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 r61267 = x_re;
        double r61268 = y_re;
        double r61269 = r61267 * r61268;
        double r61270 = x_im;
        double r61271 = y_im;
        double r61272 = r61270 * r61271;
        double r61273 = r61269 - r61272;
        return r61273;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r61274 = x_re;
        double r61275 = y_re;
        double r61276 = r61274 * r61275;
        double r61277 = x_im;
        double r61278 = y_im;
        double r61279 = r61277 * r61278;
        double r61280 = r61276 - r61279;
        return r61280;
}

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 2020001 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))