Random Jason Timeout Test 004

Average Error: 34.6 → 34.2

Time: 36.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = -5.226464616066758e-97
  2. c = 2.4018878819531603e+93

Math

\[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]

↓

\[\sqrt{\left(\left(\left(\sqrt{\frac{1}{2}} \cdot \sqrt{e^{c} + e^{-c}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt{\left(\left(\left(\sqrt{\frac{1}{2}} \cdot \sqrt{e^{c} + e^{-c}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\log_* (1 + a)\right)\right)}\]

C

double f(double a, double c) {
        double r732829 = c;
        double r732830 = cosh(r732829);
        double r732831 = a;
        double r732832 = log1p(r732831);
        double r732833 = fmod(r732830, r732832);
        return r732833;
}

↓

double f(double a, double c) {
        double r732834 = 0.5;
        double r732835 = sqrt(r732834);
        double r732836 = c;
        double r732837 = exp(r732836);
        double r732838 = -r732836;
        double r732839 = exp(r732838);
        double r732840 = r732837 + r732839;
        double r732841 = sqrt(r732840);
        double r732842 = r732835 * r732841;
        double r732843 = cosh(r732836);
        double r732844 = sqrt(r732843);
        double r732845 = r732842 * r732844;
        double r732846 = a;
        double r732847 = log1p(r732846);
        double r732848 = fmod(r732845, r732847);
        double r732849 = sqrt(r732848);
        double r732850 = r732849 * r732849;
        return r732850;
}

Error

Bits error versus a

Bits error versus c

Derivation

1. Initial program 34.6

   \[\left(\left(\cosh c\right) \bmod \left(\log_* (1 + a)\right)\right)\]
2. Using strategy rm

3. Applied add-sqr-sqrt 34.6

   \[\leadsto \left(\color{blue}{\left(\sqrt{\cosh c} \cdot \sqrt{\cosh c}\right)} \bmod \left(\log_* (1 + a)\right)\right)\]

4. Taylor expanded around -inf 34.5

   \[\leadsto \left(\left(\color{blue}{\left(\sqrt{e^{-1 \cdot c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right)} \cdot \sqrt{\cosh c}\right) \bmod \left(\log_* (1 + a)\right)\right)\]

5. Simplified 34.5

   \[\leadsto \left(\left(\color{blue}{\left(\sqrt{e^{-c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right)} \cdot \sqrt{\cosh c}\right) \bmod \left(\log_* (1 + a)\right)\right)\]
6. Using strategy rm

7. Applied add-sqr-sqrt 34.2

   \[\leadsto \color{blue}{\sqrt{\left(\left(\left(\sqrt{e^{-c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt{\left(\left(\left(\sqrt{e^{-c} + e^{c}} \cdot \sqrt{\frac{1}{2}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\log_* (1 + a)\right)\right)}}\]

8. Final simplification 34.2

   \[\leadsto \sqrt{\left(\left(\left(\sqrt{\frac{1}{2}} \cdot \sqrt{e^{c} + e^{-c}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\log_* (1 + a)\right)\right)} \cdot \sqrt{\left(\left(\left(\sqrt{\frac{1}{2}} \cdot \sqrt{e^{c} + e^{-c}}\right) \cdot \sqrt{\cosh c}\right) \bmod \left(\log_* (1 + a)\right)\right)}\]

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (a c)
  :name "Random Jason Timeout Test 004"
  (fmod (cosh c) (log1p a)))