Average Error: 0.0 → 0.0
Time: 966.0ms
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 r47750 = x_re;
        double r47751 = y_im;
        double r47752 = r47750 * r47751;
        double r47753 = x_im;
        double r47754 = y_re;
        double r47755 = r47753 * r47754;
        double r47756 = r47752 + r47755;
        return r47756;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r47757 = x_re;
        double r47758 = y_im;
        double r47759 = x_im;
        double r47760 = y_re;
        double r47761 = r47759 * r47760;
        double r47762 = fma(r47757, r47758, r47761);
        return r47762;
}

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 2020057 +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)))