Average Error: 0.3 → 0.3
Time: 3.7s
Precision: 64
\[\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}\]
↓
\[x.re \cdot y.im + x.im \cdot y.re\]
\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}
↓
x.re \cdot y.im + x.im \cdot y.re
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1536715 = x_re;
        double r1536716 = y_im;
        double r1536717 = r1536715 * r1536716;
        double r1536718 = x_im;
        double r1536719 = y_re;
        double r1536720 = r1536718 * r1536719;
        double r1536721 = r1536717 + r1536720;
        return r1536721;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1536722 = x_re;
        double r1536723 = y_im;
        double r1536724 = r1536722 * r1536723;
        double r1536725 = x_im;
        double r1536726 = y_re;
        double r1536727 = r1536725 * r1536726;
        double r1536728 = r1536724 + r1536727;
        return r1536728;
}

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Derivation

  1. Initial program 0.3

    \[\frac{\left(x.re \cdot y.im\right)}{\left(x.im \cdot y.re\right)}\]

  2. Final simplification0.3

    \[\leadsto x.re \cdot y.im + x.im \cdot y.re\]

Reproduce

herbie shell --seed 2019133 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))