Average Error: 7.4 → 0.2
Time: 2.1s
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 r296730 = x_re;
        double r296731 = r296730 * r296730;
        double r296732 = x_im;
        double r296733 = r296732 * r296732;
        double r296734 = r296731 - r296733;
        double r296735 = r296734 * r296730;
        double r296736 = r296730 * r296732;
        double r296737 = r296732 * r296730;
        double r296738 = r296736 + r296737;
        double r296739 = r296738 * r296732;
        double r296740 = r296735 - r296739;
        return r296740;
}
↓
double f(double x_re, double x_im) {
        double r296741 = x_re;
        double r296742 = 3.0;
        double r296743 = pow(r296741, r296742);
        double r296744 = x_im;
        double r296745 = r296741 * r296744;
        double r296746 = r296744 * r296745;
        double r296747 = r296742 * r296746;
        double r296748 = r296743 - r296747;
        return r296748;
}

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
Target0.2
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 7.4

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

  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 2020057 
(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)))