Average Error: 14.5 → 0.1
Time: 10.5s
Precision: 64
Internal Precision: 832
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\frac{-1}{x + 1}}{x}\]

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.5

    \[\frac{1}{x + 1} - \frac{1}{x}\]

  2. Initial simplification14.5

    \[\leadsto \frac{1}{x + 1} - \frac{1}{x}\]
  3. Using strategy rm

  4. Applied frac-sub13.8

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

  5. Simplified0.3

    \[\leadsto \frac{\color{blue}{-1}}{\left(x + 1\right) \cdot x}\]
  6. Using strategy rm

  7. Applied associate-/r*0.1

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

  8. Final simplification0.1

    \[\leadsto \frac{\frac{-1}{x + 1}}{x}\]

Runtime

Time bar (total: 10.5s)Debug logProfile

herbie shell --seed 2018249 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))