Average Error: 0.0 → 0.0
Time: 5.5s
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 r1004362 = x_re;
        double r1004363 = y_re;
        double r1004364 = r1004362 * r1004363;
        double r1004365 = x_im;
        double r1004366 = y_im;
        double r1004367 = r1004365 * r1004366;
        double r1004368 = r1004364 - r1004367;
        return r1004368;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1004369 = x_re;
        double r1004370 = y_re;
        double r1004371 = x_im;
        double r1004372 = y_im;
        double r1004373 = r1004371 * r1004372;
        double r1004374 = -r1004373;
        double r1004375 = fma(r1004369, r1004370, r1004374);
        return r1004375;
}

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 2019152 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))