Average Error: 0.0 → 0.0
Time: 2.0s
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 r37632 = x_re;
        double r37633 = y_re;
        double r37634 = r37632 * r37633;
        double r37635 = x_im;
        double r37636 = y_im;
        double r37637 = r37635 * r37636;
        double r37638 = r37634 - r37637;
        return r37638;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r37639 = x_re;
        double r37640 = y_re;
        double r37641 = r37639 * r37640;
        double r37642 = x_im;
        double r37643 = y_im;
        double r37644 = r37642 * r37643;
        double r37645 = r37641 - r37644;
        return r37645;
}

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 2019179 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  (- (* x.re y.re) (* x.im y.im)))