Average Error: 0.0 → 0.0
Time: 3.4s
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 r2096462 = x_re;
        double r2096463 = y_re;
        double r2096464 = r2096462 * r2096463;
        double r2096465 = x_im;
        double r2096466 = y_im;
        double r2096467 = r2096465 * r2096466;
        double r2096468 = r2096464 - r2096467;
        return r2096468;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2096469 = x_re;
        double r2096470 = y_re;
        double r2096471 = x_im;
        double r2096472 = y_im;
        double r2096473 = r2096471 * r2096472;
        double r2096474 = -r2096473;
        double r2096475 = fma(r2096469, r2096470, r2096474);
        return r2096475;
}

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 2019168 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))