Error

Target

Derivation

1. Initial program 9.8

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

3. Applied frac-sub25.9

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

4. Applied frac-add25.2

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

5. Taylor expanded around 0 0.3

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

7. Applied *-un-lft-identity0.3

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

8. Applied times-frac0.1

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

10. Applied associate-*l/0.1

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

11. Simplified0.1

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

12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019089 
(FPCore (x)
  :name "3frac (problem 3.3.3)"

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

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