_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 2.8s

Precision: 64

Math

\[x.re \cdot y.im + x.im \cdot y.re\]

↓

\[\mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)\]

C

double f(double x_re, double x_im, double y_re, double y_im) {
        double r94823 = x_re;
        double r94824 = y_im;
        double r94825 = r94823 * r94824;
        double r94826 = x_im;
        double r94827 = y_re;
        double r94828 = r94826 * r94827;
        double r94829 = r94825 + r94828;
        return r94829;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r94830 = x_re;
        double r94831 = y_im;
        double r94832 = x_im;
        double r94833 = y_re;
        double r94834 = r94832 * r94833;
        double r94835 = fma(r94830, r94831, r94834);
        return r94835;
}

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 0.0

   \[x.re \cdot y.im + x.im \cdot y.re\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)}\]

3. Final simplification 0.0

   \[\leadsto \mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))