Average Error: 7.2 → 0.2
Time: 11.5s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - \left(3 \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)\]
\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} - \left(3 \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)
double f(double x_re, double x_im) {
        double r77033 = x_re;
        double r77034 = r77033 * r77033;
        double r77035 = x_im;
        double r77036 = r77035 * r77035;
        double r77037 = r77034 - r77036;
        double r77038 = r77037 * r77033;
        double r77039 = r77033 * r77035;
        double r77040 = r77035 * r77033;
        double r77041 = r77039 + r77040;
        double r77042 = r77041 * r77035;
        double r77043 = r77038 - r77042;
        return r77043;
}
↓
double f(double x_re, double x_im) {
        double r77044 = x_re;
        double r77045 = 3.0;
        double r77046 = pow(r77044, r77045);
        double r77047 = x_im;
        double r77048 = r77045 * r77047;
        double r77049 = r77044 * r77047;
        double r77050 = r77048 * r77049;
        double r77051 = r77046 - r77050;
        return r77051;
}

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

Original7.2
Target0.2
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 7.2

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

  2. Simplified0.2

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(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)))