Average Error: 0.3 → 0.3
Time: 8.8s
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 r633462 = x_re;
        double r633463 = y_re;
        double r633464 = r633462 * r633463;
        double r633465 = x_im;
        double r633466 = y_im;
        double r633467 = r633465 * r633466;
        double r633468 = r633464 - r633467;
        return r633468;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r633469 = x_re;
        double r633470 = y_re;
        double r633471 = r633469 * r633470;
        double r633472 = x_im;
        double r633473 = y_im;
        double r633474 = r633472 * r633473;
        double r633475 = r633471 - r633474;
        return r633475;
}

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 2019107 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (-.p16 (*.p16 x.re y.re) (*.p16 x.im y.im)))