Random Jason Timeout Test 004

Average Error: 33.9 → 33.5

Time: 43.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.8325806633261013e-47
  2. c = 1.5165618061951008e+80

Math

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

↓

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

C

double f(double a, double c) {
        double r1260653 = c;
        double r1260654 = cosh(r1260653);
        double r1260655 = a;
        double r1260656 = log1p(r1260655);
        double r1260657 = fmod(r1260654, r1260656);
        return r1260657;
}

↓

double f(double a, double c) {
        double r1260658 = c;
        double r1260659 = cosh(r1260658);
        double r1260660 = a;
        double r1260661 = log1p(r1260660);
        double r1260662 = cbrt(r1260661);
        double r1260663 = cbrt(r1260662);
        double r1260664 = r1260663 * r1260663;
        double r1260665 = r1260663 * r1260664;
        double r1260666 = r1260665 * r1260662;
        double r1260667 = r1260662 * r1260666;
        double r1260668 = fmod(r1260659, r1260667);
        double r1260669 = sqrt(r1260668);
        double r1260670 = r1260662 * r1260662;
        double r1260671 = cbrt(r1260670);
        double r1260672 = r1260663 * r1260671;
        double r1260673 = r1260672 * r1260666;
        double r1260674 = fmod(r1260659, r1260673);
        double r1260675 = sqrt(r1260674);
        double r1260676 = r1260669 * r1260675;
        return r1260676;
}

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-cube-cbrt 33.6

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

5. Applied add-cube-cbrt 33.6

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

7. Applied add-sqr-sqrt 33.6

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

9. Applied add-cube-cbrt 33.5

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

10. Applied cbrt-prod 33.5

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

11. Final simplification 33.5

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

Reproduce

herbie shell --seed 2019142 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))