Average Error: 29.3 → 29.3
Time: 23.9s
Precision: 64
Internal Precision: 1344
\[\frac{\sqrt{x + 1}}{\sqrt{x + 1} - \sqrt{x}} - \frac{\sqrt{x}}{\sqrt{x + 1} - \sqrt{x}}\]
\[\left(\sqrt[3]{\frac{\sqrt{x + 1}}{\sqrt{x + 1} - \sqrt{x}} - \frac{\sqrt{x}}{\sqrt{x + 1} - \sqrt{x}}} \cdot \sqrt[3]{\frac{\sqrt{x + 1}}{\sqrt{x + 1} - \sqrt{x}} - \frac{\sqrt{x}}{\sqrt{x + 1} - \sqrt{x}}}\right) \cdot \sqrt[3]{\frac{\sqrt{x + 1}}{\sqrt{x + 1} - \sqrt{x}} - \frac{\sqrt{x}}{\sqrt{x + 1} - \sqrt{x}}}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.3

    \[\frac{\sqrt{x + 1}}{\sqrt{x + 1} - \sqrt{x}} - \frac{\sqrt{x}}{\sqrt{x + 1} - \sqrt{x}}\]
  2. Using strategy rm
  3. Applied add-cube-cbrt29.3

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

Runtime

Time bar (total: 23.9s)Debug log

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