Average Error: 7.0 → 0.2
Time: 3.8s
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 r371058 = x_re;
        double r371059 = r371058 * r371058;
        double r371060 = x_im;
        double r371061 = r371060 * r371060;
        double r371062 = r371059 - r371061;
        double r371063 = r371062 * r371060;
        double r371064 = r371058 * r371060;
        double r371065 = r371060 * r371058;
        double r371066 = r371064 + r371065;
        double r371067 = r371066 * r371058;
        double r371068 = r371063 + r371067;
        return r371068;
}
↓
double f(double x_re, double x_im) {
        double r371069 = 3.0;
        double r371070 = x_im;
        double r371071 = x_re;
        double r371072 = r371070 * r371071;
        double r371073 = r371072 * r371071;
        double r371074 = r371069 * r371073;
        double r371075 = pow(r371070, r371069);
        double r371076 = r371074 - r371075;
        return r371076;
}

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

Original7.0
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 7.0

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

  2. Simplified6.9

    \[\leadsto \color{blue}{3 \cdot \left(x.im \cdot \left(x.re \cdot x.re\right)\right) - {x.im}^{3}}\]
  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 2020100 
(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)))