Average Error: 6.2 → 0.2
Time: 1.3m
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[\left(\left(x.re - x.im\right) \cdot x.re\right) \cdot \left(x.im + x.re\right) - \left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im\]
\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.im + x.re\right) - \left(x.re \cdot x.im + x.re \cdot x.im\right) \cdot x.im
double f(double x_re, double x_im) {
        double r44097646 = x_re;
        double r44097647 = r44097646 * r44097646;
        double r44097648 = x_im;
        double r44097649 = r44097648 * r44097648;
        double r44097650 = r44097647 - r44097649;
        double r44097651 = r44097650 * r44097646;
        double r44097652 = r44097646 * r44097648;
        double r44097653 = r44097648 * r44097646;
        double r44097654 = r44097652 + r44097653;
        double r44097655 = r44097654 * r44097648;
        double r44097656 = r44097651 - r44097655;
        return r44097656;
}
↓
double f(double x_re, double x_im) {
        double r44097657 = x_re;
        double r44097658 = x_im;
        double r44097659 = r44097657 - r44097658;
        double r44097660 = r44097659 * r44097657;
        double r44097661 = r44097658 + r44097657;
        double r44097662 = r44097660 * r44097661;
        double r44097663 = r44097657 * r44097658;
        double r44097664 = r44097663 + r44097663;
        double r44097665 = r44097664 * r44097658;
        double r44097666 = r44097662 - r44097665;
        return r44097666;
}

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

Original6.2
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 6.2

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

  3. Applied difference-of-squares6.2

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

  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

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

Reproduce

herbie shell --seed 2019125 
(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 x.im))))

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