Average Error: 7.4 → 0.2
Time: 15.2s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\left(3 \cdot x.re\right) \cdot \left(x.im \cdot x.re\right) - {x.im}^{3}\]
\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
↓
\left(3 \cdot x.re\right) \cdot \left(x.im \cdot x.re\right) - {x.im}^{3}
double f(double x_re, double x_im) {
        double r342988 = x_re;
        double r342989 = r342988 * r342988;
        double r342990 = x_im;
        double r342991 = r342990 * r342990;
        double r342992 = r342989 - r342991;
        double r342993 = r342992 * r342990;
        double r342994 = r342988 * r342990;
        double r342995 = r342990 * r342988;
        double r342996 = r342994 + r342995;
        double r342997 = r342996 * r342988;
        double r342998 = r342993 + r342997;
        return r342998;
}
↓
double f(double x_re, double x_im) {
        double r342999 = 3.0;
        double r343000 = x_re;
        double r343001 = r342999 * r343000;
        double r343002 = x_im;
        double r343003 = r343002 * r343000;
        double r343004 = r343001 * r343003;
        double r343005 = pow(r343002, r342999);
        double r343006 = r343004 - r343005;
        return r343006;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"

  :herbie-target
  (+ (* (* x.re x.im) (* 2.0 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)))