Average Error: 0.0 → 0.0
Time: 2.7s
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 r48432 = x_re;
        double r48433 = y_re;
        double r48434 = r48432 * r48433;
        double r48435 = x_im;
        double r48436 = y_im;
        double r48437 = r48435 * r48436;
        double r48438 = r48434 - r48437;
        return r48438;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r48439 = x_re;
        double r48440 = y_re;
        double r48441 = r48439 * r48440;
        double r48442 = x_im;
        double r48443 = y_im;
        double r48444 = r48442 * r48443;
        double r48445 = r48441 - r48444;
        return r48445;
}

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 2020003 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, real part"
  :precision binary64
  (- (* x.re y.re) (* x.im y.im)))