Average Error: 59.7 → 0.3
Time: 36.1s
Precision: 64
Internal Precision: 1344
\[\sqrt{x + 1} - \sqrt{x - 1}\]
\[\frac{1 + 1}{\sqrt{x + 1} + \sqrt{x - 1}}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 59.7

    \[\sqrt{x + 1} - \sqrt{x - 1}\]
  2. Using strategy rm
  3. Applied flip--59.2

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

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

Runtime

Time bar (total: 36.1s)Debug log

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