Average Error: 0.0 → 0.0
Time: 1.1s
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 r52173 = x_re;
        double r52174 = y_im;
        double r52175 = r52173 * r52174;
        double r52176 = x_im;
        double r52177 = y_re;
        double r52178 = r52176 * r52177;
        double r52179 = r52175 + r52178;
        return r52179;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r52180 = x_re;
        double r52181 = y_im;
        double r52182 = x_im;
        double r52183 = y_re;
        double r52184 = r52182 * r52183;
        double r52185 = fma(r52180, r52181, r52184);
        return r52185;
}

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 2020001 +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)))