Random Jason Timeout Test 004

Average Error: 34.3 → 34.0

Time: 40.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = -7.775903621166249e-209
  2. c = 7.697814709229108e+217

Math

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

↓

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

C

double f(double a, double c) {
        double r931227 = c;
        double r931228 = cosh(r931227);
        double r931229 = a;
        double r931230 = log1p(r931229);
        double r931231 = fmod(r931228, r931230);
        return r931231;
}

↓

double f(double a, double c) {
        double r931232 = c;
        double r931233 = cosh(r931232);
        double r931234 = a;
        double r931235 = log1p(r931234);
        double r931236 = cbrt(r931235);
        double r931237 = r931236 * r931236;
        double r931238 = r931236 * r931237;
        double r931239 = fmod(r931233, r931238);
        double r931240 = cbrt(r931239);
        double r931241 = r931240 * r931240;
        double r931242 = r931241 * r931240;
        double r931243 = sqrt(r931242);
        double r931244 = cbrt(r931236);
        double r931245 = r931244 * r931244;
        double r931246 = r931245 * r931244;
        double r931247 = r931246 * r931237;
        double r931248 = fmod(r931233, r931247);
        double r931249 = sqrt(r931248);
        double r931250 = r931243 * r931249;
        return r931250;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.3

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

3. Applied add-cube-cbrt 34.0

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

5. Applied add-sqr-sqrt 34.0

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

7. Applied add-cube-cbrt 34.0

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

9. Applied add-cube-cbrt 34.0

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

10. Final simplification 34.0

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))