Average Error: 0.0 → 0.0
Time: 809.0ms
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.re \cdot y.im + x.im \cdot y.re\]
x.re \cdot y.im + x.im \cdot y.re
↓
x.re \cdot y.im + x.im \cdot y.re
double f(double x_re, double x_im, double y_re, double y_im) {
        double r42349 = x_re;
        double r42350 = y_im;
        double r42351 = r42349 * r42350;
        double r42352 = x_im;
        double r42353 = y_re;
        double r42354 = r42352 * r42353;
        double r42355 = r42351 + r42354;
        return r42355;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r42356 = x_re;
        double r42357 = y_im;
        double r42358 = r42356 * r42357;
        double r42359 = x_im;
        double r42360 = y_re;
        double r42361 = r42359 * r42360;
        double r42362 = r42358 + r42361;
        return r42362;
}

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2020033 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))