Average Error: 0.1 → 0.1
Time: 5.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\sqrt[3]{{\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{3}{2}\right)}}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\sqrt[3]{{\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{3}{2}\right)}}\right)
double code(double a, double b) {
	return ((double) sin(((double) pow(((double) sqrt(((double) atan2(b, b)))), ((double) (b - a))))));
}
↓
double code(double a, double b) {
	return ((double) sin(((double) cbrt(((double) pow(((double) atan2(b, b)), ((double) (((double) (b - a)) * 1.5))))))));
}

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 pow1/20.1

    \[\leadsto \sin \left({\color{blue}{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{2}}\right)}}^{\left(b - a\right)}\right)\]

  4. Applied pow-pow0.1

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

  6. Applied add-cbrt-cube0.1

    \[\leadsto \sin \color{blue}{\left(\sqrt[3]{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right) \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}}\right)}\]

  7. Simplified0.1

    \[\leadsto \sin \left(\sqrt[3]{\color{blue}{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}\right)}^{\frac{3}{2}}}}\right)\]
  8. Using strategy rm

  9. Applied add-cbrt-cube0.1

    \[\leadsto \sin \color{blue}{\left(\sqrt[3]{\left(\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}\right)}^{\frac{3}{2}}} \cdot \sqrt[3]{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}\right)}^{\frac{3}{2}}}\right) \cdot \sqrt[3]{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}\right)}^{\frac{3}{2}}}}\right)}\]

  10. Simplified0.1

    \[\leadsto \sin \left(\sqrt[3]{\color{blue}{{\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{3}{2}\right)}}}\right)\]

  11. Final simplification0.1

    \[\leadsto \sin \left(\sqrt[3]{{\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{3}{2}\right)}}\right)\]

Reproduce

herbie shell --seed 2020128 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))