Average Error: 20.0 → 0.3
Time: 24.1s
Precision: 64
Internal Precision: 1856
\[\sqrt{x + \frac{1}{x}} - \sqrt{x}\]
\[\frac{\frac{1}{x}}{\sqrt{x + \frac{1}{x}} + \sqrt{x}}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 20.0

    \[\sqrt{x + \frac{1}{x}} - \sqrt{x}\]
  2. Using strategy rm
  3. Applied flip--20.0

    \[\leadsto \color{blue}{\frac{\sqrt{x + \frac{1}{x}} \cdot \sqrt{x + \frac{1}{x}} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x + \frac{1}{x}} + \sqrt{x}}}\]
  4. Applied simplify0.3

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

Runtime

Time bar (total: 24.1s)Debug log

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