Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[x.re \cdot y.re - x.im \cdot y.im\]
↓
\[x.re \cdot y.re - x.im \cdot y.im\]
x.re \cdot y.re - x.im \cdot y.im
↓
x.re \cdot y.re - x.im \cdot y.im
double f(double x_re, double x_im, double y_re, double y_im) {
        double r44802 = x_re;
        double r44803 = y_re;
        double r44804 = r44802 * r44803;
        double r44805 = x_im;
        double r44806 = y_im;
        double r44807 = r44805 * r44806;
        double r44808 = r44804 - r44807;
        return r44808;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r44809 = x_re;
        double r44810 = y_re;
        double r44811 = r44809 * r44810;
        double r44812 = x_im;
        double r44813 = y_im;
        double r44814 = r44812 * r44813;
        double r44815 = r44811 - r44814;
        return r44815;
}

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

    \[x.re \cdot y.re - x.im \cdot y.im\]

  2. Final simplification0.0

    \[\leadsto x.re \cdot y.re - x.im \cdot y.im\]

Reproduce

herbie shell --seed 2020100 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))