Average Error: 7.2 → 0.7
Time: 25.5s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.re + \left(\sqrt[3]{x.im + x.re} \cdot \left(\left(x.re - x.im\right) \cdot x.im\right)\right) \cdot \left(\sqrt[3]{x.im + x.re} \cdot \sqrt[3]{x.im + x.re}\right)\]
\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(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.re + \left(\sqrt[3]{x.im + x.re} \cdot \left(\left(x.re - x.im\right) \cdot x.im\right)\right) \cdot \left(\sqrt[3]{x.im + x.re} \cdot \sqrt[3]{x.im + x.re}\right)
double f(double x_re, double x_im) {
        double r9611681 = x_re;
        double r9611682 = r9611681 * r9611681;
        double r9611683 = x_im;
        double r9611684 = r9611683 * r9611683;
        double r9611685 = r9611682 - r9611684;
        double r9611686 = r9611685 * r9611683;
        double r9611687 = r9611681 * r9611683;
        double r9611688 = r9611683 * r9611681;
        double r9611689 = r9611687 + r9611688;
        double r9611690 = r9611689 * r9611681;
        double r9611691 = r9611686 + r9611690;
        return r9611691;
}
↓
double f(double x_re, double x_im) {
        double r9611692 = x_re;
        double r9611693 = x_im;
        double r9611694 = r9611692 * r9611693;
        double r9611695 = r9611694 + r9611694;
        double r9611696 = r9611695 * r9611692;
        double r9611697 = r9611693 + r9611692;
        double r9611698 = cbrt(r9611697);
        double r9611699 = r9611692 - r9611693;
        double r9611700 = r9611699 * r9611693;
        double r9611701 = r9611698 * r9611700;
        double r9611702 = r9611698 * r9611698;
        double r9611703 = r9611701 * r9611702;
        double r9611704 = r9611696 + r9611703;
        return r9611704;
}

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

Original7.2
Target0.2
Herbie0.7
\[\left(x.re \cdot x.im\right) \cdot \left(2 \cdot x.re\right) + \left(x.im \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right)\]

Derivation

  1. Initial program 7.2

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

  3. Applied difference-of-squares7.2

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

  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-cbrt0.7

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

  7. Applied associate-*l*0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2019179 
(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)))