Error

Derivation

1. Initial program 14.6

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

3. Applied frac-sub14.6

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

4. Applied associate-*l/14.6

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

5. Applied frac-times14.6

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

6. Simplified0.2

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

8. Applied div-inv0.3

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

9. Applied times-frac0.3

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

10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019068 +o rules:numerics
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))