Random Jason Timeout Test 012

Average Error: 61.1 → 60.2

Time: 28.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.0551194375545526e+290

Math

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

↓

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

C

double f(double a) {
        double r3049 = a;
        double r3050 = cosh(r3049);
        double r3051 = r3049 * r3049;
        double r3052 = fmod(r3050, r3051);
        double r3053 = log1p(r3049);
        double r3054 = pow(r3052, r3053);
        double r3055 = acos(r3054);
        return r3055;
}

↓

double f(double a) {
        double r3056 = a;
        double r3057 = cosh(r3056);
        double r3058 = r3056 * r3056;
        double r3059 = fmod(r3057, r3058);
        double r3060 = exp(r3059);
        double r3061 = log(r3060);
        double r3062 = log1p(r3056);
        double r3063 = pow(r3061, r3062);
        double r3064 = acos(r3063);
        double r3065 = log(r3064);
        double r3066 = cbrt(r3065);
        double r3067 = r3066 * r3066;
        double r3068 = r3067 * r3066;
        double r3069 = exp(r3068);
        return r3069;
}

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-exp-log 60.2

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

7. Applied add-cube-cbrt 60.2

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

8. Final simplification 60.2

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

Reproduce

herbie shell --seed 2020060 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))