Average Error: 0.0 → 0.0
Time: 1.4s
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 r2922943 = x_re;
        double r2922944 = y_im;
        double r2922945 = r2922943 * r2922944;
        double r2922946 = x_im;
        double r2922947 = y_re;
        double r2922948 = r2922946 * r2922947;
        double r2922949 = r2922945 + r2922948;
        return r2922949;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r2922950 = x_im;
        double r2922951 = y_re;
        double r2922952 = r2922950 * r2922951;
        double r2922953 = x_re;
        double r2922954 = y_im;
        double r2922955 = r2922953 * r2922954;
        double r2922956 = r2922952 + r2922955;
        return r2922956;
}

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 2019158 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))