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 r1411003 = x_re;
        double r1411004 = y_im;
        double r1411005 = r1411003 * r1411004;
        double r1411006 = x_im;
        double r1411007 = y_re;
        double r1411008 = r1411006 * r1411007;
        double r1411009 = r1411005 + r1411008;
        return r1411009;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r1411010 = x_im;
        double r1411011 = y_re;
        double r1411012 = r1411010 * r1411011;
        double r1411013 = x_re;
        double r1411014 = y_im;
        double r1411015 = r1411013 * r1411014;
        double r1411016 = r1411012 + r1411015;
        return r1411016;
}

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 2019179 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))