Average Error: 0.0 → 0.0
Time: 2.2s
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 r56629 = x_re;
        double r56630 = y_im;
        double r56631 = r56629 * r56630;
        double r56632 = x_im;
        double r56633 = y_re;
        double r56634 = r56632 * r56633;
        double r56635 = r56631 + r56634;
        return r56635;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r56636 = x_re;
        double r56637 = y_im;
        double r56638 = r56636 * r56637;
        double r56639 = x_im;
        double r56640 = y_re;
        double r56641 = r56639 * r56640;
        double r56642 = r56638 + r56641;
        return r56642;
}

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 2020046 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))