Average Error: 7.4 → 0.2
Time: 13.5s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - 3 \cdot \left(x.im \cdot \left(x.im \cdot x.re\right)\right)\]
\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im
↓
{x.re}^{3} - 3 \cdot \left(x.im \cdot \left(x.im \cdot x.re\right)\right)
double f(double x_re, double x_im) {
        double r128809 = x_re;
        double r128810 = r128809 * r128809;
        double r128811 = x_im;
        double r128812 = r128811 * r128811;
        double r128813 = r128810 - r128812;
        double r128814 = r128813 * r128809;
        double r128815 = r128809 * r128811;
        double r128816 = r128811 * r128809;
        double r128817 = r128815 + r128816;
        double r128818 = r128817 * r128811;
        double r128819 = r128814 - r128818;
        return r128819;
}
↓
double f(double x_re, double x_im) {
        double r128820 = x_re;
        double r128821 = 3.0;
        double r128822 = pow(r128820, r128821);
        double r128823 = x_im;
        double r128824 = r128823 * r128820;
        double r128825 = r128823 * r128824;
        double r128826 = r128821 * r128825;
        double r128827 = r128822 - r128826;
        return r128827;
}

Error

Bits error versus x.re

Bits error versus x.im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.4
Target0.2
Herbie0.2
\[\left(x.re \cdot x.re\right) \cdot \left(x.re - x.im\right) + \left(x.re \cdot x.im\right) \cdot \left(x.re - 3 \cdot x.im\right)\]

Derivation

  1. Initial program 7.4

    \[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]

  2. Simplified0.2

    \[\leadsto \color{blue}{{x.re}^{3} - 3 \cdot \left(x.im \cdot \left(x.im \cdot x.re\right)\right)}\]

  3. Final simplification0.2

    \[\leadsto {x.re}^{3} - 3 \cdot \left(x.im \cdot \left(x.im \cdot x.re\right)\right)\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"

  :herbie-target
  (+ (* (* x.re x.re) (- x.re x.im)) (* (* x.re x.im) (- x.re (* 3.0 x.im))))

  (- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im)))