Random Jason Timeout Test 004

Average Error: 33.9 → 33.9

Time: 13.3s

Precision: 64

• could not determine a ground truth for program body

  1. a = 4.9225014020723465e+29
  2. c = 4.886220545293411e+70

Math

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

↓

\[\left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot \left({\left(\sqrt[3]{\sqrt{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{4} \cdot {\left(\sqrt[3]{\sqrt{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{4}\right)\]

C

double f(double a, double c) {
        double r10941 = c;
        double r10942 = cosh(r10941);
        double r10943 = a;
        double r10944 = log1p(r10943);
        double r10945 = fmod(r10942, r10944);
        return r10945;
}

↓

double f(double a, double c) {
        double r10946 = c;
        double r10947 = cosh(r10946);
        double r10948 = a;
        double r10949 = log1p(r10948);
        double r10950 = fmod(r10947, r10949);
        double r10951 = sqrt(r10950);
        double r10952 = cbrt(r10951);
        double r10953 = r10952 * r10952;
        double r10954 = sqrt(r10951);
        double r10955 = cbrt(r10954);
        double r10956 = 4.0;
        double r10957 = pow(r10955, r10956);
        double r10958 = r10957 * r10957;
        double r10959 = r10953 * r10958;
        return r10959;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 33.9

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

3. Applied add-sqr-sqrt 33.9

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

5. Applied add-cube-cbrt 33.9

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

6. Applied associate-*l* 33.9

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

7. Simplified 33.9

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

9. Applied add-sqr-sqrt 33.9

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

10. Applied sqrt-prod 33.9

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

11. Applied cbrt-prod 33.9

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

12. Applied unpow-prod-down 33.9

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

13. Final simplification 33.9

    \[\leadsto \left(\sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\right) \cdot \left({\left(\sqrt[3]{\sqrt{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{4} \cdot {\left(\sqrt[3]{\sqrt{\sqrt{\left(\left(\cosh c\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}}\right)}^{4}\right)\]

Reproduce

herbie shell --seed 2020003 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  :precision binary64
  (fmod (cosh c) (log1p a)))