Average Error: 0.1 → 0
Time: 2.5s
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 r4947993 = x;
        double r4947994 = r4947993 * r4947993;
        double r4947995 = r4947994 * r4947993;
        return r4947995;
}
↓
double f(double x) {
        double r4947996 = x;
        double r4947997 = 3.0;
        double r4947998 = pow(r4947996, r4947997);
        return r4947998;
}

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. Using strategy rm

  3. Applied pow20.1

    \[\leadsto \color{blue}{{x}^{2}} \cdot x\]

  4. Applied pow-plus0

    \[\leadsto \color{blue}{{x}^{\left(2 + 1\right)}}\]

  5. Simplified0

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

  6. Final simplification0

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x)
  :name "math.cube on real"

  :herbie-target
  (pow x 3)

  (* (* x x) x))