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Derivation

1. Initial program 14.7

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

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-*r/0.3

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

6. Applied frac-times0.3

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

7. Simplified0.3

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

9. Applied div-inv0.3

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

10. Applied div-inv0.3

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

11. Applied distribute-lft-out--0.3

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

12. Applied times-frac0.3

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

13. Applied associate-/l*0.3

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

14. Final simplification0.3

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

Runtime

Time bar (total: 1.7m)Debug logProfile

herbie shell --seed 2018349 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))