Average Error: 0.1 → 0.3
Time: 3.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\log \left(\mathsf{expm1}\left(\mathsf{log1p}\left(e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}\right)\right)\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\log \left(\mathsf{expm1}\left(\mathsf{log1p}\left(e^{{\left(\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 sin(log(expm1(log1p(exp(pow(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-log-exp0.3

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

  5. Applied expm1-log1p-u0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))