Average Error: 0.1 → 0.0
Time: 1.6s
Precision: binary64
\[\left(x \cdot x\right) \cdot x\]
↓
\[{x}^{3}\]
\left(x \cdot x\right) \cdot x
↓
{x}^{3}
double code(double x) {
	return ((double) (((double) (x * x)) * x));
}
↓
double code(double x) {
	return ((double) pow(x, 3.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.0
Herbie0.0
\[{x}^{3}\]

Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

    \[\leadsto \color{blue}{{x}^{3}}\]

  3. Final simplification0.0

    \[\leadsto {x}^{3}\]

Reproduce

herbie shell --seed 2020182 
(FPCore (x)
  :name "math.cube on real"
  :precision binary64

  :herbie-target
  (pow x 3.0)

  (* (* x x) x))