Average Error: 19.6 → 5.4
Time: 33.7s
Precision: 64
Internal Precision: 1088
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
\[\frac{\frac{1}{x \cdot \left(x + 1\right)}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 19.6

    \[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
  2. Using strategy rm
  3. Applied flip--19.6

    \[\leadsto \color{blue}{\frac{\frac{1}{\sqrt{x}} \cdot \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}} \cdot \frac{1}{\sqrt{x + 1}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}}\]
  4. Applied simplify19.6

    \[\leadsto \frac{\color{blue}{\frac{1}{x} - \frac{1}{x + 1}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
  5. Using strategy rm
  6. Applied frac-sub19.0

    \[\leadsto \frac{\color{blue}{\frac{1 \cdot \left(x + 1\right) - x \cdot 1}{x \cdot \left(x + 1\right)}}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
  7. Applied simplify5.4

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

Runtime

Time bar (total: 33.7s)Debug log

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