Average Error: 0.0 → 0.0
Time: 14.8s
Precision: 64
Internal Precision: 384
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot x + {x}^{3}\]

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. Using strategy rm

  4. Applied distribute-lft-in0.0

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

  5. Applied simplify0.0

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

  6. Applied simplify0.0

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

Runtime

Time bar (total: 14.8s)Debug logProfile

herbie shell --seed '#(1063185673 2139736501 2393378123 1907444849 1070993796 1007244912)' 
(FPCore (x)
  :name "Expression 3, p15"
  :pre (<= 0 x 2)

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

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