Average Error: 0.0 → 0.0
Time: 19.5s
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 r2683476 = x_re;
        double r2683477 = y_re;
        double r2683478 = r2683476 * r2683477;
        double r2683479 = x_im;
        double r2683480 = y_im;
        double r2683481 = r2683479 * r2683480;
        double r2683482 = r2683478 - r2683481;
        return r2683482;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2683483 = x_re;
        double r2683484 = y_re;
        double r2683485 = x_im;
        double r2683486 = y_im;
        double r2683487 = r2683485 * r2683486;
        double r2683488 = -r2683487;
        double r2683489 = fma(r2683483, r2683484, r2683488);
        return r2683489;
}

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 2019138 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))