Average Error: 0.0 → 0.0
Time: 8.8s
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 r1114689 = x_re;
        double r1114690 = y_re;
        double r1114691 = r1114689 * r1114690;
        double r1114692 = x_im;
        double r1114693 = y_im;
        double r1114694 = r1114692 * r1114693;
        double r1114695 = r1114691 - r1114694;
        return r1114695;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1114696 = x_re;
        double r1114697 = y_re;
        double r1114698 = x_im;
        double r1114699 = y_im;
        double r1114700 = r1114698 * r1114699;
        double r1114701 = -r1114700;
        double r1114702 = fma(r1114696, r1114697, r1114701);
        return r1114702;
}

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 2019142 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))