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 r65632 = x_re;
        double r65633 = y_re;
        double r65634 = r65632 * r65633;
        double r65635 = x_im;
        double r65636 = y_im;
        double r65637 = r65635 * r65636;
        double r65638 = r65634 - r65637;
        return r65638;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r65639 = x_re;
        double r65640 = y_re;
        double r65641 = r65639 * r65640;
        double r65642 = x_im;
        double r65643 = y_im;
        double r65644 = r65642 * r65643;
        double r65645 = r65641 - r65644;
        return r65645;
}

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 2020045 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))