_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 1.7s

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 r107519 = x_re;
        double r107520 = y_im;
        double r107521 = r107519 * r107520;
        double r107522 = x_im;
        double r107523 = y_re;
        double r107524 = r107522 * r107523;
        double r107525 = r107521 + r107524;
        return r107525;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r107526 = x_re;
        double r107527 = y_im;
        double r107528 = x_im;
        double r107529 = y_re;
        double r107530 = r107528 * r107529;
        double r107531 = fma(r107526, r107527, r107530);
        return r107531;
}

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)))