Average Error: 29.8 → 0.0
Time: 13.4s
Precision: 64
Internal Precision: 1344
\[\frac{1}{\sqrt{x + 1} - \sqrt{x}}\]
\[\frac{1}{1} \cdot \left(\sqrt{x + 1} + \sqrt{x}\right)\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.8

    \[\frac{1}{\sqrt{x + 1} - \sqrt{x}}\]
  2. Using strategy rm
  3. Applied flip--29.5

    \[\leadsto \frac{1}{\color{blue}{\frac{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}}}\]
  4. Applied associate-/r/29.5

    \[\leadsto \color{blue}{\frac{1}{\sqrt{x + 1} \cdot \sqrt{x + 1} - \sqrt{x} \cdot \sqrt{x}} \cdot \left(\sqrt{x + 1} + \sqrt{x}\right)}\]
  5. Applied simplify0.0

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

Runtime

Time bar (total: 13.4s)Debug log

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