Average Error: 7.0 → 0.2
Time: 20.6s
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 r2328224 = x_re;
        double r2328225 = r2328224 * r2328224;
        double r2328226 = x_im;
        double r2328227 = r2328226 * r2328226;
        double r2328228 = r2328225 - r2328227;
        double r2328229 = r2328228 * r2328226;
        double r2328230 = r2328224 * r2328226;
        double r2328231 = r2328226 * r2328224;
        double r2328232 = r2328230 + r2328231;
        double r2328233 = r2328232 * r2328224;
        double r2328234 = r2328229 + r2328233;
        return r2328234;
}
↓
double f(double x_re, double x_im) {
        double r2328235 = x_re;
        double r2328236 = x_im;
        double r2328237 = r2328235 - r2328236;
        double r2328238 = r2328237 * r2328236;
        double r2328239 = r2328236 + r2328235;
        double r2328240 = r2328238 * r2328239;
        double r2328241 = r2328235 * r2328236;
        double r2328242 = r2328241 + r2328241;
        double r2328243 = r2328235 * r2328242;
        double r2328244 = r2328240 + r2328243;
        return r2328244;
}

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

Original7.0
Target0.2
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 7.0

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

  2. Taylor expanded around 0 6.9

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019130 
(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)))