Average Error: 7.1 → 0.7
Time: 23.6s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\sqrt[3]{\left(x.im + x.re\right) \cdot \left(x.im \cdot \left(x.re - x.im\right)\right)} \cdot \left(\sqrt[3]{\left(x.im + x.re\right) \cdot \left(x.im \cdot \left(x.re - x.im\right)\right)} \cdot \left(\sqrt[3]{x.im + x.re} \cdot \sqrt[3]{x.im \cdot \left(x.re - x.im\right)}\right)\right) + x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)\]
\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
↓
\sqrt[3]{\left(x.im + x.re\right) \cdot \left(x.im \cdot \left(x.re - x.im\right)\right)} \cdot \left(\sqrt[3]{\left(x.im + x.re\right) \cdot \left(x.im \cdot \left(x.re - x.im\right)\right)} \cdot \left(\sqrt[3]{x.im + x.re} \cdot \sqrt[3]{x.im \cdot \left(x.re - x.im\right)}\right)\right) + x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)
double f(double x_re, double x_im) {
        double r7463335 = x_re;
        double r7463336 = r7463335 * r7463335;
        double r7463337 = x_im;
        double r7463338 = r7463337 * r7463337;
        double r7463339 = r7463336 - r7463338;
        double r7463340 = r7463339 * r7463337;
        double r7463341 = r7463335 * r7463337;
        double r7463342 = r7463337 * r7463335;
        double r7463343 = r7463341 + r7463342;
        double r7463344 = r7463343 * r7463335;
        double r7463345 = r7463340 + r7463344;
        return r7463345;
}
↓
double f(double x_re, double x_im) {
        double r7463346 = x_im;
        double r7463347 = x_re;
        double r7463348 = r7463346 + r7463347;
        double r7463349 = r7463347 - r7463346;
        double r7463350 = r7463346 * r7463349;
        double r7463351 = r7463348 * r7463350;
        double r7463352 = cbrt(r7463351);
        double r7463353 = cbrt(r7463348);
        double r7463354 = cbrt(r7463350);
        double r7463355 = r7463353 * r7463354;
        double r7463356 = r7463352 * r7463355;
        double r7463357 = r7463352 * r7463356;
        double r7463358 = r7463347 * r7463346;
        double r7463359 = r7463358 + r7463358;
        double r7463360 = r7463347 * r7463359;
        double r7463361 = r7463357 + r7463360;
        return r7463361;
}

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

Original7.1
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 7.1

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

  3. Applied difference-of-squares7.1

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

  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

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

  8. Applied cbrt-prod0.7

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

  9. Final simplification0.7

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

Reproduce

herbie shell --seed 2019172 
(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)))