Random Jason Timeout Test 012

Average Error: 61.2 → 60.3

Time: 43.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. a = 3.3915171398033327e+295

Math

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

↓

\[\log \left(e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)\]

C

double f(double a) {
        double r8193 = a;
        double r8194 = cosh(r8193);
        double r8195 = r8193 * r8193;
        double r8196 = fmod(r8194, r8195);
        double r8197 = log1p(r8193);
        double r8198 = pow(r8196, r8197);
        double r8199 = acos(r8198);
        return r8199;
}

↓

double f(double a) {
        double r8200 = a;
        double r8201 = cosh(r8200);
        double r8202 = 2.0;
        double r8203 = pow(r8200, r8202);
        double r8204 = fmod(r8201, r8203);
        double r8205 = exp(r8204);
        double r8206 = log(r8205);
        double r8207 = log1p(r8200);
        double r8208 = pow(r8206, r8207);
        double r8209 = acos(r8208);
        double r8210 = exp(r8209);
        double r8211 = log(r8210);
        return r8211;
}

Error

Bits error versus a

Derivation

1. Initial program 61.2

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

3. Applied add-log-exp 60.3

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

5. Applied add-log-exp 60.3

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

6. Simplified 61.2

   \[\leadsto \log \color{blue}{\left(e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}\]
7. Using strategy rm

8. Applied add-log-exp 60.3

   \[\leadsto \log \left(e^{\cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)\]

9. Final simplification 60.3

   \[\leadsto \log \left(e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)\]

Reproduce

herbie shell --seed 2020047 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))