Random Jason Timeout Test 004

Average Error: 34.8 → 34.9

Time: 36.4s

Precision: 64

• could not determine a ground truth for program body

  1. a = -3.207049642396392e-29
  2. c = 2.771860798667937e+293

Math

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

↓

\[\sqrt[3]{\left(\left(1 + \left(\left(\left(c \cdot c\right) \cdot \frac{1}{24}\right) \cdot \left(c \cdot c\right) + \left(c \cdot c\right) \cdot \frac{1}{2}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \left(\sqrt[3]{e^{\log \left(\left(1 + \left(\left(\left(c \cdot c\right) \cdot \frac{1}{24}\right) \cdot \left(c \cdot c\right) + \left(c \cdot c\right) \cdot \frac{1}{2}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\left(\left(1 + \left(\left(\left(c \cdot c\right) \cdot \frac{1}{24}\right) \cdot \left(c \cdot c\right) + \left(c \cdot c\right) \cdot \frac{1}{2}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\]

C

double f(double a, double c) {
        double r649212 = c;
        double r649213 = cosh(r649212);
        double r649214 = a;
        double r649215 = log1p(r649214);
        double r649216 = fmod(r649213, r649215);
        return r649216;
}

↓

double f(double a, double c) {
        double r649217 = 1.0;
        double r649218 = c;
        double r649219 = r649218 * r649218;
        double r649220 = 0.041666666666666664;
        double r649221 = r649219 * r649220;
        double r649222 = r649221 * r649219;
        double r649223 = 0.5;
        double r649224 = r649219 * r649223;
        double r649225 = r649222 + r649224;
        double r649226 = r649217 + r649225;
        double r649227 = a;
        double r649228 = log1p(r649227);
        double r649229 = fmod(r649226, r649228);
        double r649230 = cbrt(r649229);
        double r649231 = log(r649229);
        double r649232 = exp(r649231);
        double r649233 = cbrt(r649232);
        double r649234 = r649233 * r649230;
        double r649235 = r649230 * r649234;
        return r649235;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.8

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

2. Taylor expanded around 0 34.9

   \[\leadsto \left(\color{blue}{\left(\frac{1}{2} \cdot {c}^{2} + \left(\frac{1}{24} \cdot {c}^{4} + 1\right)\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]

3. Simplified 34.8

   \[\leadsto \left(\color{blue}{\left(1 + \left(c \cdot c\right) \cdot \left(\frac{1}{2} + \frac{1}{24} \cdot \left(c \cdot c\right)\right)\right)} \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
4. Using strategy rm

5. Applied distribute-lft-in 34.9

   \[\leadsto \left(\left(1 + \color{blue}{\left(\left(c \cdot c\right) \cdot \frac{1}{2} + \left(c \cdot c\right) \cdot \left(\frac{1}{24} \cdot \left(c \cdot c\right)\right)\right)}\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)\]
6. Using strategy rm

7. Applied add-cube-cbrt 34.9

   \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(1 + \left(\left(c \cdot c\right) \cdot \frac{1}{2} + \left(c \cdot c\right) \cdot \left(\frac{1}{24} \cdot \left(c \cdot c\right)\right)\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \sqrt[3]{\left(\left(1 + \left(\left(c \cdot c\right) \cdot \frac{1}{2} + \left(c \cdot c\right) \cdot \left(\frac{1}{24} \cdot \left(c \cdot c\right)\right)\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(1 + \left(\left(c \cdot c\right) \cdot \frac{1}{2} + \left(c \cdot c\right) \cdot \left(\frac{1}{24} \cdot \left(c \cdot c\right)\right)\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}\]
8. Using strategy rm

9. Applied add-exp-log 34.9

   \[\leadsto \left(\sqrt[3]{\color{blue}{e^{\log \left(\left(1 + \left(\left(c \cdot c\right) \cdot \frac{1}{2} + \left(c \cdot c\right) \cdot \left(\frac{1}{24} \cdot \left(c \cdot c\right)\right)\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}}} \cdot \sqrt[3]{\left(\left(1 + \left(\left(c \cdot c\right) \cdot \frac{1}{2} + \left(c \cdot c\right) \cdot \left(\frac{1}{24} \cdot \left(c \cdot c\right)\right)\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right) \cdot \sqrt[3]{\left(\left(1 + \left(\left(c \cdot c\right) \cdot \frac{1}{2} + \left(c \cdot c\right) \cdot \left(\frac{1}{24} \cdot \left(c \cdot c\right)\right)\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\]

10. Final simplification 34.9

    \[\leadsto \sqrt[3]{\left(\left(1 + \left(\left(\left(c \cdot c\right) \cdot \frac{1}{24}\right) \cdot \left(c \cdot c\right) + \left(c \cdot c\right) \cdot \frac{1}{2}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)} \cdot \left(\sqrt[3]{e^{\log \left(\left(1 + \left(\left(\left(c \cdot c\right) \cdot \frac{1}{24}\right) \cdot \left(c \cdot c\right) + \left(c \cdot c\right) \cdot \frac{1}{2}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}} \cdot \sqrt[3]{\left(\left(1 + \left(\left(\left(c \cdot c\right) \cdot \frac{1}{24}\right) \cdot \left(c \cdot c\right) + \left(c \cdot c\right) \cdot \frac{1}{2}\right)\right) \bmod \left(\mathsf{log1p}\left(a\right)\right)\right)}\right)\]

Reproduce

herbie shell --seed 2019172 
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))