Error

Target

Derivation

1. Initial program 9.9

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

3. Applied frac-sub25.7

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

4. Applied frac-add24.9

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

5. 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 flip-+0.3

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

8. Applied associate-*l/0.3

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

9. Applied simplify0.3

   \[\leadsto \frac{2}{\frac{\color{blue}{{x}^{3} - x}}{x - 1} \cdot \left(x - 1\right)}\]

Runtime

Time bar (total: 1.5m)Debug logProfile

herbie shell --seed '#(1070578969 3140398606 632207097 462683394 1189254563 964980650)' 
(FPCore (x)
  :name "3frac (problem 3.3.3)"

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

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