Average Error: 0.3 → 0.3
Time: 11.3s
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 r1861160 = x_re;
        double r1861161 = y_re;
        double r1861162 = r1861160 * r1861161;
        double r1861163 = x_im;
        double r1861164 = y_im;
        double r1861165 = r1861163 * r1861164;
        double r1861166 = r1861162 - r1861165;
        return r1861166;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1861167 = x_re;
        double r1861168 = y_re;
        double r1861169 = r1861167 * r1861168;
        double r1861170 = x_im;
        double r1861171 = y_im;
        double r1861172 = r1861170 * r1861171;
        double r1861173 = r1861169 - r1861172;
        return r1861173;
}

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 2019128 +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)))