_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 668.0ms

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 r49599 = x_re;
        double r49600 = y_im;
        double r49601 = r49599 * r49600;
        double r49602 = x_im;
        double r49603 = y_re;
        double r49604 = r49602 * r49603;
        double r49605 = r49601 + r49604;
        return r49605;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r49606 = x_re;
        double r49607 = y_im;
        double r49608 = x_im;
        double r49609 = y_re;
        double r49610 = r49608 * r49609;
        double r49611 = fma(r49606, r49607, r49610);
        return r49611;
}

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 2019350 +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)))