Random Jason Timeout Test 004

Average Error: 34.3 → 34.3

Time: 47.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = -8.63564454871475e-101
  2. c = 9.398956422981174e+33

Math

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

↓

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

C

double f(double a, double c) {
        double r923278 = c;
        double r923279 = cosh(r923278);
        double r923280 = a;
        double r923281 = log1p(r923280);
        double r923282 = fmod(r923279, r923281);
        return r923282;
}

↓

double f(double a, double c) {
        double r923283 = c;
        double r923284 = cosh(r923283);
        double r923285 = a;
        double r923286 = log1p(r923285);
        double r923287 = fmod(r923284, r923286);
        double r923288 = sqrt(r923287);
        double r923289 = sqrt(r923288);
        double r923290 = r923289 * r923289;
        double r923291 = r923290 * r923290;
        return r923291;
}

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-sqr-sqrt 34.3

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

5. Applied add-sqr-sqrt 34.3

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

6. Applied add-sqr-sqrt 34.3

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

7. Applied sqrt-prod 34.3

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

8. Applied swap-sqr 34.3

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

9. Final simplification 34.3

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

Reproduce

herbie shell --seed 2019151 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))