Average Error: 0.0 → 0.0
Time: 22.0s
Precision: 64
Internal Precision: 576
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\sqrt{(x \cdot x + x)_* \cdot x} \cdot \sqrt{(x \cdot x + x)_* \cdot x}\]

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-sqr-sqrt0.0

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

  4. Applied simplify0.0

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

  5. Applied simplify0.0

    \[\leadsto \sqrt{(x \cdot x + x)_* \cdot x} \cdot \color{blue}{\sqrt{(x \cdot x + x)_* \cdot x}}\]

Runtime

Time bar (total: 22.0s)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' +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)))