\[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
Test:
(/ (pow (asin (atan 3.280379569422725e-280)) (tan b)) (sqr a))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 47.6 s
Input Error: 8.3
Output Error: 5.0
Log: ⚲
Profile: 🕒
\(\frac{{1}^{\left(\tan b\right)}}{a} \cdot \frac{e^{\log \left({\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}\right)}}{a}\)
  1. Started with
    \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
    8.3
  2. Using strategy rm
    8.3
  3. Applied square-mult to get
    \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{\color{red}{{a}^2}} \leadsto \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{\color{blue}{a \cdot a}}\]
    8.3
  4. Applied *-un-lft-identity to get
    \[\frac{{\color{red}{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}}^{\left(\tan b\right)}}{a \cdot a} \leadsto \frac{{\color{blue}{\left(1 \cdot \sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}}^{\left(\tan b\right)}}{a \cdot a}\]
    8.3
  5. Applied unpow-prod-down to get
    \[\frac{\color{red}{{\left(1 \cdot \sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}}{a \cdot a} \leadsto \frac{\color{blue}{{1}^{\left(\tan b\right)} \cdot {\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}}{a \cdot a}\]
    8.3
  6. Applied times-frac to get
    \[\color{red}{\frac{{1}^{\left(\tan b\right)} \cdot {\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{a \cdot a}} \leadsto \color{blue}{\frac{{1}^{\left(\tan b\right)}}{a} \cdot \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{a}}\]
    4.9
  7. Using strategy rm
    4.9
  8. Applied add-exp-log to get
    \[\frac{{1}^{\left(\tan b\right)}}{a} \cdot \frac{\color{red}{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}}{a} \leadsto \frac{{1}^{\left(\tan b\right)}}{a} \cdot \frac{\color{blue}{e^{\log \left({\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}\right)}}}{a}\]
    5.0
  9. Removed slow pow expressions

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)))