Average Error: 0.0 → 0.0
Time: 671.0ms
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 r43926 = x_re;
        double r43927 = y_im;
        double r43928 = r43926 * r43927;
        double r43929 = x_im;
        double r43930 = y_re;
        double r43931 = r43929 * r43930;
        double r43932 = r43928 + r43931;
        return r43932;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r43933 = x_re;
        double r43934 = y_im;
        double r43935 = r43933 * r43934;
        double r43936 = x_im;
        double r43937 = y_re;
        double r43938 = r43936 * r43937;
        double r43939 = r43935 + r43938;
        return r43939;
}

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 2019353 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))