Average Error: 0.0 → 0.0
Time: 10.8s
Precision: 64
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[\mathsf{fma}\left(x.re, y.re, -x.im \cdot y.im\right)\]
x.re \cdot y.re - x.im \cdot y.im
↓
\mathsf{fma}\left(x.re, y.re, -x.im \cdot y.im\right)
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2288904 = x_re;
        double r2288905 = y_re;
        double r2288906 = r2288904 * r2288905;
        double r2288907 = x_im;
        double r2288908 = y_im;
        double r2288909 = r2288907 * r2288908;
        double r2288910 = r2288906 - r2288909;
        return r2288910;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2288911 = x_re;
        double r2288912 = y_re;
        double r2288913 = x_im;
        double r2288914 = y_im;
        double r2288915 = r2288913 * r2288914;
        double r2288916 = -r2288915;
        double r2288917 = fma(r2288911, r2288912, r2288916);
        return r2288917;
}

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

    \[x.re \cdot y.re - x.im \cdot y.im\]
  2. Using strategy rm

  3. Applied fma-neg0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))