Average Error: 7.3 → 0.2
Time: 9.5s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - 3 \cdot \left(\left(x.re \cdot x.im\right) \cdot x.im\right)\]
\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
↓
{x.re}^{3} - 3 \cdot \left(\left(x.re \cdot x.im\right) \cdot x.im\right)
double f(double x_re, double x_im) {
        double r572680 = x_re;
        double r572681 = r572680 * r572680;
        double r572682 = x_im;
        double r572683 = r572682 * r572682;
        double r572684 = r572681 - r572683;
        double r572685 = r572684 * r572680;
        double r572686 = r572680 * r572682;
        double r572687 = r572682 * r572680;
        double r572688 = r572686 + r572687;
        double r572689 = r572688 * r572682;
        double r572690 = r572685 - r572689;
        return r572690;
}
↓
double f(double x_re, double x_im) {
        double r572691 = x_re;
        double r572692 = 3.0;
        double r572693 = pow(r572691, r572692);
        double r572694 = x_im;
        double r572695 = r572691 * r572694;
        double r572696 = r572695 * r572694;
        double r572697 = r572692 * r572696;
        double r572698 = r572693 - r572697;
        return r572698;
}

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

Original7.3
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 7.3

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"
  :precision binary64

  :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)))