Average Error: 15.0 → 0.4
Time: 29.9s
Precision: 64
Internal Precision: 1408
\[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]
↓
\[\tan^{-1}_* \frac{1 + 0}{1 + \left(N + 1\right) \cdot N}\]

Error

Bits error versus N

Derivation

  1. Initial program 15.0

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

  3. Applied diff-atan13.8

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

  4. Applied simplify0.4

    \[\leadsto \tan^{-1}_* \frac{\color{blue}{1 + 0}}{1 + \left(N + 1\right) \cdot N}\]

Runtime

Time bar (total: 29.9s)Debug log

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(FPCore (N)
  :name "NMSE example 3.5"
  (- (atan (+ N 1)) (atan N)))