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

Average Error: 29.1 → 29.1

Time: 1.7s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Derivation

1. Initial program 29.1

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

2. Final simplification 29.1

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

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)))))