Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[(x.re \cdot y.im + \left(x.im \cdot y.re\right))_*\]
x.re \cdot y.im + x.im \cdot y.re
↓
(x.re \cdot y.im + \left(x.im \cdot y.re\right))_*
double f(double x_re, double x_im, double y_re, double y_im) {
        double r4547228 = x_re;
        double r4547229 = y_im;
        double r4547230 = r4547228 * r4547229;
        double r4547231 = x_im;
        double r4547232 = y_re;
        double r4547233 = r4547231 * r4547232;
        double r4547234 = r4547230 + r4547233;
        return r4547234;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r4547235 = x_re;
        double r4547236 = y_im;
        double r4547237 = x_im;
        double r4547238 = y_re;
        double r4547239 = r4547237 * r4547238;
        double r4547240 = fma(r4547235, r4547236, r4547239);
        return r4547240;
}

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

    \[\leadsto \color{blue}{(x.re \cdot y.im + \left(x.im \cdot y.re\right))_*}\]

  3. Final simplification0.0

    \[\leadsto (x.re \cdot y.im + \left(x.im \cdot y.re\right))_*\]

Reproduce

herbie shell --seed 2019107 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))