Average Error: 0.1 → 0.1
Time: 5.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)} \cdot \left({\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)} \cdot \left({\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\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 sin((pow(sqrt(sqrt((cbrt(atan2(b, b)) * cbrt(atan2(b, b))))), (b - a)) * (pow(sqrt(sqrt(cbrt(atan2(b, b)))), (b - a)) * pow(sqrt(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 add-sqr-sqrt0.1

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

  4. Applied sqrt-prod0.1

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

  5. Applied unpow-prod-down0.1

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

  7. Applied add-cube-cbrt0.1

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

  8. Applied sqrt-prod0.1

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

  9. Applied sqrt-prod0.1

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

  10. Applied unpow-prod-down0.1

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

  11. Applied associate-*l*0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020075 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))