Average Error: 0.3 → 0.3
Time: 10.7s
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 r1660551 = x_re;
        double r1660552 = y_re;
        double r1660553 = r1660551 * r1660552;
        double r1660554 = x_im;
        double r1660555 = y_im;
        double r1660556 = r1660554 * r1660555;
        double r1660557 = r1660553 - r1660556;
        return r1660557;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1660558 = x_re;
        double r1660559 = y_re;
        double r1660560 = r1660558 * r1660559;
        double r1660561 = x_im;
        double r1660562 = y_im;
        double r1660563 = r1660561 * r1660562;
        double r1660564 = r1660560 - r1660563;
        return r1660564;
}

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 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))