Average Error: 0.1 → 0
Time: 6.3s
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 r9888959 = x;
        double r9888960 = r9888959 * r9888959;
        double r9888961 = r9888960 * r9888959;
        return r9888961;
}
↓
double f(double x) {
        double r9888962 = x;
        double r9888963 = 3.0;
        double r9888964 = pow(r9888962, r9888963);
        return r9888964;
}

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. Using strategy rm

  3. Applied pow10.1

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

  4. Applied pow10.1

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

  5. Applied pow10.1

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

  6. Applied pow-prod-up0.1

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

  7. Applied pow-prod-up0

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

  8. Simplified0

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

  9. Final simplification0

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, C"
  (* (* x x) x))