Average Error: 0.0 → 0.0
Time: 720.0ms
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 r49623 = x_re;
        double r49624 = y_re;
        double r49625 = r49623 * r49624;
        double r49626 = x_im;
        double r49627 = y_im;
        double r49628 = r49626 * r49627;
        double r49629 = r49625 - r49628;
        return r49629;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r49630 = x_re;
        double r49631 = y_re;
        double r49632 = r49630 * r49631;
        double r49633 = x_im;
        double r49634 = y_im;
        double r49635 = r49633 * r49634;
        double r49636 = r49632 - r49635;
        return r49636;
}

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 2020056 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))