Error

Target

Derivation

1. Initial program 9.7

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

3. Applied +-commutative9.7

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

5. Applied frac-sub25.8

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

6. Applied frac-add25.0

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

7. Simplified25.1

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

8. Taylor expanded around -inf 0.2

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

10. Applied associate-/r*0.1

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

11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019050 
(FPCore (x)
  :name "3frac (problem 3.3.3)"

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

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