Average Error: 7.9 → 0.2
Time: 6.3s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - \left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.im\]
\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} - \left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.im
double f(double x_re, double x_im) {
        double r193495 = x_re;
        double r193496 = r193495 * r193495;
        double r193497 = x_im;
        double r193498 = r193497 * r193497;
        double r193499 = r193496 - r193498;
        double r193500 = r193499 * r193495;
        double r193501 = r193495 * r193497;
        double r193502 = r193497 * r193495;
        double r193503 = r193501 + r193502;
        double r193504 = r193503 * r193497;
        double r193505 = r193500 - r193504;
        return r193505;
}
↓
double f(double x_re, double x_im) {
        double r193506 = x_re;
        double r193507 = 3.0;
        double r193508 = pow(r193506, r193507);
        double r193509 = x_im;
        double r193510 = r193506 * r193509;
        double r193511 = r193507 * r193510;
        double r193512 = r193511 * r193509;
        double r193513 = r193508 - r193512;
        return r193513;
}

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

Original7.9
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 7.9

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

  2. Simplified0.2

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(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)))