Average Error: 0 → 0
Time: 7.7s
Precision: 64
$\left(2 \cdot {2}^{\left(-41\right)}\right) \cdot \left(0.5 + \frac{1023}{2048}\right)$
$\frac{1}{1099511627776} \cdot 0.5 + \frac{1023}{2251799813685248}$
\left(2 \cdot {2}^{\left(-41\right)}\right) \cdot \left(0.5 + \frac{1023}{2048}\right)
\frac{1}{1099511627776} \cdot 0.5 + \frac{1023}{2251799813685248}
double f() {
double r40855870 = 2.0;
double r40855871 = 41.0;
double r40855872 = -r40855871;
double r40855873 = pow(r40855870, r40855872);
double r40855874 = r40855870 * r40855873;
double r40855875 = 0.5;
double r40855876 = 1023.0;
double r40855877 = 2048.0;
double r40855878 = r40855876 / r40855877;
double r40855879 = r40855875 + r40855878;
double r40855880 = r40855874 * r40855879;
return r40855880;
}


double f() {
double r40855881 = 9.094947017729282e-13;
double r40855882 = 0.5;
double r40855883 = r40855881 * r40855882;
double r40855884 = 4.5430326167661406e-13;
double r40855885 = r40855883 + r40855884;
return r40855885;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0

$\left(2 \cdot {2}^{\left(-41\right)}\right) \cdot \left(0.5 + \frac{1023}{2048}\right)$
2. Simplified0

$\leadsto \color{blue}{\frac{1023}{2251799813685248} + 0.5 \cdot \frac{1}{1099511627776}}$
3. Final simplification0

$\leadsto \frac{1}{1099511627776} \cdot 0.5 + \frac{1023}{2251799813685248}$

# Reproduce

herbie shell --seed 1
(FPCore ()
:name "2*pow(2,-41)*(0.5+1023/2048)"
(* (* 2 (pow 2 (- 41))) (+ 0.5 (/ 1023 2048))))