Average Error: 0.0 → 0.0
Time: 4.4s
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 r29797 = x_re;
        double r29798 = y_re;
        double r29799 = r29797 * r29798;
        double r29800 = x_im;
        double r29801 = y_im;
        double r29802 = r29800 * r29801;
        double r29803 = r29799 - r29802;
        return r29803;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r29804 = x_re;
        double r29805 = y_re;
        double r29806 = r29804 * r29805;
        double r29807 = x_im;
        double r29808 = y_im;
        double r29809 = r29807 * r29808;
        double r29810 = r29806 - r29809;
        return r29810;
}

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 2019350 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))