Average Error: 7.3 → 0.2
Time: 11.4s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - x.im \cdot \left(x.im \cdot \left(3 \cdot x.re\right)\right)\]
\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} - x.im \cdot \left(x.im \cdot \left(3 \cdot x.re\right)\right)
double f(double x_re, double x_im) {
        double r198769 = x_re;
        double r198770 = r198769 * r198769;
        double r198771 = x_im;
        double r198772 = r198771 * r198771;
        double r198773 = r198770 - r198772;
        double r198774 = r198773 * r198769;
        double r198775 = r198769 * r198771;
        double r198776 = r198771 * r198769;
        double r198777 = r198775 + r198776;
        double r198778 = r198777 * r198771;
        double r198779 = r198774 - r198778;
        return r198779;
}
↓
double f(double x_re, double x_im) {
        double r198780 = x_re;
        double r198781 = 3.0;
        double r198782 = pow(r198780, r198781);
        double r198783 = x_im;
        double r198784 = r198781 * r198780;
        double r198785 = r198783 * r198784;
        double r198786 = r198783 * r198785;
        double r198787 = r198782 - r198786;
        return r198787;
}

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

Original7.3
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 7.3

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

  2. Simplified7.3

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

  4. Applied associate-*l*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019198 
(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 (* 3.0 x.im))))

  (- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im)))