Average Error: 0.1 → 0
Time: 4.0s
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 r3038452 = x;
        double r3038453 = r3038452 * r3038452;
        double r3038454 = r3038453 * r3038452;
        return r3038454;
}
↓
double f(double x) {
        double r3038455 = x;
        double r3038456 = 3.0;
        double r3038457 = pow(r3038455, r3038456);
        return r3038457;
}

Error

Bits error versus x

Try it out

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

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

  5. Applied pow-plus0.1

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

  6. Applied pow-prod-up0

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

  7. Simplified0

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

  8. Final simplification0

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (x)
  :name "math.cube on real"

  :herbie-target
  (pow x 3)

  (* (* x x) x))