Average Error: 7.3 → 0.2
Time: 2.6s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - 3 \cdot \left(x.im \cdot \left(x.re \cdot x.im\right)\right)\]
\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.re \cdot x.im\right)\right)
double f(double x_re, double x_im) {
        double r180880 = x_re;
        double r180881 = r180880 * r180880;
        double r180882 = x_im;
        double r180883 = r180882 * r180882;
        double r180884 = r180881 - r180883;
        double r180885 = r180884 * r180880;
        double r180886 = r180880 * r180882;
        double r180887 = r180882 * r180880;
        double r180888 = r180886 + r180887;
        double r180889 = r180888 * r180882;
        double r180890 = r180885 - r180889;
        return r180890;
}
↓
double f(double x_re, double x_im) {
        double r180891 = x_re;
        double r180892 = 3.0;
        double r180893 = pow(r180891, r180892);
        double r180894 = x_im;
        double r180895 = r180891 * r180894;
        double r180896 = r180894 * r180895;
        double r180897 = r180892 * r180896;
        double r180898 = r180893 - r180897;
        return r180898;
}

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

Original7.3
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 7.3

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"
  :precision binary64

  :herbie-target
  (+ (* (* x.re x.re) (- x.re x.im)) (* (* x.re x.im) (- x.re (* 3 x.im))))

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