Average Error: 7.4 → 0.2
Time: 3.2s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[3 \cdot \left(\left(x.im \cdot x.re\right) \cdot x.re\right) - {x.im}^{3}\]
\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re
↓
3 \cdot \left(\left(x.im \cdot x.re\right) \cdot x.re\right) - {x.im}^{3}
double f(double x_re, double x_im) {
        double r227295 = x_re;
        double r227296 = r227295 * r227295;
        double r227297 = x_im;
        double r227298 = r227297 * r227297;
        double r227299 = r227296 - r227298;
        double r227300 = r227299 * r227297;
        double r227301 = r227295 * r227297;
        double r227302 = r227297 * r227295;
        double r227303 = r227301 + r227302;
        double r227304 = r227303 * r227295;
        double r227305 = r227300 + r227304;
        return r227305;
}
↓
double f(double x_re, double x_im) {
        double r227306 = 3.0;
        double r227307 = x_im;
        double r227308 = x_re;
        double r227309 = r227307 * r227308;
        double r227310 = r227309 * r227308;
        double r227311 = r227306 * r227310;
        double r227312 = pow(r227307, r227306);
        double r227313 = r227311 - r227312;
        return r227313;
}

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

Original7.4
Target0.3
Herbie0.2
\[\left(x.re \cdot x.im\right) \cdot \left(2 \cdot x.re\right) + \left(x.im \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right)\]

Derivation

  1. Initial program 7.4

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

  2. Simplified7.4

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"
  :precision binary64

  :herbie-target
  (+ (* (* x.re x.im) (* 2 x.re)) (* (* x.im (- x.re x.im)) (+ x.re x.im)))

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