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

Average Error: 39.0 → 39.0

Time: 1.0s

Precision: binary64

Math

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

↓

\[\sqrt{1 - x} - 1\]

Error

Bits error versus x

Derivation

1. Initial program 39.0

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

2. Simplified 39.0

   \[\leadsto \color{blue}{\sqrt{1 - x} - 1}\]

3. Final simplification 39.0

   \[\leadsto \sqrt{1 - x} - 1\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(+ (- 1) (sqrt (- 1 x)))"
  :precision binary64
  (+ (neg 1.0) (sqrt (- 1.0 x))))