_multiplyComplex, imaginary part

Average Error: 0.0 → 0.0

Time: 5.4s

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 r88497 = x_re;
        double r88498 = y_im;
        double r88499 = r88497 * r88498;
        double r88500 = x_im;
        double r88501 = y_re;
        double r88502 = r88500 * r88501;
        double r88503 = r88499 + r88502;
        return r88503;
}

↓

double f(double x_re, double x_im, double y_re, double y_im) {
        double r88504 = x_re;
        double r88505 = y_im;
        double r88506 = x_im;
        double r88507 = y_re;
        double r88508 = r88506 * r88507;
        double r88509 = fma(r88504, r88505, r88508);
        return r88509;
}

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 2019351 +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)))