(tan (atan (+ x (pow 10 (- 50)))))

Average Error: 29.0 → 29.0

Time: 2.7s

Precision: binary64

Math

\[\tan \left(\tan^{-1} \left(x + {10}^{\left(-50\right)}\right)\right)\]

↓

\[\tan \left(\tan^{-1} \left(x + {10}^{\left(-50\right)}\right)\right)\]

Error

Bits error versus x

Derivation

1. Initial program 29.0

   \[\tan \left(\tan^{-1} \left(x + {10}^{\left(-50\right)}\right)\right)\]

2. Final simplification 29.0

   \[\leadsto \tan \left(\tan^{-1} \left(x + {10}^{\left(-50\right)}\right)\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(tan (atan (+ x (pow 10 (- 50)))))"
  :precision binary64
  (tan (atan (+ x (pow 10.0 (neg 50.0))))))