Average Error: 7.1 → 0.2
Time: 17.4s
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 r143288 = x_re;
        double r143289 = r143288 * r143288;
        double r143290 = x_im;
        double r143291 = r143290 * r143290;
        double r143292 = r143289 - r143291;
        double r143293 = r143292 * r143288;
        double r143294 = r143288 * r143290;
        double r143295 = r143290 * r143288;
        double r143296 = r143294 + r143295;
        double r143297 = r143296 * r143290;
        double r143298 = r143293 - r143297;
        return r143298;
}
↓
double f(double x_re, double x_im) {
        double r143299 = x_re;
        double r143300 = 3.0;
        double r143301 = pow(r143299, r143300);
        double r143302 = x_im;
        double r143303 = r143300 * r143299;
        double r143304 = r143302 * r143303;
        double r143305 = r143302 * r143304;
        double r143306 = r143301 - r143305;
        return r143306;
}

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

Original7.1
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 7.1

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

  2. Simplified7.1

    \[\leadsto \color{blue}{{x.re}^{3} - \left(x.im \cdot x.im\right) \cdot \left(3 \cdot x.re\right)}\]
  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 2019199 
(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)))