Average Error: 0.0 → 0.0
Time: 3.3s
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 r41419 = x_re;
        double r41420 = y_im;
        double r41421 = r41419 * r41420;
        double r41422 = x_im;
        double r41423 = y_re;
        double r41424 = r41422 * r41423;
        double r41425 = r41421 + r41424;
        return r41425;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r41426 = x_re;
        double r41427 = y_im;
        double r41428 = r41426 * r41427;
        double r41429 = x_im;
        double r41430 = y_re;
        double r41431 = r41429 * r41430;
        double r41432 = r41428 + r41431;
        return r41432;
}

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 2019198 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))