(/ (+ (- 2) (sqrt (- 4 0.001))) 2)

Average Error: 10.1 → 10.1

Time: 398.0ms

Precision: binary64

Math

\[\frac{\left(-2\right) + \sqrt{4 - 10^{-3}}}{2}\]

↓

\[\frac{\sqrt{4 - 10^{-3}}}{2} + -1\]

Derivation

1. Initial program 10.1

   \[\frac{\left(-2\right) + \sqrt{4 - 10^{-3}}}{2}\]

2. Simplified 10.1

   \[\leadsto \color{blue}{\frac{\sqrt{4 - 10^{-3}}}{2} + -1}\]

3. Final simplification 10.1

   \[\leadsto \frac{\sqrt{4 - 10^{-3}}}{2} + -1\]

Reproduce

herbie shell --seed 2020152 
(FPCore ()
  :name "(/ (+ (- 2) (sqrt (- 4 0.001))) 2)"
  :precision binary64
  (/ (+ (neg 2.0) (sqrt (- 4.0 0.001))) 2.0))