Random Jason Timeout Test 012

Average Error: 60.5 → 59.6

Time: 57.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.804422053352139e+304

Math

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

↓

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

C

double f(double a) {
        double r1471677 = a;
        double r1471678 = cosh(r1471677);
        double r1471679 = r1471677 * r1471677;
        double r1471680 = fmod(r1471678, r1471679);
        double r1471681 = log1p(r1471677);
        double r1471682 = pow(r1471680, r1471681);
        double r1471683 = acos(r1471682);
        return r1471683;
}

↓

double f(double a) {
        double r1471684 = a;
        double r1471685 = cosh(r1471684);
        double r1471686 = r1471684 * r1471684;
        double r1471687 = fmod(r1471685, r1471686);
        double r1471688 = exp(r1471687);
        double r1471689 = log(r1471688);
        double r1471690 = log1p(r1471684);
        double r1471691 = pow(r1471689, r1471690);
        double r1471692 = acos(r1471691);
        double r1471693 = sqrt(r1471692);
        double r1471694 = r1471693 * r1471693;
        return r1471694;
}

Error

Bits error versus a

Derivation

1. Initial program 60.5

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

3. Applied add-log-exp 59.6

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

5. Applied add-sqr-sqrt 59.6

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

6. Final simplification 59.6

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

Reproduce

herbie shell --seed 2019163 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))