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

⬇

\[\begin{array}{l} \mathbf{if}\;x \le -2.540618527478878:\\ \;\;\;\;\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\frac{2}{x}}{x \cdot x}\\ \mathbf{if}\;x \le 70172005.42724477:\\ \;\;\;\;-\left(2 \cdot \frac{1}{x} + \left(2 \cdot {x}^{3} + 2 \cdot x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\frac{2}{x}}{x \cdot x}\\ \end{array}\]

Original	10.4
Comparison	0.7
Herbie	0.1

Derivation

Split input into 2 regimes.
if x < -2.540618527478878 or 70172005.42724477 < x
1. Initial program 19.7
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Applied taylor 0.5
  \[\leadsto 2 \cdot \frac{1}{{x}^{3}} + \left(2 \cdot \frac{1}{{x}^{5}} + 2 \cdot \frac{1}{{x}^{7}}\right)\]
3. Taylor expanded around inf 0.5
  
  \[\leadsto \color{blue}{2 \cdot \frac{1}{{x}^{3}} + \left(2 \cdot \frac{1}{{x}^{5}} + 2 \cdot \frac{1}{{x}^{7}}\right)}\]
4. Applied simplify 0.1
  \[\leadsto \color{blue}{\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\frac{2}{x}}{x \cdot x}}\]
if -2.540618527478878 < x < 70172005.42724477
1. Initial program 0.9
  \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}\]
2. Applied taylor 0.0
  \[\leadsto -\left(2 \cdot \frac{1}{x} + \left(2 \cdot {x}^{3} + 2 \cdot x\right)\right)\]
3. Taylor expanded around 0 0.0
  
  \[\leadsto \color{blue}{-\left(2 \cdot \frac{1}{x} + \left(2 \cdot {x}^{3} + 2 \cdot x\right)\right)}\]
Recombined 2 regimes into one program.
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie shell --seed '#(1068028399 4028058041 2917032441 2563479541 765645300 1132738916)'
(FPCore (x)
  :name "3frac (problem 3.3.3)"

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

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

Error

Target

Derivation

`if x < -2.540618527478878 or 70172005.42724477 < x`

`if -2.540618527478878 < x < 70172005.42724477`

Runtime