Average Error: 7.1 → 0.3
Time: 16.3s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\left(\left(x.re - x.im\right) \cdot x.im\right) \cdot \left(x.im + x.re\right) + x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)\]
\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(\left(x.re - x.im\right) \cdot x.im\right) \cdot \left(x.im + x.re\right) + x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)
double f(double x_re, double x_im) {
        double r2259037 = x_re;
        double r2259038 = r2259037 * r2259037;
        double r2259039 = x_im;
        double r2259040 = r2259039 * r2259039;
        double r2259041 = r2259038 - r2259040;
        double r2259042 = r2259041 * r2259039;
        double r2259043 = r2259037 * r2259039;
        double r2259044 = r2259039 * r2259037;
        double r2259045 = r2259043 + r2259044;
        double r2259046 = r2259045 * r2259037;
        double r2259047 = r2259042 + r2259046;
        return r2259047;
}
↓
double f(double x_re, double x_im) {
        double r2259048 = x_re;
        double r2259049 = x_im;
        double r2259050 = r2259048 - r2259049;
        double r2259051 = r2259050 * r2259049;
        double r2259052 = r2259049 + r2259048;
        double r2259053 = r2259051 * r2259052;
        double r2259054 = r2259048 * r2259049;
        double r2259055 = r2259054 + r2259054;
        double r2259056 = r2259048 * r2259055;
        double r2259057 = r2259053 + r2259056;
        return r2259057;
}

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

Original7.1
Target0.3
Herbie0.3
\[\left(x.re \cdot x.im\right) \cdot \left(2 \cdot x.re\right) + \left(x.im \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right)\]

Derivation

  1. Initial program 7.1

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

  2. Taylor expanded around 0 7.0

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

  3. Simplified0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019152 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"

  :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)))