Average Error: 0.0 → 0.0
Time: 9.5s
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 r2217655 = x_re;
        double r2217656 = y_re;
        double r2217657 = r2217655 * r2217656;
        double r2217658 = x_im;
        double r2217659 = y_im;
        double r2217660 = r2217658 * r2217659;
        double r2217661 = r2217657 - r2217660;
        return r2217661;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2217662 = x_re;
        double r2217663 = y_re;
        double r2217664 = x_im;
        double r2217665 = y_im;
        double r2217666 = r2217664 * r2217665;
        double r2217667 = -r2217666;
        double r2217668 = fma(r2217662, r2217663, r2217667);
        return r2217668;
}

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)))