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

↓

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

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Derivation

Initial program 14.2
\[\left(\frac{\pi}{2} \cdot \frac{1}{b \cdot b - a \cdot a}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
Initial simplification8.9
\[\leadsto \frac{\frac{\frac{\pi}{a + b}}{b - a}}{\frac{2}{\frac{1}{a} - \frac{1}{b}}}\]
Using strategy rm
Applied associate-/l/0.3
\[\leadsto \color{blue}{\frac{\frac{\pi}{a + b}}{\frac{2}{\frac{1}{a} - \frac{1}{b}} \cdot \left(b - a\right)}}\]
Final simplification0.3
\[\leadsto \frac{\frac{\pi}{a + b}}{\frac{2}{\frac{1}{a} - \frac{1}{b}} \cdot \left(b - a\right)}\]

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