Average Error: 0.0 → 0.0
Time: 5.4s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.im \cdot y.re + x.re \cdot y.im\]
x.re \cdot y.im + x.im \cdot y.re
↓
x.im \cdot y.re + x.re \cdot y.im
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1016244 = x_re;
        double r1016245 = y_im;
        double r1016246 = r1016244 * r1016245;
        double r1016247 = x_im;
        double r1016248 = y_re;
        double r1016249 = r1016247 * r1016248;
        double r1016250 = r1016246 + r1016249;
        return r1016250;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1016251 = x_im;
        double r1016252 = y_re;
        double r1016253 = r1016251 * r1016252;
        double r1016254 = x_re;
        double r1016255 = y_im;
        double r1016256 = r1016254 * r1016255;
        double r1016257 = r1016253 + r1016256;
        return r1016257;
}

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

    \[\leadsto x.im \cdot y.re + x.re \cdot y.im\]

Reproduce

herbie shell --seed 2019152 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))