Average Error: 7.6 → 0.2
Time: 12.0s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\left(3 \cdot x.re\right) \cdot \left(x.im \cdot x.re\right) - {x.im}^{3}\]
\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 x.re\right) \cdot \left(x.im \cdot x.re\right) - {x.im}^{3}
double f(double x_re, double x_im) {
        double r143779 = x_re;
        double r143780 = r143779 * r143779;
        double r143781 = x_im;
        double r143782 = r143781 * r143781;
        double r143783 = r143780 - r143782;
        double r143784 = r143783 * r143781;
        double r143785 = r143779 * r143781;
        double r143786 = r143781 * r143779;
        double r143787 = r143785 + r143786;
        double r143788 = r143787 * r143779;
        double r143789 = r143784 + r143788;
        return r143789;
}
↓
double f(double x_re, double x_im) {
        double r143790 = 3.0;
        double r143791 = x_re;
        double r143792 = r143790 * r143791;
        double r143793 = x_im;
        double r143794 = r143793 * r143791;
        double r143795 = r143792 * r143794;
        double r143796 = pow(r143793, r143790);
        double r143797 = r143795 - r143796;
        return r143797;
}

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

Original7.6
Target0.3
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 7.6

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019212 
(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)))