Error

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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. Simplified0.3

   \[\leadsto \color{blue}{\frac{\frac{1}{a} - \frac{1}{b}}{b - a} \cdot \frac{\frac{\pi}{2}}{a + b}}\]
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 *-un-lft-identity0.3

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

7. Applied times-frac0.3

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

8. Simplified0.3

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

9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019008 
(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: 28.4s)Debug log