Average Error: 7.2 → 0.2
Time: 2.0s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - 3 \cdot \left(x.im \cdot \left(x.re \cdot x.im\right)\right)\]
\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 r365416 = x_re;
        double r365417 = r365416 * r365416;
        double r365418 = x_im;
        double r365419 = r365418 * r365418;
        double r365420 = r365417 - r365419;
        double r365421 = r365420 * r365416;
        double r365422 = r365416 * r365418;
        double r365423 = r365418 * r365416;
        double r365424 = r365422 + r365423;
        double r365425 = r365424 * r365418;
        double r365426 = r365421 - r365425;
        return r365426;
}
↓
double f(double x_re, double x_im) {
        double r365427 = x_re;
        double r365428 = 3.0;
        double r365429 = pow(r365427, r365428);
        double r365430 = x_im;
        double r365431 = r365427 * r365430;
        double r365432 = r365430 * r365431;
        double r365433 = r365428 * r365432;
        double r365434 = r365429 - r365433;
        return r365434;
}

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

Original7.2
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 7.2

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

  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 2020049 
(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)))