_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 r93214 = x_re;
        double r93215 = y_im;
        double r93216 = r93214 * r93215;
        double r93217 = x_im;
        double r93218 = y_re;
        double r93219 = r93217 * r93218;
        double r93220 = r93216 + r93219;
        return r93220;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r93221 = x_re;
        double r93222 = y_im;
        double r93223 = x_im;
        double r93224 = y_re;
        double r93225 = r93223 * r93224;
        double r93226 = fma(r93221, r93222, r93225);
        return r93226;
}

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 2020047 +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)))