Average Error: 0.1 → 0.1
Time: 21.0s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(e^{\frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4} \cdot \left(\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \left(b - a\right)\right) \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(e^{\frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4} \cdot \left(\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \left(b - a\right)\right) \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r763240 = b;
        double r763241 = atan2(r763240, r763240);
        double r763242 = sqrt(r763241);
        double r763243 = a;
        double r763244 = r763240 - r763243;
        double r763245 = pow(r763242, r763244);
        double r763246 = sin(r763245);
        return r763246;
}
↓
double f(double a, double b) {
        double r763247 = b;
        double r763248 = atan2(r763247, r763247);
        double r763249 = log(r763248);
        double r763250 = cbrt(r763249);
        double r763251 = 4.0;
        double r763252 = r763250 / r763251;
        double r763253 = a;
        double r763254 = r763247 - r763253;
        double r763255 = r763250 * r763254;
        double r763256 = r763255 * r763250;
        double r763257 = r763252 * r763256;
        double r763258 = exp(r763257);
        double r763259 = sqrt(r763248);
        double r763260 = sqrt(r763259);
        double r763261 = pow(r763260, r763254);
        double r763262 = r763258 * r763261;
        double r763263 = sin(r763262);
        return r763263;
}

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

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

  4. Applied unpow-prod-down0.1

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

  5. Taylor expanded around -inf 0.1

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

  6. Simplified0.1

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

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

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

  9. Applied add-cube-cbrt0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\left(b - a\right) \cdot \frac{\color{blue}{\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}\right) \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}}{1 \cdot 4}}\right)\]

  10. Applied times-frac0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\left(b - a\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{1} \cdot \frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4}\right)}}\right)\]

  11. Applied associate-*r*0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\color{blue}{\left(\left(b - a\right) \cdot \frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{1}\right) \cdot \frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4}}}\right)\]

  12. Simplified0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot e^{\color{blue}{\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \left(b - a\right)\right)\right)} \cdot \frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4}}\right)\]

  13. Final simplification0.1

    \[\leadsto \sin \left(e^{\frac{\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}}{4} \cdot \left(\left(\sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)} \cdot \left(b - a\right)\right) \cdot \sqrt[3]{\log \left(\tan^{-1}_* \frac{b}{b}\right)}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

Reproduce

herbie shell --seed 2019151 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))