Average Error: 0.1 → 0
Time: 650.0ms
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 r189469 = x;
        double r189470 = r189469 * r189469;
        double r189471 = r189470 * r189469;
        return r189471;
}
↓
double f(double x) {
        double r189472 = x;
        double r189473 = 3.0;
        double r189474 = pow(r189472, r189473);
        return r189474;
}

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 2020027 +o rules:numerics
(FPCore (x)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (* (* x x) x))