Average Error: 7.0 → 0.6
Time: 26.5s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\left(\left(x.re - x.im\right) \cdot x.im\right) \cdot \left(x.im + x.re\right) + \sqrt[3]{x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)} \cdot \left(\sqrt[3]{x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)} \cdot \sqrt[3]{x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)}\right)\]
\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(\left(x.re - x.im\right) \cdot x.im\right) \cdot \left(x.im + x.re\right) + \sqrt[3]{x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)} \cdot \left(\sqrt[3]{x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)} \cdot \sqrt[3]{x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)}\right)
double f(double x_re, double x_im) {
        double r8073868 = x_re;
        double r8073869 = r8073868 * r8073868;
        double r8073870 = x_im;
        double r8073871 = r8073870 * r8073870;
        double r8073872 = r8073869 - r8073871;
        double r8073873 = r8073872 * r8073870;
        double r8073874 = r8073868 * r8073870;
        double r8073875 = r8073870 * r8073868;
        double r8073876 = r8073874 + r8073875;
        double r8073877 = r8073876 * r8073868;
        double r8073878 = r8073873 + r8073877;
        return r8073878;
}
↓
double f(double x_re, double x_im) {
        double r8073879 = x_re;
        double r8073880 = x_im;
        double r8073881 = r8073879 - r8073880;
        double r8073882 = r8073881 * r8073880;
        double r8073883 = r8073880 + r8073879;
        double r8073884 = r8073882 * r8073883;
        double r8073885 = r8073879 * r8073880;
        double r8073886 = r8073885 + r8073885;
        double r8073887 = r8073879 * r8073886;
        double r8073888 = cbrt(r8073887);
        double r8073889 = r8073888 * r8073888;
        double r8073890 = r8073888 * r8073889;
        double r8073891 = r8073884 + r8073890;
        return r8073891;
}

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

Original7.0
Target0.2
Herbie0.6
\[\left(x.re \cdot x.im\right) \cdot \left(2 \cdot x.re\right) + \left(x.im \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right)\]

Derivation

  1. Initial program 7.0

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

  3. Applied difference-of-squares7.0

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

  4. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\left(x.re + x.im\right) \cdot \left(\left(x.re - x.im\right) \cdot x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2019146 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"

  :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)))