\[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
Test:
(/ (pow (asin (atan 3.280379569422725e-280)) (tan b)) (sqr a))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 13.2 s
Input Error: 18.3
Output Error: 4.6
Log: ⚲
Profile: 🕒
\(\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(\sqrt[3]{e^{\tan b}}\right)\right)}}{a} \cdot \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(\sqrt[3]{e^{\tan b}} \cdot \sqrt[3]{e^{\tan b}}\right)\right)}}{a}\)
  1. Started with
    \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
    18.3
  2. Using strategy rm
    18.3
  3. Applied add-log-exp to get
    \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\color{red}{\left(\tan b\right)}}}{{a}^2} \leadsto \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\color{blue}{\left(\log \left(e^{\tan b}\right)\right)}}}{{a}^2}\]
    7.0
  4. Using strategy rm
    7.0
  5. Applied add-cube-cbrt to get
    \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \color{red}{\left(e^{\tan b}\right)}\right)}}{{a}^2} \leadsto \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \color{blue}{\left({\left(\sqrt[3]{e^{\tan b}}\right)}^3\right)}\right)}}{{a}^2}\]
    6.9
  6. Using strategy rm
    6.9
  7. Applied square-mult to get
    \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left({\left(\sqrt[3]{e^{\tan b}}\right)}^3\right)\right)}}{\color{red}{{a}^2}} \leadsto \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left({\left(\sqrt[3]{e^{\tan b}}\right)}^3\right)\right)}}{\color{blue}{a \cdot a}}\]
    6.9
  8. Applied cube-mult to get
    \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \color{red}{\left({\left(\sqrt[3]{e^{\tan b}}\right)}^3\right)}\right)}}{a \cdot a} \leadsto \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \color{blue}{\left(\sqrt[3]{e^{\tan b}} \cdot \left(\sqrt[3]{e^{\tan b}} \cdot \sqrt[3]{e^{\tan b}}\right)\right)}\right)}}{a \cdot a}\]
    6.9
  9. Applied log-prod to get
    \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\color{red}{\left(\log \left(\sqrt[3]{e^{\tan b}} \cdot \left(\sqrt[3]{e^{\tan b}} \cdot \sqrt[3]{e^{\tan b}}\right)\right)\right)}}}{a \cdot a} \leadsto \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\color{blue}{\left(\log \left(\sqrt[3]{e^{\tan b}}\right) + \log \left(\sqrt[3]{e^{\tan b}} \cdot \sqrt[3]{e^{\tan b}}\right)\right)}}}{a \cdot a}\]
    6.9
  10. Applied unpow-prod-up to get
    \[\frac{\color{red}{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(\sqrt[3]{e^{\tan b}}\right) + \log \left(\sqrt[3]{e^{\tan b}} \cdot \sqrt[3]{e^{\tan b}}\right)\right)}}}{a \cdot a} \leadsto \frac{\color{blue}{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(\sqrt[3]{e^{\tan b}}\right)\right)} \cdot {\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(\sqrt[3]{e^{\tan b}} \cdot \sqrt[3]{e^{\tan b}}\right)\right)}}}{a \cdot a}\]
    6.9
  11. Applied times-frac to get
    \[\color{red}{\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(\sqrt[3]{e^{\tan b}}\right)\right)} \cdot {\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(\sqrt[3]{e^{\tan b}} \cdot \sqrt[3]{e^{\tan b}}\right)\right)}}{a \cdot a}} \leadsto \color{blue}{\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(\sqrt[3]{e^{\tan b}}\right)\right)}}{a} \cdot \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(\sqrt[3]{e^{\tan b}} \cdot \sqrt[3]{e^{\tan b}}\right)\right)}}{a}}\]
    4.6

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)))