Average Error: 0.0 → 0.0
Time: 1.5s
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 r43584 = x_re;
        double r43585 = y_re;
        double r43586 = r43584 * r43585;
        double r43587 = x_im;
        double r43588 = y_im;
        double r43589 = r43587 * r43588;
        double r43590 = r43586 - r43589;
        return r43590;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r43591 = x_re;
        double r43592 = y_re;
        double r43593 = r43591 * r43592;
        double r43594 = x_im;
        double r43595 = y_im;
        double r43596 = r43594 * r43595;
        double r43597 = r43593 - r43596;
        return r43597;
}

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