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

↓

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

double f(double x_re, double x_im, double y_re, double y_im) {
        double r10556313 = x_re;
        double r10556314 = y_im;
        double r10556315 = r10556313 * r10556314;
        double r10556316 = x_im;
        double r10556317 = y_re;
        double r10556318 = r10556316 * r10556317;
        double r10556319 = r10556315 + r10556318;
        return r10556319;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r10556320 = x_im;
        double r10556321 = y_re;
        double r10556322 = r10556320 * r10556321;
        double r10556323 = x_re;
        double r10556324 = y_im;
        double r10556325 = r10556323 * r10556324;
        double r10556326 = r10556322 + r10556325;
        return r10556326;
}

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 2019101 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))