Average Error: 7.3 → 0.2
Time: 9.8s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - 3 \cdot \left(\left(x.re \cdot x.im\right) \cdot x.im\right)\]
\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} - 3 \cdot \left(\left(x.re \cdot x.im\right) \cdot x.im\right)
double f(double x_re, double x_im) {
        double r430260 = x_re;
        double r430261 = r430260 * r430260;
        double r430262 = x_im;
        double r430263 = r430262 * r430262;
        double r430264 = r430261 - r430263;
        double r430265 = r430264 * r430260;
        double r430266 = r430260 * r430262;
        double r430267 = r430262 * r430260;
        double r430268 = r430266 + r430267;
        double r430269 = r430268 * r430262;
        double r430270 = r430265 - r430269;
        return r430270;
}
↓
double f(double x_re, double x_im) {
        double r430271 = x_re;
        double r430272 = 3.0;
        double r430273 = pow(r430271, r430272);
        double r430274 = x_im;
        double r430275 = r430271 * r430274;
        double r430276 = r430275 * r430274;
        double r430277 = r430272 * r430276;
        double r430278 = r430273 - r430277;
        return r430278;
}

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. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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)))