Average Error: 7.4 → 0.2
Time: 2.5s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - 3 \cdot \left(x.im \cdot \left(x.re \cdot x.im\right)\right)\]
\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(x.im \cdot \left(x.re \cdot x.im\right)\right)
double f(double x_re, double x_im) {
        double r323986 = x_re;
        double r323987 = r323986 * r323986;
        double r323988 = x_im;
        double r323989 = r323988 * r323988;
        double r323990 = r323987 - r323989;
        double r323991 = r323990 * r323986;
        double r323992 = r323986 * r323988;
        double r323993 = r323988 * r323986;
        double r323994 = r323992 + r323993;
        double r323995 = r323994 * r323988;
        double r323996 = r323991 - r323995;
        return r323996;
}
↓
double f(double x_re, double x_im) {
        double r323997 = x_re;
        double r323998 = 3.0;
        double r323999 = pow(r323997, r323998);
        double r324000 = x_im;
        double r324001 = r323997 * r324000;
        double r324002 = r324000 * r324001;
        double r324003 = r323998 * r324002;
        double r324004 = r323999 - r324003;
        return r324004;
}

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
\[\left(x.re \cdot x.re\right) \cdot \left(x.re - x.im\right) + \left(x.re \cdot x.im\right) \cdot \left(x.re - 3 \cdot x.im\right)\]

Derivation

  1. Initial program 7.4

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019352 
(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)))