Random Jason Timeout Test 012

Average Error: 61.1 → 60.2

Time: 26.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = 217359335082.17374

Math

\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

↓

\[\log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)\]

C

double f(double a) {
        double r4998 = a;
        double r4999 = cosh(r4998);
        double r5000 = r4998 * r4998;
        double r5001 = fmod(r4999, r5000);
        double r5002 = log1p(r4998);
        double r5003 = pow(r5001, r5002);
        double r5004 = acos(r5003);
        return r5004;
}

↓

double f(double a) {
        double r5005 = a;
        double r5006 = cosh(r5005);
        double r5007 = r5005 * r5005;
        double r5008 = fmod(r5006, r5007);
        double r5009 = exp(r5008);
        double r5010 = log(r5009);
        double r5011 = log1p(r5005);
        double r5012 = pow(r5010, r5011);
        double r5013 = acos(r5012);
        double r5014 = exp(r5013);
        double r5015 = sqrt(r5014);
        double r5016 = log(r5015);
        double r5017 = r5016 + r5016;
        return r5017;
}

Error

Bits error versus a

Derivation

1. Initial program 61.1

   \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
2. Using strategy rm

3. Applied add-log-exp 60.2

   \[\leadsto \cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
4. Using strategy rm

5. Applied add-log-exp 60.2

   \[\leadsto \color{blue}{\log \left(e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}\]
6. Using strategy rm

7. Applied add-sqr-sqrt 60.2

   \[\leadsto \log \color{blue}{\left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}} \cdot \sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)}\]

8. Applied log-prod 60.2

   \[\leadsto \color{blue}{\log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)}\]

9. Final simplification 60.2

   \[\leadsto \log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)\]

Reproduce

herbie shell --seed 2020027 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))