Random Jason Timeout Test 004

Average Error: 33.7 → 33.4

Time: 36.2s

Precision: 64

• could not determine a ground truth for program body

  1. a = 8.127274774152907e-69
  2. c = -8.077195036329744e+39

Math

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

↓

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

C

double f(double a, double c) {
        double r21381 = c;
        double r21382 = cosh(r21381);
        double r21383 = a;
        double r21384 = log1p(r21383);
        double r21385 = fmod(r21382, r21384);
        return r21385;
}

↓

double f(double a, double c) {
        double r21386 = c;
        double r21387 = cosh(r21386);
        double r21388 = a;
        double r21389 = log1p(r21388);
        double r21390 = cbrt(r21389);
        double r21391 = cbrt(r21390);
        double r21392 = r21391 * r21391;
        double r21393 = r21391 * r21392;
        double r21394 = cbrt(r21393);
        double r21395 = r21390 * r21390;
        double r21396 = cbrt(r21395);
        double r21397 = r21394 * r21396;
        double r21398 = cbrt(r21397);
        double r21399 = r21398 * r21396;
        double r21400 = r21390 * r21399;
        double r21401 = r21400 * r21390;
        double r21402 = fmod(r21387, r21401);
        return r21402;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.7

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

3. Applied add-cube-cbrt 33.4

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

5. Applied add-cube-cbrt 33.4

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

6. Applied cbrt-prod 33.4

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

8. Applied add-cube-cbrt 33.4

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

9. Applied cbrt-prod 33.4

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

11. Applied add-cube-cbrt 33.4

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

12. Final simplification 33.4

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))