Average Error: 0.0 → 0.0
Time: 1.0s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[\mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)\]
x.re \cdot y.im + x.im \cdot y.re
↓
\mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)
double f(double x_re, double x_im, double y_re, double y_im) {
        double r57951 = x_re;
        double r57952 = y_im;
        double r57953 = r57951 * r57952;
        double r57954 = x_im;
        double r57955 = y_re;
        double r57956 = r57954 * r57955;
        double r57957 = r57953 + r57956;
        return r57957;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r57958 = x_re;
        double r57959 = y_im;
        double r57960 = x_im;
        double r57961 = y_re;
        double r57962 = r57960 * r57961;
        double r57963 = fma(r57958, r57959, r57962);
        return r57963;
}

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

    \[x.re \cdot y.im + x.im \cdot y.re\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x.re, y.im, x.im \cdot y.re\right)\]

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))