Random Jason Timeout Test 012

Average Error: 60.5 → 59.3

Time: 56.6s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.5165618061951008e+80

Math

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

↓

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

C

double f(double a) {
        double r1122991 = a;
        double r1122992 = cosh(r1122991);
        double r1122993 = r1122991 * r1122991;
        double r1122994 = fmod(r1122992, r1122993);
        double r1122995 = log1p(r1122991);
        double r1122996 = pow(r1122994, r1122995);
        double r1122997 = acos(r1122996);
        return r1122997;
}

↓

double f(double a) {
        double r1122998 = a;
        double r1122999 = exp(r1122998);
        double r1123000 = 0.5;
        double r1123001 = r1123000 / r1122999;
        double r1123002 = fma(r1122999, r1123000, r1123001);
        double r1123003 = r1122998 * r1122998;
        double r1123004 = fmod(r1123002, r1123003);
        double r1123005 = sqrt(r1123004);
        double r1123006 = exp(r1123005);
        double r1123007 = log(r1123006);
        double r1123008 = r1123007 * r1123005;
        double r1123009 = log1p(r1122998);
        double r1123010 = pow(r1123008, r1123009);
        double r1123011 = acos(r1123010);
        return r1123011;
}

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

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

5. Simplified 59.6

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

7. Applied add-sqr-sqrt 59.6

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

8. Applied exp-prod 59.6

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

9. Applied log-pow 59.3

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

10. Final simplification 59.3

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

Reproduce

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