Average Error: 7.3 → 0.2
Time: 34.2s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right) + \left(x.im \cdot x.re + x.im \cdot x.re\right) \cdot x.re\]
\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(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right) + \left(x.im \cdot x.re + x.im \cdot x.re\right) \cdot x.re
double f(double x_re, double x_im) {
        double r10258274 = x_re;
        double r10258275 = r10258274 * r10258274;
        double r10258276 = x_im;
        double r10258277 = r10258276 * r10258276;
        double r10258278 = r10258275 - r10258277;
        double r10258279 = r10258278 * r10258276;
        double r10258280 = r10258274 * r10258276;
        double r10258281 = r10258276 * r10258274;
        double r10258282 = r10258280 + r10258281;
        double r10258283 = r10258282 * r10258274;
        double r10258284 = r10258279 + r10258283;
        return r10258284;
}
↓
double f(double x_re, double x_im) {
        double r10258285 = x_im;
        double r10258286 = x_re;
        double r10258287 = r10258286 + r10258285;
        double r10258288 = r10258285 * r10258287;
        double r10258289 = r10258286 - r10258285;
        double r10258290 = r10258288 * r10258289;
        double r10258291 = r10258285 * r10258286;
        double r10258292 = r10258291 + r10258291;
        double r10258293 = r10258292 * r10258286;
        double r10258294 = r10258290 + r10258293;
        return r10258294;
}

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

Original7.3
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 7.3

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

  2. Taylor expanded around 0 7.2

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

  3. Simplified0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"

  :herbie-target
  (+ (* (* x.re x.im) (* 2.0 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)))