Average Error: 0.0 → 0.0
Time: 4.2m
Precision: 64
Internal Precision: 384
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[{x}^{2} + {x}^{3}\]

Error

Bits error versus x

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(1.0 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x \cdot x\right) + x \cdot x\]

  2. Applied simplify0.0

    \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot \left(1 + x\right)}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{x}^{2} + {x}^{3}}\]
  4. Removed slow pow expressions.

Runtime

Time bar (total: 4.2m)Debug logProfile

herbie shell --seed '#(1063027428 1192549564 1443466578 604016274 3637110559 1698629644)' 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

  :herbie-target
  (* (* (+ 1.0 x) x) x)

  (+ (* x (* x x)) (* x x)))