Average Error: 0.1 → 0
Time: 2.1s
Precision: 64
\[\left(x \cdot x\right) \cdot x\]
↓
\[{x}^{3}\]
\left(x \cdot x\right) \cdot x
↓
{x}^{3}
double f(double x) {
        double r176516 = x;
        double r176517 = r176516 * r176516;
        double r176518 = r176517 * r176516;
        return r176518;
}
↓
double f(double x) {
        double r176519 = x;
        double r176520 = 3.0;
        double r176521 = pow(r176519, r176520);
        return r176521;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.1

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

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x)
  :name "math.cube on real"
  :precision binary64

  :herbie-target
  (pow x 3)

  (* (* x x) x))