Average Error: 0.0 → 0.0
Time: 2.7s
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 r58430 = x_re;
        double r58431 = y_re;
        double r58432 = r58430 * r58431;
        double r58433 = x_im;
        double r58434 = y_im;
        double r58435 = r58433 * r58434;
        double r58436 = r58432 - r58435;
        return r58436;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r58437 = x_re;
        double r58438 = y_re;
        double r58439 = x_im;
        double r58440 = y_im;
        double r58441 = r58439 * r58440;
        double r58442 = -r58441;
        double r58443 = fma(r58437, r58438, r58442);
        return r58443;
}

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 2020046 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))