Random Jason Timeout Test 012

Average Error: 61.2 → 57.8

Time: 26.9s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.4690867067816283e+246

Math

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

↓

\[\left(\sqrt[3]{\frac{\pi}{2} - \left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)} \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}} \cdot \sqrt[3]{\frac{\pi}{2} - \left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)} \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}}\right) \cdot \sqrt[3]{\frac{\pi}{2} - \left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)} \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}}\]

C

double f(double a) {
        double r4138 = a;
        double r4139 = cosh(r4138);
        double r4140 = r4138 * r4138;
        double r4141 = fmod(r4139, r4140);
        double r4142 = log1p(r4138);
        double r4143 = pow(r4141, r4142);
        double r4144 = acos(r4143);
        return r4144;
}

↓

double f(double a) {
        double r4145 = atan2(1.0, 0.0);
        double r4146 = 2.0;
        double r4147 = r4145 / r4146;
        double r4148 = a;
        double r4149 = cosh(r4148);
        double r4150 = r4148 * r4148;
        double r4151 = fmod(r4149, r4150);
        double r4152 = log1p(r4148);
        double r4153 = exp(r4152);
        double r4154 = log(r4153);
        double r4155 = pow(r4151, r4154);
        double r4156 = asin(r4155);
        double r4157 = cbrt(r4156);
        double r4158 = r4157 * r4157;
        double r4159 = r4158 * r4157;
        double r4160 = r4147 - r4159;
        double r4161 = cbrt(r4160);
        double r4162 = r4161 * r4161;
        double r4163 = r4162 * r4161;
        return r4163;
}

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 60.1

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

5. Applied acos-asin 60.1

   \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\]
6. Using strategy rm

7. Applied add-cube-cbrt 57.8

   \[\leadsto \frac{\pi}{2} - \color{blue}{\left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)} \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}}\]
8. Using strategy rm

9. Applied add-cube-cbrt 57.8

   \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{\pi}{2} - \left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)} \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}} \cdot \sqrt[3]{\frac{\pi}{2} - \left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)} \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}}\right) \cdot \sqrt[3]{\frac{\pi}{2} - \left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)} \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}}}\]

10. Final simplification 57.8

    \[\leadsto \left(\sqrt[3]{\frac{\pi}{2} - \left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)} \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}} \cdot \sqrt[3]{\frac{\pi}{2} - \left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)} \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}}\right) \cdot \sqrt[3]{\frac{\pi}{2} - \left(\sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)} \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}\right) \cdot \sqrt[3]{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\log \left(e^{\mathsf{log1p}\left(a\right)}\right)\right)}\right)}}\]

Reproduce

herbie shell --seed 2019344 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))