Average Error: 0.0 → 0.0
Time: 1.6s
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 r27239 = x_re;
        double r27240 = y_re;
        double r27241 = r27239 * r27240;
        double r27242 = x_im;
        double r27243 = y_im;
        double r27244 = r27242 * r27243;
        double r27245 = r27241 - r27244;
        return r27245;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r27246 = x_re;
        double r27247 = y_re;
        double r27248 = r27246 * r27247;
        double r27249 = x_im;
        double r27250 = y_im;
        double r27251 = r27249 * r27250;
        double r27252 = r27248 - r27251;
        return r27252;
}

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 2020018 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))