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 frac-sub26.0

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

4. Applied frac-add25.4

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

5. Simplified25.8

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

6. Simplified25.8

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

7. Taylor expanded around 0 0.3

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

9. Applied associate-/r*0.1

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

10. Final simplification0.1

    \[\leadsto \frac{\frac{2}{(x \cdot x + x)_*}}{x - 1}\]

Runtime

Time bar (total: 3.0m)Debug logProfile

herbie shell --seed 2018221 +o rules:numerics
(FPCore (x)
  :name "3frac (problem 3.3.3)"

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

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