Average Error: 15.2 → 0.4
Time: 10.6s
Precision: 64
\[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]
\[\tan^{-1}_* \frac{1}{\left(1 + N\right) \cdot N + 1}\]
\tan^{-1} \left(N + 1\right) - \tan^{-1} N
\tan^{-1}_* \frac{1}{\left(1 + N\right) \cdot N + 1}
double f(double N) {
        double r822086 = N;
        double r822087 = 1.0;
        double r822088 = r822086 + r822087;
        double r822089 = atan(r822088);
        double r822090 = atan(r822086);
        double r822091 = r822089 - r822090;
        return r822091;
}

double f(double N) {
        double r822092 = 1.0;
        double r822093 = N;
        double r822094 = r822092 + r822093;
        double r822095 = r822094 * r822093;
        double r822096 = r822095 + r822092;
        double r822097 = atan2(r822092, r822096);
        return r822097;
}

Error

Bits error versus N

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.2

    \[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]
  2. Using strategy rm
  3. Applied diff-atan14.0

    \[\leadsto \color{blue}{\tan^{-1}_* \frac{\left(N + 1\right) - N}{1 + \left(N + 1\right) \cdot N}}\]
  4. Simplified0.4

    \[\leadsto \tan^{-1}_* \frac{\color{blue}{1}}{1 + \left(N + 1\right) \cdot N}\]
  5. Final simplification0.4

    \[\leadsto \tan^{-1}_* \frac{1}{\left(1 + N\right) \cdot N + 1}\]

Reproduce

herbie shell --seed 1 
(FPCore (N)
  :name "NMSE example 3.5"
  (- (atan (+ N 1)) (atan N)))