\[\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
Test:
NMSE Section 6.1 mentioned, B
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 15.5 s
Input Error: 14.7
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(\frac{\frac{\frac{\pi}{a}}{b \cdot 2}}{a + b}\)
  1. Started with
    \[\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(\frac{1}{a} - \frac{1}{b}\right)\]
    14.7
  2. Using strategy rm
    14.7
  3. Applied frac-sub to get
    \[\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \color{red}{\left(\frac{1}{a} - \frac{1}{b}\right)} \leadsto \left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \color{blue}{\frac{1 \cdot b - a \cdot 1}{a \cdot b}}\]
    14.7
  4. Applied associate-*l/ to get
    \[\color{red}{\left(\frac{\pi}{2} \cdot \frac{1}{{b}^2 - {a}^2}\right)} \cdot \frac{1 \cdot b - a \cdot 1}{a \cdot b} \leadsto \color{blue}{\frac{\pi \cdot \frac{1}{{b}^2 - {a}^2}}{2}} \cdot \frac{1 \cdot b - a \cdot 1}{a \cdot b}\]
    14.7
  5. Applied frac-times to get
    \[\color{red}{\frac{\pi \cdot \frac{1}{{b}^2 - {a}^2}}{2} \cdot \frac{1 \cdot b - a \cdot 1}{a \cdot b}} \leadsto \color{blue}{\frac{\left(\pi \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(1 \cdot b - a \cdot 1\right)}{2 \cdot \left(a \cdot b\right)}}\]
    14.7
  6. Applied simplify to get
    \[\frac{\color{red}{\left(\pi \cdot \frac{1}{{b}^2 - {a}^2}\right) \cdot \left(1 \cdot b - a \cdot 1\right)}}{2 \cdot \left(a \cdot b\right)} \leadsto \frac{\color{blue}{\frac{\pi}{a + b}}}{2 \cdot \left(a \cdot b\right)}\]
    0.2
  7. Using strategy rm
    0.2
  8. Applied div-inv to get
    \[\color{red}{\frac{\frac{\pi}{a + b}}{2 \cdot \left(a \cdot b\right)}} \leadsto \color{blue}{\frac{\pi}{a + b} \cdot \frac{1}{2 \cdot \left(a \cdot b\right)}}\]
    0.3
  9. Using strategy rm
    0.3
  10. Applied associate-*l/ to get
    \[\color{red}{\frac{\pi}{a + b} \cdot \frac{1}{2 \cdot \left(a \cdot b\right)}} \leadsto \color{blue}{\frac{\pi \cdot \frac{1}{2 \cdot \left(a \cdot b\right)}}{a + b}}\]
    0.3
  11. Applied simplify to get
    \[\frac{\color{red}{\pi \cdot \frac{1}{2 \cdot \left(a \cdot b\right)}}}{a + b} \leadsto \frac{\color{blue}{\frac{\frac{\pi}{a}}{b \cdot 2}}}{a + b}\]
    0.3

Original test:


(lambda ((a default) (b default))
  #:name "NMSE Section 6.1 mentioned, B"
  (* (* (/ PI 2) (/ 1 (- (sqr b) (sqr a)))) (- (/ 1 a) (/ 1 b))))