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

Average Error: 29.7 → 29.7

Time: 1.4s

Precision: binary64

Math

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

↓

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

Error

Bits error versus x

Derivation

1. Initial program 29.7

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

2. Final simplification 29.7

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

Reproduce

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