0 [id GK]
+    │     │  └─ 0.0 [id GK]
+    │     └─ Switch [id IS]
+    │        ├─ GT [id FT]
+    │        │  └─ ···
+    │        ├─ 0.0 [id GK]
+    │        └─ Switch [id IT]
+    │           ├─ i2 [id FQ]
+    │           ├─ Switch [id IU]
+    │           │  ├─ i0 [id EE]
+    │           │  ├─ 0.0 [id GK]
+    │           │  └─ true_div [id IV]
+    │           │     ├─ true_div [id IW]
+    │           │     │  ├─ mul [id IX]
+    │           │     │  │  ├─ 0.5641895835477563 [id IY]
+    │           │     │  │  └─ exp [id GP]
+    │           │     │  │     └─ ···
+    │           │     │  └─ add [id HV]
+    │           │     │     └─ ···
+    │           │     └─ i4 [id BM]
+    │           └─ 0.0 [id GK]
+    └─ mul [id IZ]
+       ├─ 0.7071067932881648 [id FN]
+       └─ add [id JA]
+          ├─ Switch [id JB]
+          │  ├─ LT [id ET]
+          │  │  └─ ···
+          │  ├─ 0.0 [id GK]
+          │  └─ Switch [id JC]
+          │     ├─ i0 [id EE]
+          │     ├─ true_div [id JD]
+          │     │  ├─ true_div [id JE]
+          │     │  │  ├─ mul [id IX]
+          │     │  │  │  └─ ···
+          │     │  │  └─ add [id GT]
+          │     │  │     └─ ···
+          │     │  └─ i4 [id BM]
+          │     └─ 0.0 [id GK]
+          └─ Switch [id JF]
+             ├─ GT [id FT]
+             │  └─ ···
+             ├─ Switch [id JG]
+             │  ├─ i2 [id FQ]
+             │  ├─ Switch [id JH]
+             │  │  ├─ i0 [id EE]
+             │  │  ├─ 0.0 [id GK]
+             │  │  └─ true_div [id JI]
+             │  │     ├─ add [id GZ]
+             │  │     │  └─ ···
+             │  │     └─ i4 [id BM]
+             │  └─ 0.0 [id GK]
+             └─ 0.0 [id GK]
diff --git a/ptd_benchmark_results/before/normal_logp_dlogp_dprint.txt b/ptd_benchmark_results/before/normal_logp_dlogp_dprint.txt
new file mode 100644
index 0000000000..27d3711d37
--- /dev/null
+++ b/ptd_benchmark_results/before/normal_logp_dlogp_dprint.txt
@@ -0,0 +1,141 @@
+Composite{...}.0 [id A] d={0: [1]} 8
+ ├─ Subtensor{i} [id B] v={0: [0]} 1
+ │  ├─ joined_inputs [id C]
+ │  └─ 1 [id D]
+ ├─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.0 [id E] 6
+ │  ├─ Composite{...}.1 [id F] 5
+ │  │  └─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │     └─ Exp [id H] 3
+ │  │        └─ Subtensor{i} [id B] v={0: [0]} 1
+ │  │           └─ ···
+ │  ├─ Composite{...}.0 [id F] 5
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ obs{[ 1.320334 ... 56013e+00]} [id I]
+ │  └─ Subtensor{:stop} [id J] v={0: [0]} 0
+ │     ├─ joined_inputs [id C]
+ │     └─ 1 [id K]
+ ├─ Subtensor{i} [id L] v={0: [0]} 2
+ │  ├─ joined_inputs [id C]
+ │  └─ 0 [id M]
+ └─ Exp [id H] 3
+    └─ ···
+Join{axis=0} [id N] 12
+ ├─ Composite{...}.0 [id O] d={0: [0], 1: [1]} 11
+ │  ├─ ExpandDims{axis=0} [id G] v={0: [0]} 4
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id P] v={0: [0]} 7
+ │  │  └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.1 [id E] 6
+ │  │     └─ ···
+ │  ├─ Subtensor{:stop} [id J] v={0: [0]} 0
+ │  │  └─ ···
+ │  ├─ ExpandDims{axis=0} [id Q] v={0: [0]} 10
+ │  │  └─ Composite{...}.1 [id A] d={0: [1]} 8
+ │  │     └─ ···
+ │  └─ ExpandDims{axis=0} [id R] v={0: [0]} 9
+ │     └─ FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]}.2 [id E] 6
+ │        └─ ···
+ └─ Composite{...}.1 [id O] d={0: [0], 1: [1]} 11
+    └─ ···
+
+Inner graphs:
+
+Composite{...} [id A] d={0: [1]}
+ ← add [id S]
+    ├─ -3.221523658174155 [id T]
+    ├─ mul [id U]
+    │  ├─ -0.5 [id V]
+    │  └─ sqr [id W]
+    │     └─ mul [id X]
+    │        ├─ 0.1 [id Y]
+    │        └─ i2 [id Z]
+    ├─ Switch [id BA]
+    │  ├─ GE [id BB]
+    │  │  ├─ i3 [id BC]
+    │  │  └─ 0.0 [id BD]
+    │  ├─ add [id BE]
+    │  │  ├─ -1.83522929514961 [id BF]
+    │  │  └─ mul [id BG]
+    │  │     ├─ -0.5 [id V]
+    │  │     └─ sqr [id BH]
+    │  │        └─ mul [id BI]
+    │  │           ├─ 0.2 [id BJ]
+    │  │           └─ i3 [id BC]
+    │  └─ -inf [id BK]
+    ├─ i0 [id BL]
+    └─ i1 [id BM]
+ ← GE [id BB]
+    └─ ···
+
+FusedElemwise{Composite{...}, reduce[add@(0,), add@(0,), add@(0,)]} [id E]
+ ← Sum{axes=None} [id BN]
+    └─ Composite{...}.0 [id BO]
+       ├─ i0 [id BP]
+       ├─ i1 [id BQ]
+       ├─ i2 [id BR]
+       ├─ i3 [id BS]
+       └─ i4 [id BT]
+ ← Sum{axes=None} [id BU]
+    └─ Composite{...}.1 [id BO]
+       └─ ···
+ ← Sum{axes=None} [id BV]
+    └─ Composite{...}.2 [id BO]
+       └─ ···
+
+Composite{...} [id F]
+ ← log [id BW]
+    └─ i0 [id BL]
+ ← GT [id BX]
+    ├─ i0 [id BL]
+    └─ 0 [id BY]
+
+Composite{...} [id O] d={0: [0], 1: [1]}
+ ← add [id BZ]
+    ├─ mul [id CA]
+    │  ├─ -0.0100000 ... 0000000002 [id CB]
+    │  └─ i2 [id Z]
+    └─ true_div [id CC]
+       ├─ true_div [id CD]
+       │  ├─ i1 [id BM]
+       │  └─ i0 [id BL]
+       └─ i0 [id BL]
+ ← add [id CE]
+    ├─ -999.0 [id CF]
+    ├─ Switch [id CG]
+    │  ├─ i3 [id CH]
+    │  ├─ mul [id CI]
+    │  │  ├─ -0.04000000000000001 [id CJ]
+    │  │  ├─ i0 [id BL]
+    │  │  └─ i0 [id BL]
+    │  └─ 0.0 [id CK]
+    └─ mul [id CL]
+       ├─ true_div [id CM]
+       │  ├─ i4 [id CN]
+       │  └─ sqr [id CO]
+       │     └─ i0 [id BL]
+       └─ i0 [id BL]
+
+Composite{...} [id BO]
+ ← Switch [id CP]
+    ├─ i0 [id CQ]
+    ├─ sub [id CR]
+    │  ├─ add [id CS]
+    │  │  ├─ -0.9189385332046727 [id CT]
+    │  │  └─ mul [id CU]
+    │  │     ├─ -0.5 [id CV]
+    │  │     └─ sqr [id CW]
+    │  │        └─ true_div [id CX]
+    │  │           ├─ sub [id CY]
+    │  │           │  ├─ i3 [id BC]
+    │  │           │  └─ i4 [id CN]
+    │  │           └─ i2 [id Z]
+    │  └─ i1 [id BM]
+    └─ -inf [id CZ]
+ ← sub [id CY]
+    └─ ···
+ ← mul [id DA]
+    ├─ true_div [id CX]
+    │  └─ ···
+    └─ sub [id CY]
+       └─ ···
diff --git a/ptd_benchmark_results/before/op_counts.json b/ptd_benchmark_results/before/op_counts.json
new file mode 100644
index 0000000000..dd8348aa2b
--- /dev/null
+++ b/ptd_benchmark_results/before/op_counts.json
@@ -0,0 +1,19 @@
+{
+  "normal": {
+    "DimShuffle": 4,
+    "Elemwise": 4,
+    "Subtensor": 3,
+    "Join": 1,
+    "FusedElemwise": 1
+  },
+  "normal_censored": {
+    "DimShuffle": 8,
+    "Elemwise": 4,
+    "Subtensor": 3,
+    "FusedElemwise": 2,
+    "Join": 1
+  },
+  "icdf": {
+    "Elemwise": 3
+  }
+}
diff --git a/ptd_benchmark_results/before/timings.json b/ptd_benchmark_results/before/timings.json
new file mode 100644
index 0000000000..7e649b9740
--- /dev/null
+++ b/ptd_benchmark_results/before/timings.json
@@ -0,0 +1,20 @@
+{
+  "normal": {
+    "min_us": 2.1420849952846766,
+    "median_us": 2.3026051349006593,
+    "repeat": 30,
+    "number": 200
+  },
+  "normal_censored": {
+    "min_us": 26.86437452211976,
+    "median_us": 28.312082577031106,
+    "repeat": 30,
+    "number": 200
+  },
+  "icdf": {
+    "min_us": 7.897705072537065,
+    "median_us": 8.54020967381075,
+    "repeat": 30,
+    "number": 200
+  }
+}
diff --git a/ptd_benchmark_results/before/values.json b/ptd_benchmark_results/before/values.json
new file mode 100644
index 0000000000..23926920d3
--- /dev/null
+++ b/ptd_benchmark_results/before/values.json
@@ -0,0 +1,28 @@
+{
+  "normal": {
+    "logp": "-2565.649159845185",
+    "dlogp": [
+      "19.75972105470103",
+      "-933.3492016689559"
+    ]
+  },
+  "normal_censored": {
+    "logp": "-3569.201218890812",
+    "dlogp": [
+      "20.518081388517615",
+      "-1241.858721191814"
+    ]
+  },
+  "icdf": [
+    "-6.225580765419534",
+    "-1.691101585985116",
+    "-0.5969196055813767",
+    "0.194027091012722",
+    "0.8705114551654742",
+    "1.5031301497393552",
+    "2.135952587027799",
+    "2.8131538074356452",
+    "3.605832423092286",
+    "4.705291106465695"
+  ]
+}
diff --git a/pymc/distributions/continuous.py b/pymc/distributions/continuous.py
index 4b3eeb53d0..23f8b1d2bf 100644
--- a/pymc/distributions/continuous.py
+++ b/pymc/distributions/continuous.py
@@ -51,6 +51,7 @@
 from pytensor.tensor.random.op import RandomVariable
 from pytensor.tensor.random.utils import normalize_size_param
 from pytensor.tensor.variable import TensorConstant, TensorVariable
+from pytensor_distributions import normal as ptd_normal
 
 from pymc.distributions.custom import CustomDist
 from pymc.logprob.abstract import _logprob_helper
@@ -524,32 +525,29 @@ def support_point(rv, size, mu, sigma):
         return mu
 
     def logp(value, mu, sigma):
-        res = -0.5 * pt.pow((value - mu) / sigma, 2) - pt.log(pt.sqrt(2.0 * np.pi)) - pt.log(sigma)
         return check_parameters(
-            res,
+            ptd_normal.logpdf(value, mu, sigma),
             sigma > 0,
             msg="sigma > 0",
         )
 
     def logcdf(value, mu, sigma):
         return check_parameters(
-            normal_lcdf(mu, sigma, value),
+            ptd_normal.logcdf(value, mu, sigma),
             sigma > 0,
             msg="sigma > 0",
         )
 
     def logccdf(value, mu, sigma):
         return check_parameters(
-            normal_lccdf(mu, sigma, value),
+            ptd_normal.logsf(value, mu, sigma),
             sigma > 0,
             msg="sigma > 0",
         )
 
     def icdf(value, mu, sigma):
-        res = mu + sigma * -np.sqrt(2.0) * pt.erfcinv(2 * value)
-        res = check_icdf_value(res, value)
         return check_icdf_parameters(
-            res,
+            ptd_normal.ppf(value, mu, sigma),
             sigma > 0,
             msg="sigma > 0",
         )
diff --git a/requirements-dev.txt b/requirements-dev.txt
index 8a10c9b0d3..ab615a17cc 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -17,6 +17,7 @@ pandas>=0.24.0
 polyagamma
 pre-commit>=2.8.0
 pymc-sphinx-theme>=0.16.0
+pytensor-distributions>=0.2.0,<=0.3.0
 pytensor>=3.2.2,<3.3
 pytest-cov>=2.5
 pytest>=3.0
diff --git a/requirements.txt b/requirements.txt
index 52ca0d21dc..51f984c3c5 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -4,6 +4,7 @@ cloudpickle
 numpy>=1.25.0
 pandas>=0.24.0
 pytensor>=3.2.2,<3.3
+pytensor-distributions>=0.2.0,<=0.3.0
 rich>=13.7.1
 scipy>=1.4.1
 threadpoolctl>=3.1.0,<4.0.0