Error

Derivation

1. Initial program 20.1

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

3. Applied flip-- 20.1

   \[\leadsto \color{blue}{\frac{{\left(\frac{1}{\sqrt{x}}\right)}^2 - {\left(\frac{1}{\sqrt{x + 1}}\right)}^2}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}}\]

4. Applied simplify 20.2

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

6. Applied frac-sub 19.5

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

7. Applied simplify 5.9

   \[\leadsto \frac{\frac{\color{blue}{1 - 0}}{x \cdot \left(x + 1\right)}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
8. Using strategy rm

9. Applied *-un-lft-identity 5.9

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

10. Applied *-un-lft-identity 5.9

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

11. Applied times-frac 5.5

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

12. Applied times-frac 0.4

    \[\leadsto \color{blue}{\frac{\frac{1}{x}}{1} \cdot \frac{\frac{1 - 0}{x + 1}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}}\]

13. Applied simplify 0.4

    \[\leadsto \color{blue}{\frac{1}{x}} \cdot \frac{\frac{1 - 0}{x + 1}}{\frac{1}{\sqrt{x}} + \frac{1}{\sqrt{x + 1}}}\]
14. Removed slow pow expressions

Runtime

Time bar (total: 13.7s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (x)
  :name "NMSE example 3.6"
  :pre (>= x 0)
  (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))