Average Error: 0.1 → 0.1
Time: 22.8s
Precision: 64
Internal Precision: 384
\[\left(x \cdot 3.0\right) \cdot y - z\]
↓
\[3.0 \cdot \left(y \cdot x\right) - z\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot \left(3.0 \cdot y\right) - z\]

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around 0 0.1

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

Runtime

Time bar (total: 22.8s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"

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

  (- (* (* x 3.0) y) z))