Average Error: 0.0 → 0.0
Time: 16.2s
Precision: 64
Internal Precision: 320
\[\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{\sqrt{x + 1} - \sqrt{x}}{2}\]
\[\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{\frac{1}{\sqrt{x + 1} + \sqrt{x}}}{2}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{\sqrt{x + 1} - \sqrt{x}}{2}\]
  2. Using strategy rm
  3. Applied flip--0.0

    \[\leadsto \frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{\color{blue}{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}}}{2}\]
  4. Applied simplify0.0

    \[\leadsto \frac{\sqrt{x + 1} + \sqrt{x}}{2} + \frac{\frac{\color{blue}{1}}{\sqrt{x + 1} + \sqrt{x}}}{2}\]

Runtime

Time bar (total: 16.2s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "(sqrt(x+1)+sqrt(x))/2+(sqrt(x+1)-sqrt(x))/2"
  (+ (/ (+ (sqrt (+ x 1)) (sqrt x)) 2) (/ (- (sqrt (+ x 1)) (sqrt x)) 2)))