\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
Test:
Random Jason Timeout Test 012
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Time: 2.0 m
Input Error: 28.0
Output Error: 21.6
Log:
Profile: 🕒
\(\begin{cases} {e}^{\left(\log \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\right)\right)} & \text{when } a \le 1839.8596f0 \\ \cos^{-1} \left({\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}^{\left(\log_* (1 + a)\right)}\right) & \text{otherwise} \end{cases}\)

    if a < 1839.8596f0

    1. Started with
      \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
      26.2
    2. Applied simplify to get
      \[\color{red}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)} \leadsto \color{blue}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)}\]
      26.2
    3. Using strategy rm
      26.2
    4. Applied add-exp-log to get
      \[\color{red}{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)} \leadsto \color{blue}{e^{\log \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\right)}}\]
      26.2
    5. Using strategy rm
      26.2
    6. Applied pow1 to get
      \[e^{\log \color{red}{\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\right)}} \leadsto e^{\log \color{blue}{\left({\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\right)}^{1}\right)}}\]
      26.2
    7. Applied log-pow to get
      \[e^{\color{red}{\log \left({\left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\right)}^{1}\right)}} \leadsto e^{\color{blue}{1 \cdot \log \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\right)}}\]
      26.2
    8. Applied exp-prod to get
      \[\color{red}{e^{1 \cdot \log \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\right)}} \leadsto \color{blue}{{\left(e^{1}\right)}^{\left(\log \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\right)\right)}}\]
      26.2
    9. Applied simplify to get
      \[{\color{red}{\left(e^{1}\right)}}^{\left(\log \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\right)\right)} \leadsto {\color{blue}{e}}^{\left(\log \left(\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\right)\right)}\]
      26.2

    if 1839.8596f0 < 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
      \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^2\right)\right)}^{\left(\log_* (1 + a)\right)}\right) \leadsto \cos^{-1} \left({\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
      16.6
    4. Taylor expanded around inf to get
      \[\cos^{-1} \left({\color{red}{\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right) \leadsto \cos^{-1} \left({\color{blue}{\left(\left(\cosh \left(\frac{1}{a}\right)\right) \bmod \left(\frac{1}{{a}^2}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right)\]
      16.6

  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))))