Error

Try it out

Derivation

1. Initial program 14.2

   \[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]

2. Initial simplification0.3

   \[\leadsto \frac{\left(\frac{1}{a} - \frac{1}{b}\right) \cdot \frac{\frac{\pi}{2}}{b - a}}{a + b}\]
3. Using strategy rm

4. Applied frac-sub0.3

   \[\leadsto \frac{\color{blue}{\frac{1 \cdot b - a \cdot 1}{a \cdot b}} \cdot \frac{\frac{\pi}{2}}{b - a}}{a + b}\]

5. Applied associate-*l/0.3

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

6. Simplified0.2

   \[\leadsto \frac{\frac{\color{blue}{\frac{\pi}{2}}}{a \cdot b}}{a + b}\]
7. Using strategy rm

8. Applied div-inv0.3

   \[\leadsto \color{blue}{\frac{\frac{\pi}{2}}{a \cdot b} \cdot \frac{1}{a + b}}\]
9. Using strategy rm

10. Applied associate-*l/0.3

    \[\leadsto \color{blue}{\frac{\frac{\pi}{2} \cdot \frac{1}{a + b}}{a \cdot b}}\]

11. Simplified0.2

    \[\leadsto \frac{\color{blue}{\frac{\frac{\pi}{2}}{b + a}}}{a \cdot b}\]

12. Final simplification0.2

    \[\leadsto \frac{\frac{\frac{\pi}{2}}{b + a}}{b \cdot a}\]

Runtime

Time bar (total: 37.7s)Debug logProfile

herbie shell --seed 2018234 +o rules:numerics
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))