Average Error: 7.4 → 0.2
Time: 19.8s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[3 \cdot \left(\left(x.re \cdot x.im\right) \cdot x.re\right) - {x.im}^{3}\]
\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re
↓
3 \cdot \left(\left(x.re \cdot x.im\right) \cdot x.re\right) - {x.im}^{3}
double f(double x_re, double x_im) {
        double r229965 = x_re;
        double r229966 = r229965 * r229965;
        double r229967 = x_im;
        double r229968 = r229967 * r229967;
        double r229969 = r229966 - r229968;
        double r229970 = r229969 * r229967;
        double r229971 = r229965 * r229967;
        double r229972 = r229967 * r229965;
        double r229973 = r229971 + r229972;
        double r229974 = r229973 * r229965;
        double r229975 = r229970 + r229974;
        return r229975;
}
↓
double f(double x_re, double x_im) {
        double r229976 = 3.0;
        double r229977 = x_re;
        double r229978 = x_im;
        double r229979 = r229977 * r229978;
        double r229980 = r229979 * r229977;
        double r229981 = r229976 * r229980;
        double r229982 = pow(r229978, r229976);
        double r229983 = r229981 - r229982;
        return r229983;
}

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
\[\left(x.re \cdot x.im\right) \cdot \left(2 \cdot x.re\right) + \left(x.im \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right)\]

Derivation

  1. Initial program 7.4

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"
  :precision binary64

  :herbie-target
  (+ (* (* x.re x.im) (* 2 x.re)) (* (* x.im (- x.re x.im)) (+ x.re x.im)))

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