Average Error: 7.0 → 0.2
Time: 43.0s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[\left(\left(x.re - x.im\right) \cdot x.re\right) \cdot \left(x.re + x.im\right) - \left(x.im \cdot x.re + x.im \cdot x.re\right) \cdot x.im\]
\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im
↓
\left(\left(x.re - x.im\right) \cdot x.re\right) \cdot \left(x.re + x.im\right) - \left(x.im \cdot x.re + x.im \cdot x.re\right) \cdot x.im
double f(double x_re, double x_im) {
        double r8908600 = x_re;
        double r8908601 = r8908600 * r8908600;
        double r8908602 = x_im;
        double r8908603 = r8908602 * r8908602;
        double r8908604 = r8908601 - r8908603;
        double r8908605 = r8908604 * r8908600;
        double r8908606 = r8908600 * r8908602;
        double r8908607 = r8908602 * r8908600;
        double r8908608 = r8908606 + r8908607;
        double r8908609 = r8908608 * r8908602;
        double r8908610 = r8908605 - r8908609;
        return r8908610;
}
↓
double f(double x_re, double x_im) {
        double r8908611 = x_re;
        double r8908612 = x_im;
        double r8908613 = r8908611 - r8908612;
        double r8908614 = r8908613 * r8908611;
        double r8908615 = r8908611 + r8908612;
        double r8908616 = r8908614 * r8908615;
        double r8908617 = r8908612 * r8908611;
        double r8908618 = r8908617 + r8908617;
        double r8908619 = r8908618 * r8908612;
        double r8908620 = r8908616 - r8908619;
        return r8908620;
}

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

Derivation

  1. Initial program 7.0

    \[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
  2. Using strategy rm

  3. Applied difference-of-squares7.0

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

  4. Applied associate-*l*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"

  :herbie-target
  (+ (* (* x.re x.re) (- x.re x.im)) (* (* x.re x.im) (- x.re (* 3.0 x.im))))

  (- (* (- (* x.re x.re) (* x.im x.im)) x.re) (* (+ (* x.re x.im) (* x.im x.re)) x.im)))