Average Error: 0.0 → 0.0
Time: 13.4s
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 r2310722 = x_re;
        double r2310723 = y_re;
        double r2310724 = r2310722 * r2310723;
        double r2310725 = x_im;
        double r2310726 = y_im;
        double r2310727 = r2310725 * r2310726;
        double r2310728 = r2310724 - r2310727;
        return r2310728;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2310729 = x_re;
        double r2310730 = y_re;
        double r2310731 = x_im;
        double r2310732 = y_im;
        double r2310733 = r2310731 * r2310732;
        double r2310734 = -r2310733;
        double r2310735 = fma(r2310729, r2310730, r2310734);
        return r2310735;
}

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 2019169 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))