_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 709.0ms

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 r83931 = x_re;
        double r83932 = y_im;
        double r83933 = r83931 * r83932;
        double r83934 = x_im;
        double r83935 = y_re;
        double r83936 = r83934 * r83935;
        double r83937 = r83933 + r83936;
        return r83937;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r83938 = x_re;
        double r83939 = y_im;
        double r83940 = x_im;
        double r83941 = y_re;
        double r83942 = r83940 * r83941;
        double r83943 = fma(r83938, r83939, r83942);
        return r83943;
}

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 2019354 +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)))