Average Error: 0.0 → 0.0
Time: 7.3s
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 r1628688 = x_re;
        double r1628689 = y_re;
        double r1628690 = r1628688 * r1628689;
        double r1628691 = x_im;
        double r1628692 = y_im;
        double r1628693 = r1628691 * r1628692;
        double r1628694 = r1628690 - r1628693;
        return r1628694;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1628695 = x_re;
        double r1628696 = y_re;
        double r1628697 = x_im;
        double r1628698 = y_im;
        double r1628699 = r1628697 * r1628698;
        double r1628700 = -r1628699;
        double r1628701 = fma(r1628695, r1628696, r1628700);
        return r1628701;
}

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)))