Average Error: 0.1 → 0.1
Time: 18.3s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{\sqrt[3]{2} \cdot \sqrt[3]{2}}\right)}\right)}^{\left(\frac{b - a}{\sqrt[3]{2}}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{\sqrt[3]{2} \cdot \sqrt[3]{2}}\right)}\right)}^{\left(\frac{b - a}{\sqrt[3]{2}}\right)}\right)
double f(double a, double b) {
        double r1926355 = b;
        double r1926356 = atan2(r1926355, r1926355);
        double r1926357 = sqrt(r1926356);
        double r1926358 = a;
        double r1926359 = r1926355 - r1926358;
        double r1926360 = pow(r1926357, r1926359);
        double r1926361 = sin(r1926360);
        return r1926361;
}
↓
double f(double a, double b) {
        double r1926362 = b;
        double r1926363 = atan2(r1926362, r1926362);
        double r1926364 = 1.0;
        double r1926365 = 2.0;
        double r1926366 = cbrt(r1926365);
        double r1926367 = r1926366 * r1926366;
        double r1926368 = r1926364 / r1926367;
        double r1926369 = pow(r1926363, r1926368);
        double r1926370 = a;
        double r1926371 = r1926362 - r1926370;
        double r1926372 = r1926371 / r1926366;
        double r1926373 = pow(r1926369, r1926372);
        double r1926374 = sin(r1926373);
        return r1926374;
}

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 sqrt-pow20.1

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

  5. Applied add-cube-cbrt0.1

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

  6. Applied *-un-lft-identity0.1

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

  7. Applied times-frac0.1

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

  8. Applied pow-unpow0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))