Average Error: 7.2 → 0.2
Time: 19.7s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[3 \cdot \left(x.re \cdot \left(x.im \cdot x.re\right)\right) - {x.im}^{3}\]
\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
↓
3 \cdot \left(x.re \cdot \left(x.im \cdot x.re\right)\right) - {x.im}^{3}
double f(double x_re, double x_im) {
        double r192325 = x_re;
        double r192326 = r192325 * r192325;
        double r192327 = x_im;
        double r192328 = r192327 * r192327;
        double r192329 = r192326 - r192328;
        double r192330 = r192329 * r192327;
        double r192331 = r192325 * r192327;
        double r192332 = r192327 * r192325;
        double r192333 = r192331 + r192332;
        double r192334 = r192333 * r192325;
        double r192335 = r192330 + r192334;
        return r192335;
}
↓
double f(double x_re, double x_im) {
        double r192336 = 3.0;
        double r192337 = x_re;
        double r192338 = x_im;
        double r192339 = r192338 * r192337;
        double r192340 = r192337 * r192339;
        double r192341 = r192336 * r192340;
        double r192342 = pow(r192338, r192336);
        double r192343 = r192341 - r192342;
        return r192343;
}

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
Target0.2
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 7.2

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

  2. Simplified0.2

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

  4. Applied associate-*l*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019199 
(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)))