Average Error: 6.8 → 0.7
Time: 1.0m
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[\left(\sqrt[3]{x.im + x.re} \cdot \left(\left(x.re - x.im\right) \cdot x.re\right)\right) \cdot \left(\sqrt[3]{x.im + x.re} \cdot \sqrt[3]{x.im + x.re}\right) - \left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im\]
\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
↓
\left(\sqrt[3]{x.im + x.re} \cdot \left(\left(x.re - x.im\right) \cdot x.re\right)\right) \cdot \left(\sqrt[3]{x.im + x.re} \cdot \sqrt[3]{x.im + x.re}\right) - \left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im
double f(double x_re, double x_im) {
        double r44095830 = x_re;
        double r44095831 = r44095830 * r44095830;
        double r44095832 = x_im;
        double r44095833 = r44095832 * r44095832;
        double r44095834 = r44095831 - r44095833;
        double r44095835 = r44095834 * r44095830;
        double r44095836 = r44095830 * r44095832;
        double r44095837 = r44095832 * r44095830;
        double r44095838 = r44095836 + r44095837;
        double r44095839 = r44095838 * r44095832;
        double r44095840 = r44095835 - r44095839;
        return r44095840;
}
↓
double f(double x_re, double x_im) {
        double r44095841 = x_im;
        double r44095842 = x_re;
        double r44095843 = r44095841 + r44095842;
        double r44095844 = cbrt(r44095843);
        double r44095845 = r44095842 - r44095841;
        double r44095846 = r44095845 * r44095842;
        double r44095847 = r44095844 * r44095846;
        double r44095848 = r44095844 * r44095844;
        double r44095849 = r44095847 * r44095848;
        double r44095850 = r44095842 * r44095841;
        double r44095851 = r44095850 + r44095850;
        double r44095852 = r44095851 * r44095841;
        double r44095853 = r44095849 - r44095852;
        return r44095853;
}

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

Original6.8
Target0.2
Herbie0.7
\[\left(x.re \cdot x.re\right) \cdot \left(x.re - x.im\right) + \left(x.re \cdot x.im\right) \cdot \left(x.re - 3 \cdot x.im\right)\]

Derivation

  1. Initial program 6.8

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

  3. Applied difference-of-squares6.8

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

  4. Applied associate-*l*0.2

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

  6. Applied add-cube-cbrt0.7

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

  7. Applied associate-*l*0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2019128 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"

  :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)))