Average Error: 0.0 → 0.0
Time: 2.8s
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 r92070 = x_re;
        double r92071 = y_im;
        double r92072 = r92070 * r92071;
        double r92073 = x_im;
        double r92074 = y_re;
        double r92075 = r92073 * r92074;
        double r92076 = r92072 + r92075;
        return r92076;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r92077 = x_re;
        double r92078 = y_im;
        double r92079 = r92077 * r92078;
        double r92080 = x_im;
        double r92081 = y_re;
        double r92082 = r92080 * r92081;
        double r92083 = r92079 + r92082;
        return r92083;
}

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 2020062 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))