Random Jason Timeout Test 012

Average Error: 60.3 → 59.1

Time: 42.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 2.7115938426145936e+256

Math

\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]

↓

\[\cos^{-1} \left({\left(\left(\log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \left(\log \left(\sqrt{\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}}\right) + \log \left(\sqrt{\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}}\right)\right)\right) \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)\]

C

double f(double a) {
        double r100048 = a;
        double r100049 = cosh(r100048);
        double r100050 = r100048 * r100048;
        double r100051 = fmod(r100049, r100050);
        double r100052 = log1p(r100048);
        double r100053 = pow(r100051, r100052);
        double r100054 = acos(r100053);
        return r100054;
}

↓

double f(double a) {
        double r100055 = a;
        double r100056 = cosh(r100055);
        double r100057 = r100055 * r100055;
        double r100058 = fmod(r100056, r100057);
        double r100059 = sqrt(r100058);
        double r100060 = exp(r100059);
        double r100061 = sqrt(r100060);
        double r100062 = log(r100061);
        double r100063 = sqrt(r100061);
        double r100064 = log(r100063);
        double r100065 = r100064 + r100064;
        double r100066 = r100062 + r100065;
        double r100067 = r100066 * r100059;
        double r100068 = log1p(r100055);
        double r100069 = pow(r100067, r100068);
        double r100070 = acos(r100069);
        return r100070;
}

Error

Bits error versus a

Derivation

1. Initial program 60.3

   \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]
2. Using strategy rm

3. Applied add-log-exp 59.4

   \[\leadsto \cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right)\]
4. Using strategy rm

5. Applied add-sqr-sqrt 59.4

   \[\leadsto \cos^{-1} \left({\left(\log \left(e^{\color{blue}{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]

6. Applied exp-prod 59.4

   \[\leadsto \cos^{-1} \left({\left(\log \color{blue}{\left({\left(e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)}^{\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)\]

7. Applied log-pow 59.1

   \[\leadsto \cos^{-1} \left({\color{blue}{\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \log \left(e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}\right)\right)}}^{\left(\log_* (1 + a)\right)}\right)\]
8. Using strategy rm

9. Applied add-sqr-sqrt 59.1

   \[\leadsto \cos^{-1} \left({\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \log \color{blue}{\left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}} \cdot \sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)\]

10. Applied log-prod 59.1

    \[\leadsto \cos^{-1} \left({\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \color{blue}{\left(\log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)\]
11. Using strategy rm

12. Applied add-sqr-sqrt 59.1

    \[\leadsto \cos^{-1} \left({\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \left(\log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \log \color{blue}{\left(\sqrt{\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}} \cdot \sqrt{\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}}\right)}\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]

13. Applied log-prod 59.1

    \[\leadsto \cos^{-1} \left({\left(\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)} \cdot \left(\log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \color{blue}{\left(\log \left(\sqrt{\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}}\right) + \log \left(\sqrt{\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}}\right)\right)}\right)\right)}^{\left(\log_* (1 + a)\right)}\right)\]

14. Final simplification 59.1

    \[\leadsto \cos^{-1} \left({\left(\left(\log \left(\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}\right) + \left(\log \left(\sqrt{\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}}\right) + \log \left(\sqrt{\sqrt{e^{\sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}}}}\right)\right)\right) \cdot \sqrt{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)}^{\left(\log_* (1 + a)\right)}\right)\]

Reproduce

herbie shell --seed 2019104 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))