Average Error: 0.0 → 0.0
Time: 1.1s
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 r105053 = x_re;
        double r105054 = y_im;
        double r105055 = r105053 * r105054;
        double r105056 = x_im;
        double r105057 = y_re;
        double r105058 = r105056 * r105057;
        double r105059 = r105055 + r105058;
        return r105059;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r105060 = x_re;
        double r105061 = y_im;
        double r105062 = r105060 * r105061;
        double r105063 = x_im;
        double r105064 = y_re;
        double r105065 = r105063 * r105064;
        double r105066 = r105062 + r105065;
        return r105066;
}

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 2019323 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))