Average Error: 0.0 → 0.0
Time: 3.8s
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 r1885159 = x_re;
        double r1885160 = y_re;
        double r1885161 = r1885159 * r1885160;
        double r1885162 = x_im;
        double r1885163 = y_im;
        double r1885164 = r1885162 * r1885163;
        double r1885165 = r1885161 - r1885164;
        return r1885165;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1885166 = x_re;
        double r1885167 = y_re;
        double r1885168 = x_im;
        double r1885169 = y_im;
        double r1885170 = r1885168 * r1885169;
        double r1885171 = -r1885170;
        double r1885172 = fma(r1885166, r1885167, r1885171);
        return r1885172;
}

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 2019174 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))