Average Error: 0.0 → 0.0
Time: 26.4s
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 r2643544 = x_re;
        double r2643545 = y_im;
        double r2643546 = r2643544 * r2643545;
        double r2643547 = x_im;
        double r2643548 = y_re;
        double r2643549 = r2643547 * r2643548;
        double r2643550 = r2643546 + r2643549;
        return r2643550;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2643551 = x_im;
        double r2643552 = y_re;
        double r2643553 = r2643551 * r2643552;
        double r2643554 = x_re;
        double r2643555 = y_im;
        double r2643556 = r2643554 * r2643555;
        double r2643557 = r2643553 + r2643556;
        return r2643557;
}

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 2019124 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))