Error

Try it out

Derivation

1. Initial program 13.9

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

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 *-un-lft-identity0.3

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

5. Applied div-inv0.3

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

6. Applied times-frac0.3

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

7. Applied associate-*r*0.3

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

8. Simplified0.3

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

9. Taylor expanded around 0 0.3

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

10. Final simplification0.3

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

Reproduce

herbie shell --seed 2019004 
(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: 24.8s)Debug log