Average Error: 0.0 → 0.0
Time: 2.7s
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 r1037028 = x_re;
        double r1037029 = y_im;
        double r1037030 = r1037028 * r1037029;
        double r1037031 = x_im;
        double r1037032 = y_re;
        double r1037033 = r1037031 * r1037032;
        double r1037034 = r1037030 + r1037033;
        return r1037034;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1037035 = x_im;
        double r1037036 = y_re;
        double r1037037 = r1037035 * r1037036;
        double r1037038 = x_re;
        double r1037039 = y_im;
        double r1037040 = r1037038 * r1037039;
        double r1037041 = r1037037 + r1037040;
        return r1037041;
}

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 2019141 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))