Average Error: 0.2 → 0.2
Time: 8.9s
Precision: 64
$\frac{x}{65535} \cdot 3.299999999999999822364316059974953532219$
$x \cdot \frac{3.299999999999999822364316059974953532219}{65535}$
\frac{x}{65535} \cdot 3.299999999999999822364316059974953532219
x \cdot \frac{3.299999999999999822364316059974953532219}{65535}
double f(double x) {
double r3483017 = x;
double r3483018 = 65535.0;
double r3483019 = r3483017 / r3483018;
double r3483020 = 3.3;
double r3483021 = r3483019 * r3483020;
return r3483021;
}


double f(double x) {
double r3483022 = x;
double r3483023 = 3.3;
double r3483024 = 65535.0;
double r3483025 = r3483023 / r3483024;
double r3483026 = r3483022 * r3483025;
return r3483026;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 0.2

$\frac{x}{65535} \cdot 3.299999999999999822364316059974953532219$
2. Using strategy rm
3. Applied div-inv0.2

$\leadsto \color{blue}{\left(x \cdot \frac{1}{65535}\right)} \cdot 3.299999999999999822364316059974953532219$
4. Applied associate-*l*0.2

$\leadsto \color{blue}{x \cdot \left(\frac{1}{65535} \cdot 3.299999999999999822364316059974953532219\right)}$
5. Simplified0.2

$\leadsto x \cdot \color{blue}{\frac{3.299999999999999822364316059974953532219}{65535}}$
6. Final simplification0.2

$\leadsto x \cdot \frac{3.299999999999999822364316059974953532219}{65535}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "x / 65535 * 3.3"
:precision binary64
(* (/ x 65535) 3.2999999999999998))