\[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
Test:
(/ (pow (asin (atan 3.280379569422725e-280)) (tan b)) (sqr a))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 9.4 s
Input Error: 18.3
Output Error: 5.1
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(e^{\tan b}\right)\right)}}{{a}^2} & \text{when } a \le -1.1871537f-23 \\ {\left(\frac{\sqrt{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}}{a}\right)}^2 & \text{when } a \le 3.7877513f-23 \\ \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(e^{\tan b}\right)\right)}}{{a}^2} & \text{otherwise} \end{cases}\)

    if a < -1.1871537f-23 or 3.7877513f-23 < a

    1. Started with
      \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
      17.3
    2. Using strategy rm
      17.3
    3. Applied add-log-exp to get
      \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\color{red}{\left(\tan b\right)}}}{{a}^2} \leadsto \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\color{blue}{\left(\log \left(e^{\tan b}\right)\right)}}}{{a}^2}\]
      5.1

    if -1.1871537f-23 < a < 3.7877513f-23

    1. Started with
      \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
      30.7
    2. Using strategy rm
      30.7
    3. Applied add-sqr-sqrt to get
      \[\frac{\color{red}{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}}{{a}^2} \leadsto \frac{\color{blue}{{\left(\sqrt{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}\right)}^2}}{{a}^2}\]
      30.7
    4. Applied square-undiv to get
      \[\color{red}{\frac{{\left(\sqrt{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}\right)}^2}{{a}^2}} \leadsto \color{blue}{{\left(\frac{\sqrt{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}}{a}\right)}^2}\]
      5.3
  1. 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)))