Random Jason Timeout Test 004

Average Error: 34.2 → 33.9

Time: 44.9s

Precision: 64

• could not determine a ground truth for program body

  1. a = 5.0362447883134526e+148
  2. c = 1.0422426701817188e+213

Math

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

↓

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

C

double f(double a, double c) {
        double r471564 = c;
        double r471565 = cosh(r471564);
        double r471566 = a;
        double r471567 = log1p(r471566);
        double r471568 = fmod(r471565, r471567);
        return r471568;
}

↓

double f(double a, double c) {
        double r471569 = c;
        double r471570 = cosh(r471569);
        double r471571 = a;
        double r471572 = log1p(r471571);
        double r471573 = cbrt(r471572);
        double r471574 = r471573 * r471573;
        double r471575 = cbrt(r471574);
        double r471576 = log(r471575);
        double r471577 = exp(r471576);
        double r471578 = cbrt(r471573);
        double r471579 = r471577 * r471578;
        double r471580 = cbrt(r471579);
        double r471581 = r471580 * r471578;
        double r471582 = r471581 * r471578;
        double r471583 = r471574 * r471582;
        double r471584 = fmod(r471570, r471583);
        return r471584;
}

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-cube-cbrt 33.9

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

5. Applied add-cube-cbrt 33.9

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

7. Applied add-cube-cbrt 33.9

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

8. Applied cbrt-prod 33.9

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

10. Applied add-exp-log 33.9

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

11. Final simplification 33.9

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

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))