Random Jason Timeout Test 012

Average Error: 60.5 → 59.3

Time: 57.7s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.5165618061951008e+80

Math

\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

↓

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

C

double f(double a) {
        double r1054519 = a;
        double r1054520 = cosh(r1054519);
        double r1054521 = r1054519 * r1054519;
        double r1054522 = fmod(r1054520, r1054521);
        double r1054523 = log1p(r1054519);
        double r1054524 = pow(r1054522, r1054523);
        double r1054525 = acos(r1054524);
        return r1054525;
}

↓

double f(double a) {
        double r1054526 = 0.5;
        double r1054527 = a;
        double r1054528 = exp(r1054527);
        double r1054529 = r1054526 * r1054528;
        double r1054530 = r1054526 / r1054528;
        double r1054531 = r1054529 + r1054530;
        double r1054532 = r1054527 * r1054527;
        double r1054533 = fmod(r1054531, r1054532);
        double r1054534 = sqrt(r1054533);
        double r1054535 = exp(r1054534);
        double r1054536 = log(r1054535);
        double r1054537 = r1054534 * r1054536;
        double r1054538 = log1p(r1054527);
        double r1054539 = pow(r1054537, r1054538);
        double r1054540 = acos(r1054539);
        return r1054540;
}

Error

Bits error versus a

Derivation

1. Initial program 60.5

   \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
2. Using strategy rm

3. Applied add-log-exp 59.5

   \[\leadsto \cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

4. Taylor expanded around inf 59.6

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

5. Simplified 59.6

   \[\leadsto \cos^{-1} \left({\left(\log \left(e^{\left(\color{blue}{\left(\frac{1}{2} \cdot e^{a} + \frac{\frac{1}{2}}{e^{a}}\right)} \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
6. Using strategy rm

7. Applied add-sqr-sqrt 59.6

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

8. Applied exp-prod 59.6

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

9. Applied log-pow 59.3

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

10. Final simplification 59.3

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

Reproduce

herbie shell --seed 2019142 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))