Average Error: 33.5 → 33.5
Time: 16.7s
Precision: 64
\[\left|\left(\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right) \bmod a\right)\right|\]
↓
\[\left|\left(\left(\sqrt[3]{\log \left(\sqrt[3]{{\left({\left(e^{{\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}}\right)}^{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)}\right)}^{\left(\sqrt[3]{3}\right)}}\right)}\right) \bmod a\right)\right|\]
\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(\left(\sqrt[3]{\log \left(\sqrt[3]{{\left({\left(e^{{\left(\tan^{-1}_* \frac{\mathsf{expm1}\left(\sin \left(\mathsf{expm1}\left(a\right)\right)\right)}{\tan^{-1} a}\right)}^{3}}\right)}^{\left(\sqrt[3]{3} \cdot \sqrt[3]{3}\right)}\right)}^{\left(\sqrt[3]{3}\right)}}\right)}\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(fmod(cbrt(log(cbrt(pow(pow(exp(pow(atan2(expm1(sin(expm1(a))), atan(a)), 3.0)), (cbrt(3.0) * cbrt(3.0))), cbrt(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 33.5

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

  3. Applied add-cbrt-cube33.6

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

  4. Simplified33.6

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

  6. Applied add-log-exp33.6

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

  8. Applied add-cbrt-cube33.6

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

  9. Simplified33.6

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

  11. Applied add-cube-cbrt33.6

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

  12. Applied pow-unpow33.5

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

  13. Final simplification33.5

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

Reproduce

herbie shell --seed 2020053 
(FPCore (a)
  :name "Random Jason Timeout Test 006"
  :precision binary64
  (fabs (fmod (atan2 (expm1 (sin (expm1 a))) (atan a)) a)))