Average Error: 0.1 → 0
Time: 2.2s
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 r47637834 = x;
        double r47637835 = r47637834 * r47637834;
        double r47637836 = r47637835 * r47637834;
        return r47637836;
}
↓
double f(double x) {
        double r47637837 = x;
        double r47637838 = 3.0;
        double r47637839 = pow(r47637837, r47637838);
        return r47637839;
}

Error

Bits error versus x

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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 pow10.1

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

  4. Applied pow20.1

    \[\leadsto \color{blue}{{x}^{2}} \cdot {x}^{1}\]

  5. Applied pow-prod-up0

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

  6. Simplified0

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

  7. Final simplification0

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

Reproduce

herbie shell --seed 2019104 +o rules:numerics
(FPCore (x)
  :name "math.cube on real"

  :herbie-target
  (pow x 3)

  (* (* x x) x))