_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 1.6s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r99308 = x_re;
        double r99309 = y_im;
        double r99310 = r99308 * r99309;
        double r99311 = x_im;
        double r99312 = y_re;
        double r99313 = r99311 * r99312;
        double r99314 = r99310 + r99313;
        return r99314;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r99315 = x_re;
        double r99316 = y_im;
        double r99317 = x_im;
        double r99318 = y_re;
        double r99319 = r99317 * r99318;
        double r99320 = fma(r99315, r99316, r99319);
        return r99320;
}

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 2020046 +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)))