Average Error: 33.4 → 33.4
Time: 17.6s
Precision: 64
\[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]
↓
\[\left|\left(\sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}\right)}^{3}}}\right) \bmod a\right)}\right|\]
\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|
↓
\left|\left(\sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}\right)}^{3}}}\right) \bmod a\right)}\right|
double code(double a) {
	return fabs(fmod(atan2(expm1(sin(expm1(a))), atan(a)), a));
}
↓
double code(double a) {
	return fabs(((cbrt(fmod(cbrt(cbrt(pow(pow(atan2(expm1(sin(expm1(a))), atan(a)), 3.0), 3.0))), a)) * cbrt(fmod(cbrt(cbrt(pow(pow(atan2(expm1(sin(expm1(a))), atan(a)), 3.0), 3.0))), a))) * cbrt(fmod(cbrt(cbrt(pow(cbrt(pow(pow(atan2(expm1(sin(expm1(a))), atan(a)), 3.0), 3.0)), 3.0))), a))));
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 33.4

    \[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]
  2. Using strategy rm

  3. Applied add-cbrt-cube33.4

    \[\leadsto \left|\left(\color{blue}{\left(\sqrt[3]{\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a} \cdot \tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \cdot \tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}}\right)} \bmod a\right)\right|\]

  4. Simplified33.4

    \[\leadsto \left|\left(\left(\sqrt[3]{\color{blue}{{\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}}}\right) \bmod a\right)\right|\]
  5. Using strategy rm

  6. Applied add-cbrt-cube33.5

    \[\leadsto \left|\left(\left(\sqrt[3]{\color{blue}{\sqrt[3]{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3} \cdot {\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right) \cdot {\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}}}}\right) \bmod a\right)\right|\]

  7. Simplified33.5

    \[\leadsto \left|\left(\left(\sqrt[3]{\sqrt[3]{\color{blue}{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}}\right) \bmod a\right)\right|\]
  8. Using strategy rm

  9. Applied add-cube-cbrt33.5

    \[\leadsto \left|\color{blue}{\left(\sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)}}\right|\]
  10. Using strategy rm

  11. Applied add-cbrt-cube33.4

    \[\leadsto \left|\left(\sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\color{blue}{\left(\sqrt[3]{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3} \cdot {\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right) \cdot {\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}}\right)}}^{3}}}\right) \bmod a\right)}\right|\]

  12. Simplified33.4

    \[\leadsto \left|\left(\sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{\color{blue}{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right)}^{3}}}\right) \bmod a\right)}\right|\]

  13. Final simplification33.4

    \[\leadsto \left|\left(\sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}}\right) \bmod a\right)}\right) \cdot \sqrt[3]{\left(\left(\sqrt[3]{\sqrt[3]{{\left(\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}\right)}^{3}}\right)}^{3}}}\right) \bmod a\right)}\right|\]

Reproduce

herbie shell --seed 2020106 
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  :precision binary64
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))