Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sqrt[3]{{\left(\sin \left({\left({\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{3} \cdot \sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\right)}^{3}}\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sqrt[3]{{\left(\sin \left({\left({\left(\sqrt{\sqrt[3]{\sqrt{\tan^{-1}_* \frac{b}{b}}}}\right)}^{3} \cdot \sqrt{\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)}^{3}}
double code(double a, double b) {
	return sin(pow(sqrt(atan2(b, b)), (b - a)));
}
↓
double code(double a, double b) {
	return cbrt(pow(sin((pow((pow(sqrt(cbrt(sqrt(atan2(b, b)))), 3.0) * sqrt(cbrt(sqrt(atan2(b, b))))), (b - a)) * pow(cbrt(sqrt(atan2(b, b))), (b - a)))), 3.0));
}

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 add-cube-cbrt0.1

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

  4. Applied unpow-prod-down0.1

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

  6. Applied add-sqr-sqrt0.1

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

  7. Applied associate-*r*0.1

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

  8. Simplified0.1

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

  10. Applied add-cbrt-cube0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020053 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))