Random Jason Timeout Test 012

Average Error: 60.4 → 59.2

Time: 47.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.866964364183374e+192

Math

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

↓

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

C

double f(double a) {
        double r298291 = a;
        double r298292 = cosh(r298291);
        double r298293 = r298291 * r298291;
        double r298294 = fmod(r298292, r298293);
        double r298295 = log1p(r298291);
        double r298296 = pow(r298294, r298295);
        double r298297 = acos(r298296);
        return r298297;
}

↓

double f(double a) {
        double r298298 = atan2(1.0, 0.0);
        double r298299 = 2.0;
        double r298300 = r298298 / r298299;
        double r298301 = a;
        double r298302 = cosh(r298301);
        double r298303 = r298301 * r298301;
        double r298304 = fmod(r298302, r298303);
        double r298305 = sqrt(r298304);
        double r298306 = exp(r298305);
        double r298307 = log(r298306);
        double r298308 = r298307 * r298305;
        double r298309 = log1p(r298301);
        double r298310 = pow(r298308, r298309);
        double r298311 = asin(r298310);
        double r298312 = r298300 - r298311;
        return r298312;
}

Error

Bits error versus a

Derivation

1. Initial program 60.4

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

3. Applied add-log-exp 59.5

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

5. Applied add-sqr-sqrt 59.5

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

6. Applied exp-prod 59.5

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

7. Applied log-pow 59.2

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

9. Applied acos-asin 59.2

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

10. Final simplification 59.2

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

Reproduce

herbie shell --seed 2019120 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))