Average Error: 0.3 → 0.3
Time: 3.9s
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 r1801116 = x_re;
        double r1801117 = y_im;
        double r1801118 = r1801116 * r1801117;
        double r1801119 = x_im;
        double r1801120 = y_re;
        double r1801121 = r1801119 * r1801120;
        double r1801122 = r1801118 + r1801121;
        return r1801122;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1801123 = x_re;
        double r1801124 = y_im;
        double r1801125 = r1801123 * r1801124;
        double r1801126 = x_im;
        double r1801127 = y_re;
        double r1801128 = r1801126 * r1801127;
        double r1801129 = r1801125 + r1801128;
        return r1801129;
}

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 2019128 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+.p16 (*.p16 x.re y.im) (*.p16 x.im y.re)))