Average Error: 0.0 → 0.0
Time: 2.1s
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 r40699 = x_re;
        double r40700 = y_im;
        double r40701 = r40699 * r40700;
        double r40702 = x_im;
        double r40703 = y_re;
        double r40704 = r40702 * r40703;
        double r40705 = r40701 + r40704;
        return r40705;
}
↓
double f(double x_re, double x_im, double y_re, double y_im) {
        double r40706 = x_re;
        double r40707 = y_im;
        double r40708 = r40706 * r40707;
        double r40709 = x_im;
        double r40710 = y_re;
        double r40711 = r40709 * r40710;
        double r40712 = r40708 + r40711;
        return r40712;
}

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 2020056 
(FPCore (x.re x.im y.re y.im)
  :name "_multiplyComplex, imaginary part"
  :precision binary64
  (+ (* x.re y.im) (* x.im y.re)))