Average Error: 0.0 → 0.0
Time: 6.6s
Precision: 64
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[\mathsf{fma}\left(-y.im, x.im, x.re \cdot y.re\right)\]
x.re \cdot y.re - x.im \cdot y.im
↓
\mathsf{fma}\left(-y.im, x.im, x.re \cdot y.re\right)
double f(double x_re, double x_im, double y_re, double y_im) {
        double r38632 = x_re;
        double r38633 = y_re;
        double r38634 = r38632 * r38633;
        double r38635 = x_im;
        double r38636 = y_im;
        double r38637 = r38635 * r38636;
        double r38638 = r38634 - r38637;
        return r38638;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r38639 = y_im;
        double r38640 = -r38639;
        double r38641 = x_im;
        double r38642 = x_re;
        double r38643 = y_re;
        double r38644 = r38642 * r38643;
        double r38645 = fma(r38640, r38641, r38644);
        return r38645;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))