Average Error: 0.0 → 0.0
Time: 4.0s
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 r74916 = x_re;
        double r74917 = y_re;
        double r74918 = r74916 * r74917;
        double r74919 = x_im;
        double r74920 = y_im;
        double r74921 = r74919 * r74920;
        double r74922 = r74918 - r74921;
        return r74922;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r74923 = x_re;
        double r74924 = y_re;
        double r74925 = r74923 * r74924;
        double r74926 = x_im;
        double r74927 = y_im;
        double r74928 = r74926 * r74927;
        double r74929 = r74925 - r74928;
        return r74929;
}

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 2020034 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))