Average Error: 0.0 → 0.0
Time: 6.5s
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 r2085871 = x_re;
        double r2085872 = y_im;
        double r2085873 = r2085871 * r2085872;
        double r2085874 = x_im;
        double r2085875 = y_re;
        double r2085876 = r2085874 * r2085875;
        double r2085877 = r2085873 + r2085876;
        return r2085877;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2085878 = x_im;
        double r2085879 = y_re;
        double r2085880 = r2085878 * r2085879;
        double r2085881 = x_re;
        double r2085882 = y_im;
        double r2085883 = r2085881 * r2085882;
        double r2085884 = r2085880 + r2085883;
        return r2085884;
}

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 2019168 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))