Error

Target

Derivation

1. Initial program 9.6

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

3. Applied frac-sub25.8

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

4. Applied frac-add25.1

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

5. Applied simplify25.6

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

6. Applied simplify25.6

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

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

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

Runtime

Time bar (total: 1.9m)Debug logProfile

herbie shell --seed '#(1071948828 1180510430 2986424009 997076509 406109801 420189285)' +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))))