Random Jason Timeout Test 012

Average Error: 60.3 → 59.4

Time: 52.1s

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.608700736709935e+77

Math

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

↓

\[\sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \left(\sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)\]

C

double f(double a) {
        double r484173 = a;
        double r484174 = cosh(r484173);
        double r484175 = r484173 * r484173;
        double r484176 = fmod(r484174, r484175);
        double r484177 = log1p(r484173);
        double r484178 = pow(r484176, r484177);
        double r484179 = acos(r484178);
        return r484179;
}

↓

double f(double a) {
        double r484180 = a;
        double r484181 = cosh(r484180);
        double r484182 = r484180 * r484180;
        double r484183 = fmod(r484181, r484182);
        double r484184 = exp(r484183);
        double r484185 = log(r484184);
        double r484186 = log1p(r484180);
        double r484187 = pow(r484185, r484186);
        double r484188 = acos(r484187);
        double r484189 = cbrt(r484188);
        double r484190 = r484189 * r484189;
        double r484191 = r484189 * r484190;
        return r484191;
}

Error

Bits error versus a

Derivation

1. Initial program 60.3

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

3. Applied add-log-exp 59.4

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

5. Applied add-cube-cbrt 59.4

   \[\leadsto \color{blue}{\left(\sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right) \cdot \sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\]

6. Final simplification 59.4

   \[\leadsto \sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \left(\sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt[3]{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)\]

Reproduce

herbie shell --seed 2019154 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))