Average Error: 0.0 → 0.0
Time: 13.5s
Precision: 64
Internal Precision: 128
\[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
↓
\[(d1 \cdot \left(d2 + \left(5 + d3\right)\right) + \left(d1 \cdot 32\right))_*\]

Error

Bits error versus d1

Bits error versus d2

Bits error versus d3

Target

Original0.0
Target0.0
Herbie0.0
\[d1 \cdot \left(\left(37 + d3\right) + d2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(d1 \cdot d2 + \left(d3 + 5\right) \cdot d1\right) + d1 \cdot 32\]
  2. Using strategy rm

  3. Applied *-commutative0.0

    \[\leadsto \left(d1 \cdot d2 + \color{blue}{d1 \cdot \left(d3 + 5\right)}\right) + d1 \cdot 32\]

  4. Applied distribute-lft-out0.0

    \[\leadsto \color{blue}{d1 \cdot \left(d2 + \left(d3 + 5\right)\right)} + d1 \cdot 32\]

  5. Applied fma-def0.0

    \[\leadsto \color{blue}{(d1 \cdot \left(d2 + \left(d3 + 5\right)\right) + \left(d1 \cdot 32\right))_*}\]

  6. Final simplification0.0

    \[\leadsto (d1 \cdot \left(d2 + \left(5 + d3\right)\right) + \left(d1 \cdot 32\right))_*\]

Reproduce

herbie shell --seed 2019072 +o rules:numerics
(FPCore (d1 d2 d3)
  :name "FastMath dist3"

  :herbie-target
  (* d1 (+ (+ 37 d3) d2))

  (+ (+ (* d1 d2) (* (+ d3 5) d1)) (* d1 32)))