Average Error: 0.0 → 0.0
Time: 701.0ms
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[\mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)\]
x.re \cdot y.im + x.im \cdot y.re
↓
\mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)
double f(double x_re, double x_im, double y_re, double y_im) {
        double r27370 = x_re;
        double r27371 = y_im;
        double r27372 = r27370 * r27371;
        double r27373 = x_im;
        double r27374 = y_re;
        double r27375 = r27373 * r27374;
        double r27376 = r27372 + r27375;
        return r27376;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r27377 = x_re;
        double r27378 = y_im;
        double r27379 = x_im;
        double r27380 = y_re;
        double r27381 = r27379 * r27380;
        double r27382 = fma(r27377, r27378, r27381);
        return r27382;
}

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. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)\]

Reproduce

herbie shell --seed 2019344 +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)))