Average Error: 0.0 → 0.0
Time: 680.0ms
Precision: 64
\[x.re \cdot y.im + x.im \cdot y.re\]
↓
\[x.re \cdot y.im + x.im \cdot y.re\]
x.re \cdot y.im + x.im \cdot y.re
↓
x.re \cdot y.im + x.im \cdot y.re
double f(double x_re, double x_im, double y_re, double y_im) {
        double r44344 = x_re;
        double r44345 = y_im;
        double r44346 = r44344 * r44345;
        double r44347 = x_im;
        double r44348 = y_re;
        double r44349 = r44347 * r44348;
        double r44350 = r44346 + r44349;
        return r44350;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r44351 = x_re;
        double r44352 = y_im;
        double r44353 = r44351 * r44352;
        double r44354 = x_im;
        double r44355 = y_re;
        double r44356 = r44354 * r44355;
        double r44357 = r44353 + r44356;
        return r44357;
}

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

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))