Average Error: 0.0 → 0.0
Time: 27.7s
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 r2408447 = x_re;
        double r2408448 = y_re;
        double r2408449 = r2408447 * r2408448;
        double r2408450 = x_im;
        double r2408451 = y_im;
        double r2408452 = r2408450 * r2408451;
        double r2408453 = r2408449 - r2408452;
        return r2408453;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2408454 = x_re;
        double r2408455 = y_re;
        double r2408456 = x_im;
        double r2408457 = y_im;
        double r2408458 = r2408456 * r2408457;
        double r2408459 = -r2408458;
        double r2408460 = fma(r2408454, r2408455, r2408459);
        return r2408460;
}

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)))