Average Error: 7.2 → 0.2
Time: 55.4s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[\left(\left(x.re - x.im\right) \cdot x.re\right) \cdot \left(x.re + x.im\right) - x.im \cdot \left(x.im \cdot x.re + x.im \cdot x.re\right)\]
\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
↓
\left(\left(x.re - x.im\right) \cdot x.re\right) \cdot \left(x.re + x.im\right) - x.im \cdot \left(x.im \cdot x.re + x.im \cdot x.re\right)
double f(double x_re, double x_im) {
        double r47175667 = x_re;
        double r47175668 = r47175667 * r47175667;
        double r47175669 = x_im;
        double r47175670 = r47175669 * r47175669;
        double r47175671 = r47175668 - r47175670;
        double r47175672 = r47175671 * r47175667;
        double r47175673 = r47175667 * r47175669;
        double r47175674 = r47175669 * r47175667;
        double r47175675 = r47175673 + r47175674;
        double r47175676 = r47175675 * r47175669;
        double r47175677 = r47175672 - r47175676;
        return r47175677;
}
↓
double f(double x_re, double x_im) {
        double r47175678 = x_re;
        double r47175679 = x_im;
        double r47175680 = r47175678 - r47175679;
        double r47175681 = r47175680 * r47175678;
        double r47175682 = r47175678 + r47175679;
        double r47175683 = r47175681 * r47175682;
        double r47175684 = r47175679 * r47175678;
        double r47175685 = r47175684 + r47175684;
        double r47175686 = r47175679 * r47175685;
        double r47175687 = r47175683 - r47175686;
        return r47175687;
}

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
Target0.3
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 7.2

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

  2. Taylor expanded around 0 7.1

    \[\leadsto \color{blue}{\left({x.re}^{3} - {x.im}^{2} \cdot x.re\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019120 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"

  :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)))