Average Error: 0.0 → 0.0
Time: 5.2s
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 r1941992 = x_re;
        double r1941993 = y_re;
        double r1941994 = r1941992 * r1941993;
        double r1941995 = x_im;
        double r1941996 = y_im;
        double r1941997 = r1941995 * r1941996;
        double r1941998 = r1941994 - r1941997;
        return r1941998;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1941999 = x_re;
        double r1942000 = y_re;
        double r1942001 = x_im;
        double r1942002 = y_im;
        double r1942003 = r1942001 * r1942002;
        double r1942004 = -r1942003;
        double r1942005 = fma(r1941999, r1942000, r1942004);
        return r1942005;
}

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 2019158 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))