Average Error: 0.0 → 0.0
Time: 757.0ms
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 r55305 = x_re;
        double r55306 = y_im;
        double r55307 = r55305 * r55306;
        double r55308 = x_im;
        double r55309 = y_re;
        double r55310 = r55308 * r55309;
        double r55311 = r55307 + r55310;
        return r55311;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r55312 = x_re;
        double r55313 = y_im;
        double r55314 = r55312 * r55313;
        double r55315 = x_im;
        double r55316 = y_re;
        double r55317 = r55315 * r55316;
        double r55318 = r55314 + r55317;
        return r55318;
}

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 2020065 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))