Error

Target

Derivation

1. Initial program 9.2

   \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Using strategy rm

3. Applied frac-sub 25.6

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

4. Applied frac-add 24.9

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

5. Applied simplify 25.0

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

6. Applied taylor 24.9

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

7. Taylor expanded around 0 24.9

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

8. Applied simplify 0.1

   \[\leadsto \color{blue}{\frac{\frac{2}{1 + x}}{\left(x - 1\right) \cdot x}}\]
9. Using strategy rm

10. Applied associate-/r* 0.1

    \[\leadsto \color{blue}{\frac{\frac{\frac{2}{1 + x}}{x - 1}}{x}}\]
11. Removed slow pow expressions

Runtime

Time bar (total: 29.4s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1065003094 2074156664 2352254222 753858891 3745550101 3374585842)'
(FPCore (x)
  :name "3frac (problem 3.3.3)"

  :target
  (/ 2 (* x (- (sqr x) 1)))

  (+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))