Average Error: 0.0 → 0.0
Time: 2.3s
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 r84459 = x_re;
        double r84460 = y_im;
        double r84461 = r84459 * r84460;
        double r84462 = x_im;
        double r84463 = y_re;
        double r84464 = r84462 * r84463;
        double r84465 = r84461 + r84464;
        return r84465;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r84466 = x_re;
        double r84467 = y_im;
        double r84468 = r84466 * r84467;
        double r84469 = x_im;
        double r84470 = y_re;
        double r84471 = r84469 * r84470;
        double r84472 = r84468 + r84471;
        return r84472;
}

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 2020100 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))