Average Error: 7.6 → 0.2
Time: 4.0s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - \left(3 \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)\]
\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} - \left(3 \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)
double f(double x_re, double x_im) {
        double r223827 = x_re;
        double r223828 = r223827 * r223827;
        double r223829 = x_im;
        double r223830 = r223829 * r223829;
        double r223831 = r223828 - r223830;
        double r223832 = r223831 * r223827;
        double r223833 = r223827 * r223829;
        double r223834 = r223829 * r223827;
        double r223835 = r223833 + r223834;
        double r223836 = r223835 * r223829;
        double r223837 = r223832 - r223836;
        return r223837;
}
↓
double f(double x_re, double x_im) {
        double r223838 = x_re;
        double r223839 = 3.0;
        double r223840 = pow(r223838, r223839);
        double r223841 = x_im;
        double r223842 = r223839 * r223841;
        double r223843 = r223838 * r223841;
        double r223844 = r223842 * r223843;
        double r223845 = r223840 - r223844;
        return r223845;
}

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

Original7.6
Target0.2
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 7.6

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

  2. Simplified0.2

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019322 
(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)))