Average Error: 7.6 → 0.2
Time: 4.1s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - \left(3 \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)\]
\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
↓
{x.re}^{3} - \left(3 \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)
double f(double x_re, double x_im) {
        double r293825 = x_re;
        double r293826 = r293825 * r293825;
        double r293827 = x_im;
        double r293828 = r293827 * r293827;
        double r293829 = r293826 - r293828;
        double r293830 = r293829 * r293825;
        double r293831 = r293825 * r293827;
        double r293832 = r293827 * r293825;
        double r293833 = r293831 + r293832;
        double r293834 = r293833 * r293827;
        double r293835 = r293830 - r293834;
        return r293835;
}
↓
double f(double x_re, double x_im) {
        double r293836 = x_re;
        double r293837 = 3.0;
        double r293838 = pow(r293836, r293837);
        double r293839 = x_im;
        double r293840 = r293837 * r293839;
        double r293841 = r293836 * r293839;
        double r293842 = r293840 * r293841;
        double r293843 = r293838 - r293842;
        return r293843;
}

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

Original7.6
Target0.3
Herbie0.2
\[\left(x.re \cdot x.re\right) \cdot \left(x.re - x.im\right) + \left(x.re \cdot x.im\right) \cdot \left(x.re - 3 \cdot x.im\right)\]

Derivation

  1. Initial program 7.6

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

  2. Simplified0.2

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019318 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"
  :precision binary64

  :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)))