Average Error: 0.0 → 0.0
Time: 6.7s
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 r116443 = x_re;
        double r116444 = y_re;
        double r116445 = r116443 * r116444;
        double r116446 = x_im;
        double r116447 = y_im;
        double r116448 = r116446 * r116447;
        double r116449 = r116445 - r116448;
        return r116449;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r116450 = x_re;
        double r116451 = y_re;
        double r116452 = r116450 * r116451;
        double r116453 = x_im;
        double r116454 = y_im;
        double r116455 = r116453 * r116454;
        double r116456 = r116452 - r116455;
        return r116456;
}

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 2020047 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))