Average Error: 6.8 → 0.3
Time: 56.4s
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 r26416628 = x_re;
        double r26416629 = r26416628 * r26416628;
        double r26416630 = x_im;
        double r26416631 = r26416630 * r26416630;
        double r26416632 = r26416629 - r26416631;
        double r26416633 = r26416632 * r26416628;
        double r26416634 = r26416628 * r26416630;
        double r26416635 = r26416630 * r26416628;
        double r26416636 = r26416634 + r26416635;
        double r26416637 = r26416636 * r26416630;
        double r26416638 = r26416633 - r26416637;
        return r26416638;
}
↓
double f(double x_re, double x_im) {
        double r26416639 = x_re;
        double r26416640 = x_im;
        double r26416641 = r26416639 - r26416640;
        double r26416642 = r26416641 * r26416639;
        double r26416643 = r26416640 + r26416639;
        double r26416644 = r26416642 * r26416643;
        double r26416645 = r26416639 * r26416640;
        double r26416646 = r26416645 + r26416645;
        double r26416647 = r26416646 * r26416640;
        double r26416648 = r26416644 - r26416647;
        return r26416648;
}

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

Original6.8
Target0.3
Herbie0.3
\[\left(x.re \cdot x.re\right) \cdot \left(x.re - x.im\right) + \left(x.re \cdot x.im\right) \cdot \left(x.re - 3 \cdot x.im\right)\]

Derivation

  1. Initial program 6.8

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

  3. Applied difference-of-squares6.8

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

  4. Applied associate-*l*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019124 
(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)))