Error

Target

Derivation

1. Initial program 19.6

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

3. Applied frac-sub 19.6

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

4. Applied simplify 19.6

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

6. Applied flip-- 19.3

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

7. Applied simplify 0.4

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

9. Applied div-inv 0.4

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

Runtime

Total time: 18.6s Debug log

Please report a bug with the following info:

herbie --seed '#(1230430190 4065338517 1808987078 805337187 564116593 575471959)'
(FPCore (x)
  :name "NMSE example 3.6"

  :target
  (/ 1 (+ (* (+ x 1) (sqrt x)) (* x (sqrt (+ x 1)))))

  (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1)))))