Average Error: 0.1 → 0
Time: 2.6s
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 r22564964 = x;
        double r22564965 = r22564964 * r22564964;
        double r22564966 = r22564965 * r22564964;
        return r22564966;
}
↓
double f(double x) {
        double r22564967 = x;
        double r22564968 = 3.0;
        double r22564969 = pow(r22564967, r22564968);
        return r22564969;
}

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 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-sqr0.1

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

  7. Applied pow-prod-up0

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

  8. Simplified0

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

  9. Final simplification0

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

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (x)
  :name "math.cube on real"

  :herbie-target
  (pow x 3)

  (* (* x x) x))