Average Error: 15.3 → 0.3
Time: 9.4s
Precision: 64
Internal Precision: 1344
\[\tan^{-1} \left(n + 1\right) - \tan^{-1} n\]
\[\tan^{-1}_* \frac{1}{1 + \left(n + 1\right) \cdot n}\]

Error

Bits error versus n

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.3

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

    \[\leadsto \color{blue}{\tan^{-1}_* \frac{\left(n + 1\right) - n}{1 + \left(n + 1\right) \cdot n}}\]
  4. Applied simplify0.3

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

Runtime

Time bar (total: 9.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (n)
  :name "atan(n+1)-atan(n)"
  (- (atan (+ n 1)) (atan n)))