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 r1593200 = x_re;
        double r1593201 = y_im;
        double r1593202 = r1593200 * r1593201;
        double r1593203 = x_im;
        double r1593204 = y_re;
        double r1593205 = r1593203 * r1593204;
        double r1593206 = r1593202 + r1593205;
        return r1593206;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1593207 = x_im;
        double r1593208 = y_re;
        double r1593209 = r1593207 * r1593208;
        double r1593210 = x_re;
        double r1593211 = y_im;
        double r1593212 = r1593210 * r1593211;
        double r1593213 = r1593209 + r1593212;
        return r1593213;
}

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 2019165 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))