_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 2.5s

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 r92709 = x_re;
        double r92710 = y_im;
        double r92711 = r92709 * r92710;
        double r92712 = x_im;
        double r92713 = y_re;
        double r92714 = r92712 * r92713;
        double r92715 = r92711 + r92714;
        return r92715;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r92716 = x_re;
        double r92717 = y_im;
        double r92718 = x_im;
        double r92719 = y_re;
        double r92720 = r92718 * r92719;
        double r92721 = fma(r92716, r92717, r92720);
        return r92721;
}

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)))