Error

Target

Derivation

1. Split input into 3 regimes.

2. if x < -2.3416378887887987e-05

   1. Initial program 21.3

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

   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

      \[\leadsto \color{blue}{\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\frac{2}{x}}{x \cdot x}}\]
   5. Using strategy rm

   6. Applied associate-/r* 0.1

      \[\leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \color{blue}{\frac{\frac{\frac{2}{x}}{x}}{x}}\]

   7. Applied simplify 0.1

      \[\leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\color{blue}{\frac{2}{{x}^2}}}{x}\]
   8. Using strategy rm

   9. Applied square-mult 0.1

      \[\leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\frac{2}{\color{blue}{x \cdot x}}}{x}\]

   10. Applied associate-/r* 0.1

       \[\leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\color{blue}{\frac{\frac{2}{x}}{x}}}{x}\]

   if -2.3416378887887987e-05 < x < 1843.611849545597

   1. Initial program 0.1

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

   if 1843.611849545597 < x

   1. Initial program 19.1

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

   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

      \[\leadsto \color{blue}{\left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\frac{2}{x}}{x \cdot x}}\]
   5. Using strategy rm

   6. Applied associate-/r* 0.1

      \[\leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \color{blue}{\frac{\frac{\frac{2}{x}}{x}}{x}}\]

   7. Applied simplify 0.1

      \[\leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\color{blue}{\frac{2}{{x}^2}}}{x}\]
   8. Using strategy rm

   9. Applied square-mult 0.1

      \[\leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\frac{2}{\color{blue}{x \cdot x}}}{x}\]

   10. Applied associate-/r* 0.1

       \[\leadsto \left(\frac{2}{{x}^{7}} + \frac{2}{{x}^{5}}\right) + \frac{\color{blue}{\frac{\frac{2}{x}}{x}}}{x}\]
3. Recombined 3 regimes into one program.
4. Removed slow pow expressions

Runtime

Time bar (total: 6.5s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064555532 179913862 452496668 2441903500 287849034 462453547)'
(FPCore (x)
  :name "3frac (problem 3.3.3)"

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

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