Average Error: 7.3 → 0.2
Time: 12.8s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - 3 \cdot \left(x.im \cdot \left(x.re \cdot x.im\right)\right)\]
\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(x.im \cdot \left(x.re \cdot x.im\right)\right)
double f(double x_re, double x_im) {
        double r190135 = x_re;
        double r190136 = r190135 * r190135;
        double r190137 = x_im;
        double r190138 = r190137 * r190137;
        double r190139 = r190136 - r190138;
        double r190140 = r190139 * r190135;
        double r190141 = r190135 * r190137;
        double r190142 = r190137 * r190135;
        double r190143 = r190141 + r190142;
        double r190144 = r190143 * r190137;
        double r190145 = r190140 - r190144;
        return r190145;
}
↓
double f(double x_re, double x_im) {
        double r190146 = x_re;
        double r190147 = 3.0;
        double r190148 = pow(r190146, r190147);
        double r190149 = x_im;
        double r190150 = r190146 * r190149;
        double r190151 = r190149 * r190150;
        double r190152 = r190147 * r190151;
        double r190153 = r190148 - r190152;
        return r190153;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019294 
(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)))