Average Error: 0.0 → 0.0
Time: 3.6s
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 r1018699 = x_re;
        double r1018700 = y_re;
        double r1018701 = r1018699 * r1018700;
        double r1018702 = x_im;
        double r1018703 = y_im;
        double r1018704 = r1018702 * r1018703;
        double r1018705 = r1018701 - r1018704;
        return r1018705;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1018706 = x_re;
        double r1018707 = y_re;
        double r1018708 = x_im;
        double r1018709 = y_im;
        double r1018710 = r1018708 * r1018709;
        double r1018711 = -r1018710;
        double r1018712 = fma(r1018706, r1018707, r1018711);
        return r1018712;
}

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 2019152 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))