Error

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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. Simplified0.3

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

3. Taylor expanded around inf 0.3

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

5. Applied associate-*l/0.2

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

6. Simplified0.2

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

7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019005 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))

Details

Time bar (total: 28.3s)Debug log