Average Error: 0.1 → 0
Time: 736.0ms
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 r171838 = x;
        double r171839 = r171838 * r171838;
        double r171840 = r171839 * r171838;
        return r171840;
}
↓
double f(double x) {
        double r171841 = x;
        double r171842 = 3.0;
        double r171843 = pow(r171841, r171842);
        return r171843;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2020036 +o rules:numerics
(FPCore (x)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (* (* x x) x))