_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 3.6s

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 r26262 = x_re;
        double r26263 = y_im;
        double r26264 = r26262 * r26263;
        double r26265 = x_im;
        double r26266 = y_re;
        double r26267 = r26265 * r26266;
        double r26268 = r26264 + r26267;
        return r26268;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r26269 = x_re;
        double r26270 = y_im;
        double r26271 = x_im;
        double r26272 = y_re;
        double r26273 = r26271 * r26272;
        double r26274 = fma(r26269, r26270, r26273);
        return r26274;
}

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 2019209 +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)))