(/ (+ (- 1) (sqrt (+ 1 x))) (+ 1 (sqrt (+ 1 x))))

Average Error: 39.2 → 39.2

Time: 1.6s

Precision: binary64

Math

\[\frac{\left(-1\right) + \sqrt{1 + x}}{1 + \sqrt{1 + x}}\]

↓

\[\frac{\left(-1\right) + \sqrt{1 + x}}{1 + \sqrt{1 + x}}\]

Error

Bits error versus x

Derivation

1. Initial program 39.2

   \[\frac{\left(-1\right) + \sqrt{1 + x}}{1 + \sqrt{1 + x}}\]

2. Final simplification 39.2

   \[\leadsto \frac{\left(-1\right) + \sqrt{1 + x}}{1 + \sqrt{1 + x}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (+ (- 1) (sqrt (+ 1 x))) (+ 1 (sqrt (+ 1 x))))"
  :precision binary64
  (/ (+ (neg 1.0) (sqrt (+ 1.0 x))) (+ 1.0 (sqrt (+ 1.0 x)))))