\[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
Test:
(- b (+ (pow (cotan b) a) (asin b)))
Bits:
128 bits
Bits error versus a
Bits error versus b
Time: 32.9 s
Input Error: 4.0
Output Error: 4.3
Log: ⚲
Profile: 🕒
\(\begin{cases} {\left({\left(b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}^{\frac{1}{3}}\right)}^3 & \text{when } b \le -2.701136f-20 \\ \frac{{\left(\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}\right)}^3}{{\left(\cot b\right)}^{a} + \left(\sin^{-1} b + b\right)} & \text{when } b \le 3.667267f-23 \\ {\left(\frac{\sqrt[3]{{b}^3 - {\left(\sin^{-1} b + {\left(\cot b\right)}^{a}\right)}^3}}{\sqrt[3]{{\left(\sin^{-1} b + {\left(\cot b\right)}^{a}\right)}^2 + b \cdot \left({\left(\cot b\right)}^{a} + \left(b + \sin^{-1} b\right)\right)}}\right)}^3 & \text{otherwise} \end{cases}\)

    if b < -2.701136f-20

    1. Started with
      \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
      16.3
    2. Using strategy rm
      16.3
    3. Applied add-cube-cbrt to get
      \[\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}\]
      16.3
    4. Using strategy rm
      16.3
    5. Applied pow1/3 to get
      \[{\color{red}{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}}^3 \leadsto {\color{blue}{\left({\left(b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}^{\frac{1}{3}}\right)}}^3\]
      16.3

    if -2.701136f-20 < b < 3.667267f-23

    1. Started with
      \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
      0.1
    2. Using strategy rm
      0.1
    3. Applied add-cube-cbrt to get
      \[\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}\]
      0.1
    4. Using strategy rm
      0.1
    5. Applied flip-- to get
      \[{\left(\sqrt[3]{\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}}\right)}^3\]
      13.9
    6. Applied cbrt-div to get
      \[{\color{red}{\left(\sqrt[3]{\frac{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}}^3 \leadsto {\color{blue}{\left(\frac{\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}}{\sqrt[3]{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}}^3\]
      0.3
    7. Applied cube-div to get
      \[\color{red}{{\left(\frac{\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}}{\sqrt[3]{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}^3} \leadsto \color{blue}{\frac{{\left(\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}\right)}^3}{{\left(\sqrt[3]{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}}\]
      0.3
    8. Applied simplify to get
      \[\frac{{\left(\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}\right)}^3}{\color{red}{{\left(\sqrt[3]{b + \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}} \leadsto \frac{{\left(\sqrt[3]{{b}^2 - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2}\right)}^3}{\color{blue}{{\left(\cot b\right)}^{a} + \left(\sin^{-1} b + b\right)}}\]
      0.3

    if 3.667267f-23 < b

    1. Started with
      \[b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\]
      4.7
    2. Using strategy rm
      4.7
    3. Applied add-cube-cbrt to get
      \[\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)} \leadsto \color{blue}{{\left(\sqrt[3]{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}\right)}^3}\]
      4.8
    4. Using strategy rm
      4.8
    5. Applied flip3-- to get
      \[{\left(\sqrt[3]{\color{red}{b - \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}}\right)}^3 \leadsto {\left(\sqrt[3]{\color{blue}{\frac{{b}^{3} - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^{3}}{{b}^2 + \left({\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2 + b \cdot \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}}\right)}^3\]
      5.1
    6. Applied cbrt-div to get
      \[{\color{red}{\left(\sqrt[3]{\frac{{b}^{3} - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^{3}}{{b}^2 + \left({\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2 + b \cdot \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}\right)}}^3 \leadsto {\color{blue}{\left(\frac{\sqrt[3]{{b}^{3} - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^{3}}}{\sqrt[3]{{b}^2 + \left({\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2 + b \cdot \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}\right)}}^3\]
      5.1
    7. Applied simplify to get
      \[{\left(\frac{\color{red}{\sqrt[3]{{b}^{3} - {\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^{3}}}}{\sqrt[3]{{b}^2 + \left({\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2 + b \cdot \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}\right)}^3 \leadsto {\left(\frac{\color{blue}{\sqrt[3]{{b}^3 - {\left(\sin^{-1} b + {\left(\cot b\right)}^{a}\right)}^3}}}{\sqrt[3]{{b}^2 + \left({\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2 + b \cdot \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}\right)}^3\]
      5.1
    8. Applied simplify to get
      \[{\left(\frac{\sqrt[3]{{b}^3 - {\left(\sin^{-1} b + {\left(\cot b\right)}^{a}\right)}^3}}{\color{red}{\sqrt[3]{{b}^2 + \left({\left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)}^2 + b \cdot \left({\left(\cot b\right)}^{a} + \sin^{-1} b\right)\right)}}}\right)}^3 \leadsto {\left(\frac{\sqrt[3]{{b}^3 - {\left(\sin^{-1} b + {\left(\cot b\right)}^{a}\right)}^3}}{\color{blue}{\sqrt[3]{{\left(\sin^{-1} b + {\left(\cot b\right)}^{a}\right)}^2 + b \cdot \left({\left(\cot b\right)}^{a} + \left(b + \sin^{-1} b\right)\right)}}}\right)}^3\]
      5.1
  1. Removed slow pow expressions

Original test:


(lambda ((a default) (b default))
  #:name "(- b (+ (pow (cotan b) a) (asin b)))"
  (- b (+ (pow (cotan b) a) (asin b))))