\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
Test:
Random Jason Timeout Test 012
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Time: 52.2 s
Input Error: 61.2
Output Error: 45.1
Log: ⚲
Profile: 🕒
\(\begin{cases} \cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}\right)\right)}^{\left(\log_* (1 + a)\right)}\right) & \text{when } a \le 8727.195470384844 \\ \cos^{-1} \left({\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}^{\left(\log_* (1 + a)\right)}\right) & \text{otherwise} \end{cases}\)

    if a < 8727.195470384844

    1. Started with
      \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
      60.4
    2. Applied simplify to get
      \[\color{red}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)} \leadsto \color{blue}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)}\]
      60.4
    3. Using strategy rm
      60.4
    4. Applied add-log-exp to get
      \[\cos^{-1} \left({\color{red}{\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}}^{\left(\log_* (1 + a)\right)}\right) \leadsto \cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right)\]
      59.5

    if 8727.195470384844 < a

    1. Started with
      \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
      62.0
    2. Applied simplify to get
      \[\color{red}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)} \leadsto \color{blue}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)}\]
      62.0
    3. Applied taylor to get
      \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right) \leadsto \cos^{-1} \left({\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
      30.9
    4. Taylor expanded around inf to get
      \[\cos^{-1} \left({\color{red}{\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right) \leadsto \cos^{-1} \left({\color{blue}{\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right)\]
      30.9
  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))))