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

↓

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

double f(double x_re, double x_im, double y_re, double y_im) {
        double r5982107 = x_re;
        double r5982108 = y_im;
        double r5982109 = r5982107 * r5982108;
        double r5982110 = x_im;
        double r5982111 = y_re;
        double r5982112 = r5982110 * r5982111;
        double r5982113 = r5982109 + r5982112;
        return r5982113;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r5982114 = x_im;
        double r5982115 = y_re;
        double r5982116 = r5982114 * r5982115;
        double r5982117 = x_re;
        double r5982118 = y_im;
        double r5982119 = r5982117 * r5982118;
        double r5982120 = r5982116 + r5982119;
        return r5982120;
}

x.re \cdot y.im + x.im \cdot y.re

↓

x.im \cdot y.re + x.re \cdot y.im

Error

The X axis uses an exponential scale — Bits error versus `x.re`

Derivation

Initial program 0.0
\[x.re \cdot y.im + x.im \cdot y.re\]
Final simplification0.0
\[\leadsto x.im \cdot y.re + x.re \cdot y.im\]

Reproduce

herbie shell --seed 2019102 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))