Average Error: 0.0 → 0.0
Time: 2.0s
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.im \cdot y.re + x.re \cdot y.im\]
x.re \cdot y.im + x.im \cdot y.re
↓
x.im \cdot y.re + x.re \cdot y.im
double f(double x_re, double x_im, double y_re, double y_im) {
        double r34575 = x_re;
        double r34576 = y_im;
        double r34577 = r34575 * r34576;
        double r34578 = x_im;
        double r34579 = y_re;
        double r34580 = r34578 * r34579;
        double r34581 = r34577 + r34580;
        return r34581;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r34582 = x_im;
        double r34583 = y_re;
        double r34584 = r34582 * r34583;
        double r34585 = x_re;
        double r34586 = y_im;
        double r34587 = r34585 * r34586;
        double r34588 = r34584 + r34587;
        return r34588;
}

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

    \[x.re \cdot y.im + x.im \cdot y.re\]

  2. Final simplification0.0

    \[\leadsto x.im \cdot y.re + x.re \cdot y.im\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  (+ (* x.re y.im) (* x.im y.re)))