Average Error: 6.9 → 0.6
Time: 30.3s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[\left(\left(x.re - x.im\right) \cdot x.re\right) \cdot \left(x.im + x.re\right) - \sqrt[3]{\left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im} \cdot \left(\sqrt[3]{\left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im} \cdot \sqrt[3]{\left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im}\right)\]
\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(\left(x.re - x.im\right) \cdot x.re\right) \cdot \left(x.im + x.re\right) - \sqrt[3]{\left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im} \cdot \left(\sqrt[3]{\left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im} \cdot \sqrt[3]{\left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im}\right)
double f(double x_re, double x_im) {
        double r7732665 = x_re;
        double r7732666 = r7732665 * r7732665;
        double r7732667 = x_im;
        double r7732668 = r7732667 * r7732667;
        double r7732669 = r7732666 - r7732668;
        double r7732670 = r7732669 * r7732665;
        double r7732671 = r7732665 * r7732667;
        double r7732672 = r7732667 * r7732665;
        double r7732673 = r7732671 + r7732672;
        double r7732674 = r7732673 * r7732667;
        double r7732675 = r7732670 - r7732674;
        return r7732675;
}
↓
double f(double x_re, double x_im) {
        double r7732676 = x_re;
        double r7732677 = x_im;
        double r7732678 = r7732676 - r7732677;
        double r7732679 = r7732678 * r7732676;
        double r7732680 = r7732677 + r7732676;
        double r7732681 = r7732679 * r7732680;
        double r7732682 = r7732676 * r7732677;
        double r7732683 = r7732682 + r7732682;
        double r7732684 = r7732683 * r7732677;
        double r7732685 = cbrt(r7732684);
        double r7732686 = r7732685 * r7732685;
        double r7732687 = r7732685 * r7732686;
        double r7732688 = r7732681 - r7732687;
        return r7732688;
}

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

Original6.9
Target0.2
Herbie0.6
\[\left(x.re \cdot x.re\right) \cdot \left(x.re - x.im\right) + \left(x.re \cdot x.im\right) \cdot \left(x.re - 3 \cdot x.im\right)\]

Derivation

  1. Initial program 6.9

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

  3. Applied difference-of-squares6.9

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

  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-cbrt0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2019143 
(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)))