Average Error: 0.0 → 0.0
Time: 14.1s
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 r38066 = x_re;
        double r38067 = y_im;
        double r38068 = r38066 * r38067;
        double r38069 = x_im;
        double r38070 = y_re;
        double r38071 = r38069 * r38070;
        double r38072 = r38068 + r38071;
        return r38072;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r38073 = x_re;
        double r38074 = y_im;
        double r38075 = r38073 * r38074;
        double r38076 = x_im;
        double r38077 = y_re;
        double r38078 = r38076 * r38077;
        double r38079 = r38075 + r38078;
        return r38079;
}

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 2019306 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))