Random Jason Timeout Test 004

Average Error: 34.8 → 34.9

Time: 39.6s

Precision: 64

• could not determine a ground truth for program body

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

Math

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

↓

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

C

double f(double a, double c) {
        double r624211 = c;
        double r624212 = cosh(r624211);
        double r624213 = a;
        double r624214 = log1p(r624213);
        double r624215 = fmod(r624212, r624214);
        return r624215;
}

↓

double f(double a, double c) {
        double r624216 = 1.0;
        double r624217 = c;
        double r624218 = r624217 * r624217;
        double r624219 = 0.041666666666666664;
        double r624220 = r624218 * r624219;
        double r624221 = r624218 * r624220;
        double r624222 = 0.5;
        double r624223 = r624218 * r624222;
        double r624224 = r624221 + r624223;
        double r624225 = r624216 + r624224;
        double r624226 = a;
        double r624227 = log1p(r624226);
        double r624228 = fmod(r624225, r624227);
        double r624229 = cbrt(r624228);
        double r624230 = log(r624228);
        double r624231 = exp(r624230);
        double r624232 = cbrt(r624231);
        double r624233 = r624232 * r624229;
        double r624234 = r624229 * r624233;
        return r624234;
}

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-rgt-in 34.9

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

7. Applied add-cube-cbrt 34.9

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

9. Applied add-exp-log 34.9

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

10. Final simplification 34.9

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

Reproduce

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