Error

Try it out

Derivation

1. Initial program 14.5

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

2. Initial simplification9.1

   \[\leadsto \frac{\frac{\frac{\pi}{a + b}}{b - a}}{\frac{2}{\frac{1}{a} - \frac{1}{b}}}\]
3. Using strategy rm

4. Applied frac-sub9.1

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

5. Applied associate-/r/9.1

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

6. Applied div-inv9.1

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

7. Applied times-frac0.3

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

8. Simplified0.3

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

10. Applied frac-times0.4

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

11. Applied associate-*l/0.5

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

12. Simplified0.3

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

13. Final simplification0.3

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

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed 2018227 
(FPCore (a b)
  :name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (* b b) (* a a)))) (- (/ 1 a) (/ 1 b))))