Average Error: 30.3 → 30.0
Time: 19.1s
Precision: 64
Internal Precision: 1344
\[\frac{1}{\sqrt{x + 2} - \sqrt{x}}\]
\[\frac{1}{\sqrt{x + 2} \cdot \sqrt{x + 2} - \sqrt{x} \cdot \sqrt{x}} \cdot \left(\sqrt{x + 2} + \sqrt{x}\right)\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.3

    \[\frac{1}{\sqrt{x + 2} - \sqrt{x}}\]
  2. Initial simplification30.3

    \[\leadsto \frac{1}{\sqrt{x + 2} - \sqrt{x}}\]
  3. Using strategy rm
  4. Applied flip--30.3

    \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt{x + 2} \cdot \sqrt{x + 2} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + 2} + \sqrt{x}}}}\]
  5. Applied associate-/r/30.0

    \[\leadsto \color{blue}{\frac{1}{\sqrt{x + 2} \cdot \sqrt{x + 2} - \sqrt{x} \cdot \sqrt{x}} \cdot \left(\sqrt{x + 2} + \sqrt{x}\right)}\]
  6. Final simplification30.0

    \[\leadsto \frac{1}{\sqrt{x + 2} \cdot \sqrt{x + 2} - \sqrt{x} \cdot \sqrt{x}} \cdot \left(\sqrt{x + 2} + \sqrt{x}\right)\]

Runtime

Time bar (total: 19.1s)Debug log

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