Average Error: 7.3 → 0.2
Time: 6.3s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - \left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.im\]
\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
↓
{x.re}^{3} - \left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.im
double f(double x_re, double x_im) {
        double r329024 = x_re;
        double r329025 = r329024 * r329024;
        double r329026 = x_im;
        double r329027 = r329026 * r329026;
        double r329028 = r329025 - r329027;
        double r329029 = r329028 * r329024;
        double r329030 = r329024 * r329026;
        double r329031 = r329026 * r329024;
        double r329032 = r329030 + r329031;
        double r329033 = r329032 * r329026;
        double r329034 = r329029 - r329033;
        return r329034;
}
↓
double f(double x_re, double x_im) {
        double r329035 = x_re;
        double r329036 = 3.0;
        double r329037 = pow(r329035, r329036);
        double r329038 = x_im;
        double r329039 = r329035 * r329038;
        double r329040 = r329036 * r329039;
        double r329041 = r329040 * r329038;
        double r329042 = r329037 - r329041;
        return r329042;
}

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
Target0.2
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 7.3

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

  2. Simplified0.2

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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)))