Average Error: 0.0 → 0.0
Time: 33.8s
Precision: 64
Internal Precision: 576
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[e^{3 \cdot \log x} + x \cdot x\]

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. Using strategy rm

  3. Applied add-exp-log0.0

    \[\leadsto \color{blue}{e^{\log \left(x \cdot \left(x \cdot x\right)\right)}} + x \cdot x\]

  4. Applied simplify0.0

    \[\leadsto e^{\color{blue}{3 \cdot \log x}} + x \cdot x\]

Runtime

Time bar (total: 33.8s)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' +o rules:numerics
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

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

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