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 r1401152 = x_re;
        double r1401153 = y_im;
        double r1401154 = r1401152 * r1401153;
        double r1401155 = x_im;
        double r1401156 = y_re;
        double r1401157 = r1401155 * r1401156;
        double r1401158 = r1401154 + r1401157;
        return r1401158;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1401159 = x_im;
        double r1401160 = y_re;
        double r1401161 = r1401159 * r1401160;
        double r1401162 = x_re;
        double r1401163 = y_im;
        double r1401164 = r1401162 * r1401163;
        double r1401165 = r1401161 + r1401164;
        return r1401165;
}

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 2019135 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))