Random Jason Timeout Test 012

Average Error: 61.1 → 60.2

Time: 1.2m

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.9756105794475683e+22

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 r1284361 = a;
        double r1284362 = cosh(r1284361);
        double r1284363 = r1284361 * r1284361;
        double r1284364 = fmod(r1284362, r1284363);
        double r1284365 = log1p(r1284361);
        double r1284366 = pow(r1284364, r1284365);
        double r1284367 = acos(r1284366);
        return r1284367;
}

↓

double f(double a) {
        double r1284368 = a;
        double r1284369 = cosh(r1284368);
        double r1284370 = r1284368 * r1284368;
        double r1284371 = fmod(r1284369, r1284370);
        double r1284372 = exp(r1284371);
        double r1284373 = log(r1284372);
        double r1284374 = log1p(r1284368);
        double r1284375 = pow(r1284373, r1284374);
        double r1284376 = acos(r1284375);
        double r1284377 = sqrt(r1284376);
        double r1284378 = r1284377 * r1284377;
        return r1284378;
}

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-sqr-sqrt 60.2

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

6. Final simplification 60.2

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

Reproduce

herbie shell --seed 2019168 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))