Average Error: 60.2 → 0.3
Time: 45.9s
Precision: 64
Internal Precision: 1344
\[\sqrt{x - y} - \sqrt{\left(x - y\right) - 1}\]
\[\frac{1}{\sqrt{x - y} + \sqrt{\left(x - y\right) - 1}}\]

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 60.2

    \[\sqrt{x - y} - \sqrt{\left(x - y\right) - 1}\]
  2. Using strategy rm
  3. Applied flip--60.0

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

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

Runtime

Time bar (total: 45.9s)Debug log

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