Average Error: 7.7 → 0.2
Time: 7.2s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re\]
↓
\[3 \cdot \left(\left(x.im \cdot x.re\right) \cdot x.re\right) - {x.im}^{3}\]
\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re
↓
3 \cdot \left(\left(x.im \cdot x.re\right) \cdot x.re\right) - {x.im}^{3}
double f(double x_re, double x_im) {
        double r200031 = x_re;
        double r200032 = r200031 * r200031;
        double r200033 = x_im;
        double r200034 = r200033 * r200033;
        double r200035 = r200032 - r200034;
        double r200036 = r200035 * r200033;
        double r200037 = r200031 * r200033;
        double r200038 = r200033 * r200031;
        double r200039 = r200037 + r200038;
        double r200040 = r200039 * r200031;
        double r200041 = r200036 + r200040;
        return r200041;
}
↓
double f(double x_re, double x_im) {
        double r200042 = 3.0;
        double r200043 = x_im;
        double r200044 = x_re;
        double r200045 = r200043 * r200044;
        double r200046 = r200045 * r200044;
        double r200047 = r200042 * r200046;
        double r200048 = pow(r200043, r200042);
        double r200049 = r200047 - r200048;
        return r200049;
}

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

Original7.7
Target0.2
Herbie0.2
\[\left(x.re \cdot x.im\right) \cdot \left(2 \cdot x.re\right) + \left(x.im \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right)\]

Derivation

  1. Initial program 7.7

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

  2. Simplified7.7

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

  4. Applied associate-*r*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"
  :precision binary64

  :herbie-target
  (+ (* (* x.re x.im) (* 2 x.re)) (* (* x.im (- x.re x.im)) (+ x.re x.im)))

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