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

↓

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

double f(double x_re, double x_im, double y_re, double y_im) {
        double r4214949 = x_re;
        double r4214950 = y_re;
        double r4214951 = r4214949 * r4214950;
        double r4214952 = x_im;
        double r4214953 = y_im;
        double r4214954 = r4214952 * r4214953;
        double r4214955 = r4214951 - r4214954;
        return r4214955;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r4214956 = x_re;
        double r4214957 = y_re;
        double r4214958 = r4214956 * r4214957;
        double r4214959 = x_im;
        double r4214960 = y_im;
        double r4214961 = r4214959 * r4214960;
        double r4214962 = r4214958 - r4214961;
        return r4214962;
}

x.re \cdot y.re - x.im \cdot y.im

↓

x.re \cdot y.re - x.im \cdot y.im

Error

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

Derivation

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

Reproduce

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