Error

Derivation

1. Initial program 14.1

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

2. Simplified14.1

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

4. Applied difference-of-squares9.7

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

5. Applied associate-/r*9.0

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

7. Applied associate-/l/0.3

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

9. Applied associate-/r*0.3

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

11. Applied *-un-lft-identity0.3

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

12. Applied *-un-lft-identity0.3

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

13. Applied times-frac0.3

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

14. Simplified0.3

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

15. Simplified0.3

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

16. Final simplification0.3

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

Reproduce

herbie shell --seed 2019051 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))