Random Jason Timeout Test 012

Average Error: 61.2 → 60.2

Time: 57.1s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.8423430180599544e+124

Math

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

↓

\[2 \cdot \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)\]

C

double f(double a) {
        double r13471 = a;
        double r13472 = cosh(r13471);
        double r13473 = r13471 * r13471;
        double r13474 = fmod(r13472, r13473);
        double r13475 = log1p(r13471);
        double r13476 = pow(r13474, r13475);
        double r13477 = acos(r13476);
        return r13477;
}

↓

double f(double a) {
        double r13478 = 2.0;
        double r13479 = a;
        double r13480 = cosh(r13479);
        double r13481 = r13479 * r13479;
        double r13482 = fmod(r13480, r13481);
        double r13483 = log1p(r13479);
        double r13484 = pow(r13482, r13483);
        double r13485 = acos(r13484);
        double r13486 = exp(r13485);
        double r13487 = cbrt(r13486);
        double r13488 = log(r13487);
        double r13489 = r13478 * r13488;
        double r13490 = exp(r13482);
        double r13491 = log(r13490);
        double r13492 = pow(r13491, r13483);
        double r13493 = acos(r13492);
        double r13494 = exp(r13493);
        double r13495 = cbrt(r13494);
        double r13496 = log(r13495);
        double r13497 = r13489 + r13496;
        return r13497;
}

Error

Bits error versus a

Derivation

1. Initial program 61.2

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

3. Applied add-log-exp 61.2

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

5. Applied add-cube-cbrt 61.2

   \[\leadsto \log \color{blue}{\left(\left(\sqrt[3]{e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}} \cdot \sqrt[3]{e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) \cdot \sqrt[3]{e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)}\]

6. Applied log-prod 61.2

   \[\leadsto \color{blue}{\log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}} \cdot \sqrt[3]{e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)}\]

7. Simplified 61.2

   \[\leadsto \color{blue}{2 \cdot \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)} + \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)\]
8. Using strategy rm

9. Applied add-log-exp 60.2

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

10. Final simplification 60.2

    \[\leadsto 2 \cdot \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right) + \log \left(\sqrt[3]{e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}}\right)\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))