\[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
Test:
(/ (pow (asin (atan 3.280379569422725e-280)) (tan b)) (sqr a))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 10.1 s
Input Error: 18.2
Output Error: 5.1
Log: ⚲
Profile: 🕒
\(\begin{cases} {\left(\frac{\sqrt{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}}{a}\right)}^2 & \text{when } b \le -0.00010876831f0 \\ \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\log \left(e^{\tan b}\right)\right)}}{{a}^2} & \text{when } b \le 1.0048907f0 \\ {\left(\frac{\sqrt{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}}{a}\right)}^2 & \text{otherwise} \end{cases}\)

    if b < -0.00010876831f0 or 1.0048907f0 < b

    1. Started with
      \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
      10.1
    2. Using strategy rm
      10.1
    3. Applied add-sqr-sqrt to get
      \[\frac{\color{red}{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}}{{a}^2} \leadsto \frac{\color{blue}{{\left(\sqrt{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}\right)}^2}}{{a}^2}\]
      10.1
    4. Applied square-undiv to get
      \[\color{red}{\frac{{\left(\sqrt{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}\right)}^2}{{a}^2}} \leadsto \color{blue}{{\left(\frac{\sqrt{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}}{a}\right)}^2}\]
      6.0

    if -0.00010876831f0 < b < 1.0048907f0

    1. Started with
      \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\left(\tan b\right)}}{{a}^2}\]
      24.8
    2. Using strategy rm
      24.8
    3. Applied add-log-exp to get
      \[\frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\color{red}{\left(\tan b\right)}}}{{a}^2} \leadsto \frac{{\left(\sin^{-1} \left(\tan^{-1} \left( 3.280379569422725 \cdot 10^{-280} \right)\right)\right)}^{\color{blue}{\left(\log \left(e^{\tan b}\right)\right)}}}{{a}^2}\]
      4.3
  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)))