Average Error: 0.0 → 0.0
Time: 30.2s
Precision: 64
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[\mathsf{fma}\left(x.re, y.re, \left(-x.im \cdot y.im\right)\right)\]
x.re \cdot y.re - x.im \cdot y.im
↓
\mathsf{fma}\left(x.re, y.re, \left(-x.im \cdot y.im\right)\right)
double f(double x_re, double x_im, double y_re, double y_im) {
        double r3208361 = x_re;
        double r3208362 = y_re;
        double r3208363 = r3208361 * r3208362;
        double r3208364 = x_im;
        double r3208365 = y_im;
        double r3208366 = r3208364 * r3208365;
        double r3208367 = r3208363 - r3208366;
        return r3208367;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r3208368 = x_re;
        double r3208369 = y_re;
        double r3208370 = x_im;
        double r3208371 = y_im;
        double r3208372 = r3208370 * r3208371;
        double r3208373 = -r3208372;
        double r3208374 = fma(r3208368, r3208369, r3208373);
        return r3208374;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(x.re, y.re, \left(-x.im \cdot y.im\right)\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x.re, y.re, \left(-x.im \cdot y.im\right)\right)\]

Reproduce

herbie shell --seed 2019125 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))