Average Error: 6.5 → 0.2
Time: 23.6s
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 r6049292 = x_re;
        double r6049293 = r6049292 * r6049292;
        double r6049294 = x_im;
        double r6049295 = r6049294 * r6049294;
        double r6049296 = r6049293 - r6049295;
        double r6049297 = r6049296 * r6049294;
        double r6049298 = r6049292 * r6049294;
        double r6049299 = r6049294 * r6049292;
        double r6049300 = r6049298 + r6049299;
        double r6049301 = r6049300 * r6049292;
        double r6049302 = r6049297 + r6049301;
        return r6049302;
}
↓
double f(double x_re, double x_im) {
        double r6049303 = x_re;
        double r6049304 = x_im;
        double r6049305 = r6049303 - r6049304;
        double r6049306 = r6049305 * r6049304;
        double r6049307 = r6049304 + r6049303;
        double r6049308 = r6049306 * r6049307;
        double r6049309 = r6049303 * r6049304;
        double r6049310 = r6049309 + r6049309;
        double r6049311 = r6049303 * r6049310;
        double r6049312 = r6049308 + r6049311;
        return r6049312;
}

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

Original6.5
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 6.5

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

  2. Taylor expanded around -inf 6.4

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

  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 2019139 
(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)))