Average Error: 0.0 → 0.0
Time: 10.2s
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 r2279451 = x_re;
        double r2279452 = y_re;
        double r2279453 = r2279451 * r2279452;
        double r2279454 = x_im;
        double r2279455 = y_im;
        double r2279456 = r2279454 * r2279455;
        double r2279457 = r2279453 - r2279456;
        return r2279457;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2279458 = x_re;
        double r2279459 = y_re;
        double r2279460 = x_im;
        double r2279461 = y_im;
        double r2279462 = r2279460 * r2279461;
        double r2279463 = -r2279462;
        double r2279464 = fma(r2279458, r2279459, r2279463);
        return r2279464;
}

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 2019164 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))