Average Error: 0.3 → 0.3
Time: 13.3s
Precision: 64
\[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]
\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)
↓
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 r2390950 = x_re;
        double r2390951 = y_re;
        double r2390952 = r2390950 * r2390951;
        double r2390953 = x_im;
        double r2390954 = y_im;
        double r2390955 = r2390953 * r2390954;
        double r2390956 = r2390952 - r2390955;
        return r2390956;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2390957 = x_re;
        double r2390958 = y_re;
        double r2390959 = r2390957 * r2390958;
        double r2390960 = x_im;
        double r2390961 = y_im;
        double r2390962 = r2390960 * r2390961;
        double r2390963 = r2390959 - r2390962;
        return r2390963;
}

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

    \[\left(x.re \cdot y.re\right) - \left(x.im \cdot y.im\right)\]

  2. Final simplification0.3

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

Reproduce

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