\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
Test:
Random Jason Timeout Test 012
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Time: 4.8 m
Input Error: 27.9
Output Error: 21.8
Log: ⚲
Profile: 🕒
\(\begin{cases} {\left(\sqrt[3]{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)}\right)}^3 & \text{when } a \le 16810.443f0 \\ \cos^{-1} \left({\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}^{\left(\log_* (1 + a)\right)}\right) & \text{otherwise} \end{cases}\)

    if a < 16810.443f0

    1. Started with
      \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
      25.9
    2. Applied simplify to get
      \[\color{red}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)} \leadsto \color{blue}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)}\]
      25.9
    3. Using strategy rm
      25.9
    4. Applied add-cube-cbrt to get
      \[\color{red}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)} \leadsto \color{blue}{{\left(\sqrt[3]{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)}\right)}^3}\]
      25.9

    if 16810.443f0 < a

    1. Started with
      \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
      30.0
    2. Applied simplify to get
      \[\color{red}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)} \leadsto \color{blue}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)}\]
      30.0
    3. Applied taylor to get
      \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right) \leadsto \cos^{-1} \left({\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
      17.2
    4. Taylor expanded around inf to get
      \[\cos^{-1} \left({\color{red}{\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right) \leadsto \cos^{-1} \left({\color{blue}{\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right)\]
      17.2
  1. Removed slow pow expressions

Original test:


(lambda ((a default) (b default) (c default))
  #:name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))