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;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

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))