Average Error: 0.3 → 0.3
Time: 9.2s
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 r633457 = x_re;
        double r633458 = y_re;
        double r633459 = r633457 * r633458;
        double r633460 = x_im;
        double r633461 = y_im;
        double r633462 = r633460 * r633461;
        double r633463 = r633459 - r633462;
        return r633463;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r633464 = x_re;
        double r633465 = y_re;
        double r633466 = r633464 * r633465;
        double r633467 = x_im;
        double r633468 = y_im;
        double r633469 = r633467 * r633468;
        double r633470 = r633466 - r633469;
        return r633470;
}

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 +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)))