\[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
Test:
(/ (pow (asin (atan 3.280379569422725e-280)) (tan b)) (sqr a))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 6.8 s
Input Error: 8.1
Output Error: 5.0
Log: ⚲
Profile: 🕒
\(\frac{e^{\log \left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right) \cdot \tan b}}{a} \cdot \frac{1}{a}\)
  1. Started with
    \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
    8.1
  2. Using strategy rm
    8.1
  3. Applied square-mult to get
    \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{\color{red}{{a}^2}} \leadsto \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{\color{blue}{a \cdot a}}\]
    8.1
  4. Applied associate-/r* to get
    \[\color{red}{\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{a \cdot a}} \leadsto \color{blue}{\frac{\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{a}}{a}}\]
    4.7
  5. Using strategy rm
    4.7
  6. Applied add-exp-log to get
    \[\frac{\frac{{\color{red}{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}}^{\left(\tan b\right)}}{a}}{a} \leadsto \frac{\frac{{\color{blue}{\left(e^{\log \left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}\right)}}^{\left(\tan b\right)}}{a}}{a}\]
    4.9
  7. Applied pow-exp to get
    \[\frac{\frac{\color{red}{{\left(e^{\log \left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}\right)}^{\left(\tan b\right)}}}{a}}{a} \leadsto \frac{\frac{\color{blue}{e^{\log \left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right) \cdot \tan b}}}{a}}{a}\]
    4.9
  8. Using strategy rm
    4.9
  9. Applied div-inv to get
    \[\color{red}{\frac{\frac{e^{\log \left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right) \cdot \tan b}}{a}}{a}} \leadsto \color{blue}{\frac{e^{\log \left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right) \cdot \tan b}}{a} \cdot \frac{1}{a}}\]
    5.0

Original test:


(lambda ((a default) (b default))
  #:name "(/ (pow (asin (atan 3.280379569422725e-280)) (tan b)) (sqr a))"
  (/ (pow (asin (atan 3.280379569422725e-280)) (tan b)) (sqr a)))