Random Jason Timeout Test 012

Average Error: 60.4 → 59.5

Time: 1.2m

Precision: 64

• could not determine a ground truth for program body

  1. a = 5.03993005917793e+140

Math

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

↓

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

C

double f(double a) {
        double r1656906 = a;
        double r1656907 = cosh(r1656906);
        double r1656908 = r1656906 * r1656906;
        double r1656909 = fmod(r1656907, r1656908);
        double r1656910 = log1p(r1656906);
        double r1656911 = pow(r1656909, r1656910);
        double r1656912 = acos(r1656911);
        return r1656912;
}

↓

double f(double a) {
        double r1656913 = a;
        double r1656914 = cosh(r1656913);
        double r1656915 = r1656913 * r1656913;
        double r1656916 = fmod(r1656914, r1656915);
        double r1656917 = exp(r1656916);
        double r1656918 = log(r1656917);
        double r1656919 = log1p(r1656913);
        double r1656920 = pow(r1656918, r1656919);
        double r1656921 = acos(r1656920);
        double r1656922 = sqrt(r1656921);
        double r1656923 = r1656922 * r1656922;
        return r1656923;
}

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

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

6. Final simplification 59.5

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

Reproduce

herbie shell --seed 2019151 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))