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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. Initial simplification0.3

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

4. Applied associate-*l/0.3

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

5. Simplified0.3

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

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

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

8. Applied associate-/l*0.3

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

10. Applied frac-sub0.5

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

11. Applied associate-/r/0.4

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

12. Applied associate-/r*0.3

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

13. Final simplification0.3

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

Runtime

Time bar (total: 55.9s)Debug logProfile

herbie shell --seed 2018274 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))