Random Jason Timeout Test 012

Average Error: 60.5 → 59.6

Time: 1.1m

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 r997498 = a;
        double r997499 = cosh(r997498);
        double r997500 = r997498 * r997498;
        double r997501 = fmod(r997499, r997500);
        double r997502 = log1p(r997498);
        double r997503 = pow(r997501, r997502);
        double r997504 = acos(r997503);
        return r997504;
}

↓

double f(double a) {
        double r997505 = a;
        double r997506 = cosh(r997505);
        double r997507 = r997505 * r997505;
        double r997508 = fmod(r997506, r997507);
        double r997509 = exp(r997508);
        double r997510 = log(r997509);
        double r997511 = log1p(r997505);
        double r997512 = pow(r997510, r997511);
        double r997513 = acos(r997512);
        double r997514 = sqrt(r997513);
        double r997515 = r997514 * r997514;
        return r997515;
}

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 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))