Average Error: 0.3 → 0.2
Time: 23.4s
Precision: 64
Internal Precision: 384
\[\left(\left(x \cdot 3.0\right) \cdot y\right) \cdot y\]
↓
\[\left(3.0 \cdot \left(y \cdot x\right)\right) \cdot y\]

Error

Bits error versus x

Bits error versus y

Target

Original0.3
Target0.2
Herbie0.2
\[\left(x \cdot \left(3.0 \cdot y\right)\right) \cdot y\]

Derivation

  1. Initial program 0.3

    \[\left(\left(x \cdot 3.0\right) \cdot y\right) \cdot y\]

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(3.0 \cdot \left(y \cdot x\right)\right)} \cdot y\]
  3. Removed slow pow expressions.

Runtime

Time bar (total: 23.4s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (x y)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, B"

  :herbie-target
  (* (* x (* 3.0 y)) y)

  (* (* (* x 3.0) y) y))