Average Error: 0.0 → 0.0
Time: 6.6s
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 r94403 = x_re;
        double r94404 = y_im;
        double r94405 = r94403 * r94404;
        double r94406 = x_im;
        double r94407 = y_re;
        double r94408 = r94406 * r94407;
        double r94409 = r94405 + r94408;
        return r94409;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r94410 = x_re;
        double r94411 = y_im;
        double r94412 = r94410 * r94411;
        double r94413 = x_im;
        double r94414 = y_re;
        double r94415 = r94413 * r94414;
        double r94416 = r94412 + r94415;
        return r94416;
}

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 2020043 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))