Average Error: 0.0 → 0.0
Time: 1.8s
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 r2038192 = x_re;
        double r2038193 = y_im;
        double r2038194 = r2038192 * r2038193;
        double r2038195 = x_im;
        double r2038196 = y_re;
        double r2038197 = r2038195 * r2038196;
        double r2038198 = r2038194 + r2038197;
        return r2038198;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2038199 = x_im;
        double r2038200 = y_re;
        double r2038201 = r2038199 * r2038200;
        double r2038202 = x_re;
        double r2038203 = y_im;
        double r2038204 = r2038202 * r2038203;
        double r2038205 = r2038201 + r2038204;
        return r2038205;
}

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 2019107 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))