Random Jason Timeout Test 004

Average Error: 34.4 → 34.5

Time: 15.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = -4.7537565269336305e-207
  2. c = -2.9035703808313647e+94

Math

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

↓

\[{\left({\left(\sqrt[3]{\sqrt{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{\left(\sqrt{5}\right)}\right)}^{\left(\sqrt{5}\right)} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

C

double f(double a, double c) {
        double r13296 = c;
        double r13297 = cosh(r13296);
        double r13298 = a;
        double r13299 = log1p(r13298);
        double r13300 = fmod(r13297, r13299);
        return r13300;
}

↓

double f(double a, double c) {
        double r13301 = c;
        double r13302 = cosh(r13301);
        double r13303 = a;
        double r13304 = log1p(r13303);
        double r13305 = fmod(r13302, r13304);
        double r13306 = log(r13305);
        double r13307 = exp(r13306);
        double r13308 = sqrt(r13307);
        double r13309 = cbrt(r13308);
        double r13310 = 5.0;
        double r13311 = sqrt(r13310);
        double r13312 = pow(r13309, r13311);
        double r13313 = pow(r13312, r13311);
        double r13314 = sqrt(r13305);
        double r13315 = cbrt(r13314);
        double r13316 = r13313 * r13315;
        return r13316;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.4

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

3. Applied add-sqr-sqrt 34.5

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

5. Applied add-cube-cbrt 34.5

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

6. Applied associate-*r* 34.5

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

7. Simplified 34.5

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{5}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]
8. Using strategy rm

9. Applied add-sqr-sqrt 34.5

   \[\leadsto {\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\color{blue}{\left(\sqrt{5} \cdot \sqrt{5}\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

10. Applied pow-unpow 34.5

    \[\leadsto \color{blue}{{\left({\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right)}^{\left(\sqrt{5}\right)}\right)}^{\left(\sqrt{5}\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]
11. Using strategy rm

12. Applied add-exp-log 34.5

    \[\leadsto {\left({\left(\sqrt[3]{\sqrt{\color{blue}{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}}\right)}^{\left(\sqrt{5}\right)}\right)}^{\left(\sqrt{5}\right)} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

13. Final simplification 34.5

    \[\leadsto {\left({\left(\sqrt[3]{\sqrt{e^{\log \left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{\left(\sqrt{5}\right)}\right)}^{\left(\sqrt{5}\right)} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))