Average Error: 6.9 → 0.7
Time: 20.7s
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 r6834660 = x_re;
        double r6834661 = r6834660 * r6834660;
        double r6834662 = x_im;
        double r6834663 = r6834662 * r6834662;
        double r6834664 = r6834661 - r6834663;
        double r6834665 = r6834664 * r6834660;
        double r6834666 = r6834660 * r6834662;
        double r6834667 = r6834662 * r6834660;
        double r6834668 = r6834666 + r6834667;
        double r6834669 = r6834668 * r6834662;
        double r6834670 = r6834665 - r6834669;
        return r6834670;
}
↓
double f(double x_re, double x_im) {
        double r6834671 = x_im;
        double r6834672 = x_re;
        double r6834673 = r6834671 + r6834672;
        double r6834674 = cbrt(r6834673);
        double r6834675 = r6834672 - r6834671;
        double r6834676 = r6834675 * r6834672;
        double r6834677 = r6834674 * r6834676;
        double r6834678 = r6834674 * r6834674;
        double r6834679 = r6834677 * r6834678;
        double r6834680 = r6834672 * r6834671;
        double r6834681 = r6834680 + r6834680;
        double r6834682 = r6834681 * r6834671;
        double r6834683 = r6834679 - r6834682;
        return r6834683;
}

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

Derivation

  1. Initial program 6.9

    \[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
  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-cbrt0.7

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

  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 2019133 
(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)))