Average Error: 7.3 → 0.2
Time: 12.7s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.re - {x.im}^{3}\]
\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
↓
\left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.re - {x.im}^{3}
double f(double x_re, double x_im) {
        double r202492 = x_re;
        double r202493 = r202492 * r202492;
        double r202494 = x_im;
        double r202495 = r202494 * r202494;
        double r202496 = r202493 - r202495;
        double r202497 = r202496 * r202494;
        double r202498 = r202492 * r202494;
        double r202499 = r202494 * r202492;
        double r202500 = r202498 + r202499;
        double r202501 = r202500 * r202492;
        double r202502 = r202497 + r202501;
        return r202502;
}
↓
double f(double x_re, double x_im) {
        double r202503 = 3.0;
        double r202504 = x_re;
        double r202505 = x_im;
        double r202506 = r202504 * r202505;
        double r202507 = r202503 * r202506;
        double r202508 = r202507 * r202504;
        double r202509 = pow(r202505, r202503);
        double r202510 = r202508 - r202509;
        return r202510;
}

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
Target0.2
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 7.3

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

  2. Simplified0.2

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(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)))