Average Error: 7.5 → 0.6
Time: 17.8s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\left(\left(x.re - x.im\right) \cdot x.im\right) \cdot \left(x.im + x.re\right) + \left(\sqrt[3]{x.re \cdot x.im + x.re \cdot x.im} \cdot \left(\sqrt[3]{x.re \cdot x.im + x.re \cdot x.im} \cdot \sqrt[3]{x.re \cdot x.im + x.re \cdot x.im}\right)\right) \cdot x.re\]
\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) + \left(\sqrt[3]{x.re \cdot x.im + x.re \cdot x.im} \cdot \left(\sqrt[3]{x.re \cdot x.im + x.re \cdot x.im} \cdot \sqrt[3]{x.re \cdot x.im + x.re \cdot x.im}\right)\right) \cdot x.re
double f(double x_re, double x_im) {
        double r10523924 = x_re;
        double r10523925 = r10523924 * r10523924;
        double r10523926 = x_im;
        double r10523927 = r10523926 * r10523926;
        double r10523928 = r10523925 - r10523927;
        double r10523929 = r10523928 * r10523926;
        double r10523930 = r10523924 * r10523926;
        double r10523931 = r10523926 * r10523924;
        double r10523932 = r10523930 + r10523931;
        double r10523933 = r10523932 * r10523924;
        double r10523934 = r10523929 + r10523933;
        return r10523934;
}
↓
double f(double x_re, double x_im) {
        double r10523935 = x_re;
        double r10523936 = x_im;
        double r10523937 = r10523935 - r10523936;
        double r10523938 = r10523937 * r10523936;
        double r10523939 = r10523936 + r10523935;
        double r10523940 = r10523938 * r10523939;
        double r10523941 = r10523935 * r10523936;
        double r10523942 = r10523941 + r10523941;
        double r10523943 = cbrt(r10523942);
        double r10523944 = r10523943 * r10523943;
        double r10523945 = r10523943 * r10523944;
        double r10523946 = r10523945 * r10523935;
        double r10523947 = r10523940 + r10523946;
        return r10523947;
}

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

Original7.5
Target0.3
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 7.5

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

  3. Applied difference-of-squares7.5

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

  4. Applied associate-*l*0.3

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

  6. Applied add-cube-cbrt0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2019174 
(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)))