Average Error: 0.1 → 0.2
Time: 5.0s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\mathsf{log1p}\left(\log \left(e^{\mathsf{expm1}\left(\sin \left({\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}} \cdot {\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{3}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\mathsf{log1p}\left(\log \left(e^{\mathsf{expm1}\left(\sin \left({\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}} \cdot {\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{3}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)
double code(double a, double b) {
	return sin(pow(sqrt(atan2(b, b)), (b - a)));
}
↓
double code(double a, double b) {
	return log1p(log(exp(expm1(sin((pow((sqrt(cbrt(sqrt(atan2(b, b)))) * pow(sqrt(cbrt(sqrt(atan2(b, b)))), 3.0)), (b - a)) * pow(cbrt(sqrt(atan2(b, b))), (b - a))))))));
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
  2. Using strategy rm

  3. Applied log1p-expm1-u0.1

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)}\]
  4. Using strategy rm

  5. Applied add-log-exp0.2

    \[\leadsto \mathsf{log1p}\left(\color{blue}{\log \left(e^{\mathsf{expm1}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)}\right)}\right)\]
  6. Using strategy rm

  7. Applied add-cube-cbrt0.2

    \[\leadsto \mathsf{log1p}\left(\log \left(e^{\mathsf{expm1}\left(\sin \left({\color{blue}{\left(\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right) \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}}^{\left(b - a\right)}\right)\right)}\right)\right)\]

  8. Applied unpow-prod-down0.2

    \[\leadsto \mathsf{log1p}\left(\log \left(e^{\mathsf{expm1}\left(\sin \color{blue}{\left({\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}\right)}\right)\right)\]
  9. Using strategy rm

  10. Applied add-sqr-sqrt0.2

    \[\leadsto \mathsf{log1p}\left(\log \left(e^{\mathsf{expm1}\left(\sin \left({\left(\color{blue}{\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}} \cdot \sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)\]

  11. Applied associate-*l*0.2

    \[\leadsto \mathsf{log1p}\left(\log \left(e^{\mathsf{expm1}\left(\sin \left({\color{blue}{\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}} \cdot \left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}} \cdot \sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)\right)}}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)\]

  12. Simplified0.2

    \[\leadsto \mathsf{log1p}\left(\log \left(e^{\mathsf{expm1}\left(\sin \left({\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}} \cdot \color{blue}{{\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{3}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)\]

  13. Final simplification0.2

    \[\leadsto \mathsf{log1p}\left(\log \left(e^{\mathsf{expm1}\left(\sin \left({\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}} \cdot {\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{3}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)\]

Reproduce

herbie shell --seed 2020053 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))