Average Error: 0.0 → 0.0
Time: 11.2s
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 r958313 = x_re;
        double r958314 = y_re;
        double r958315 = r958313 * r958314;
        double r958316 = x_im;
        double r958317 = y_im;
        double r958318 = r958316 * r958317;
        double r958319 = r958315 - r958318;
        return r958319;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r958320 = x_re;
        double r958321 = y_re;
        double r958322 = x_im;
        double r958323 = y_im;
        double r958324 = r958322 * r958323;
        double r958325 = -r958324;
        double r958326 = fma(r958320, r958321, r958325);
        return r958326;
}

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 2019151 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))