Random Jason Timeout Test 004

Average Error: 34.2 → 34.2

Time: 15.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.8761317066315612e+62
  2. c = -9.598405931812191e+260

Math

\[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

↓

\[\sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

C

double f(double a, double c) {
        double r17028 = c;
        double r17029 = cosh(r17028);
        double r17030 = a;
        double r17031 = log1p(r17030);
        double r17032 = fmod(r17029, r17031);
        return r17032;
}

↓

double f(double a, double c) {
        double r17033 = c;
        double r17034 = cosh(r17033);
        double r17035 = cbrt(r17034);
        double r17036 = r17035 * r17035;
        double r17037 = sqrt(r17036);
        double r17038 = sqrt(r17035);
        double r17039 = sqrt(r17034);
        double r17040 = r17038 * r17039;
        double r17041 = r17037 * r17040;
        double r17042 = a;
        double r17043 = log1p(r17042);
        double r17044 = fmod(r17041, r17043);
        double r17045 = sqrt(r17044);
        double r17046 = r17045 * r17045;
        return r17046;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.2

   \[\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
2. Using strategy rm

3. Applied add-sqr-sqrt 34.2

   \[\leadsto \left(\color{blue}{\left(\sqrt{\cosh c} \cdot \sqrt{\cosh c}\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
4. Using strategy rm

5. Applied add-cube-cbrt 34.2

   \[\leadsto \left(\left(\sqrt{\color{blue}{\left(\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}\right) \cdot \sqrt[3]{\cosh c}}} \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

6. Applied sqrt-prod 34.2

   \[\leadsto \left(\left(\color{blue}{\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \sqrt{\sqrt[3]{\cosh c}}\right)} \cdot \sqrt{\cosh c}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

7. Applied associate-*l* 34.2

   \[\leadsto \left(\color{blue}{\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
8. Using strategy rm

9. Applied add-sqr-sqrt 34.2

   \[\leadsto \color{blue}{\sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

10. Final simplification 34.2

    \[\leadsto \sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt{\left(\left(\sqrt{\sqrt[3]{\cosh c} \cdot \sqrt[3]{\cosh c}} \cdot \left(\sqrt{\sqrt[3]{\cosh c}} \cdot \sqrt{\cosh c}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))