Average Error: 0.0 → 0.0
Time: 11.3s
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 r1523865 = x_re;
        double r1523866 = y_re;
        double r1523867 = r1523865 * r1523866;
        double r1523868 = x_im;
        double r1523869 = y_im;
        double r1523870 = r1523868 * r1523869;
        double r1523871 = r1523867 - r1523870;
        return r1523871;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1523872 = x_re;
        double r1523873 = y_re;
        double r1523874 = x_im;
        double r1523875 = y_im;
        double r1523876 = r1523874 * r1523875;
        double r1523877 = -r1523876;
        double r1523878 = fma(r1523872, r1523873, r1523877);
        return r1523878;
}

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 2019146 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))