Average Error: 7.3 → 0.2
Time: 10.0s
Precision: 64
\[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im\]
↓
\[{x.re}^{3} - \left(3 \cdot \left(x.re \cdot x.im\right)\right) \cdot x.im\]
\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 r390989 = x_re;
        double r390990 = r390989 * r390989;
        double r390991 = x_im;
        double r390992 = r390991 * r390991;
        double r390993 = r390990 - r390992;
        double r390994 = r390993 * r390989;
        double r390995 = r390989 * r390991;
        double r390996 = r390991 * r390989;
        double r390997 = r390995 + r390996;
        double r390998 = r390997 * r390991;
        double r390999 = r390994 - r390998;
        return r390999;
}
↓
double f(double x_re, double x_im) {
        double r391000 = x_re;
        double r391001 = 3.0;
        double r391002 = pow(r391000, r391001);
        double r391003 = x_im;
        double r391004 = r391000 * r391003;
        double r391005 = r391001 * r391004;
        double r391006 = r391005 * r391003;
        double r391007 = r391002 - r391006;
        return r391007;
}

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)))