Average Error: 0.0 → 0.0
Time: 19.4s
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 r2159459 = x_re;
        double r2159460 = y_re;
        double r2159461 = r2159459 * r2159460;
        double r2159462 = x_im;
        double r2159463 = y_im;
        double r2159464 = r2159462 * r2159463;
        double r2159465 = r2159461 - r2159464;
        return r2159465;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2159466 = x_re;
        double r2159467 = y_re;
        double r2159468 = x_im;
        double r2159469 = y_im;
        double r2159470 = r2159468 * r2159469;
        double r2159471 = -r2159470;
        double r2159472 = fma(r2159466, r2159467, r2159471);
        return r2159472;
}

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 2019200 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))