Average Error: 14.5 → 0.1
Time: 40.8s
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. Using strategy rm

  3. Applied frac-sub13.9

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

  4. Simplified13.9

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

  6. Applied *-un-lft-identity13.9

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

  7. Applied times-frac13.9

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

  8. Simplified0.1

    \[\leadsto \frac{1}{x + 1} \cdot \color{blue}{\frac{0 - 1}{x}}\]
  9. Using strategy rm

  10. Applied associate-*r/0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{x + 1} \cdot \left(0 - 1\right)}{x}}\]

  11. Final simplification0.1

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

Runtime

Time bar (total: 40.8s)Debug logProfile

herbie shell --seed 2018214 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))