Average Error: 0.2 → 0.1
Time: 1.1m
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{b - a}{4}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{b - a}{4}\right)}\right)
double f(double a, double b) {
        double r3276014 = b;
        double r3276015 = atan2(r3276014, r3276014);
        double r3276016 = sqrt(r3276015);
        double r3276017 = a;
        double r3276018 = r3276014 - r3276017;
        double r3276019 = pow(r3276016, r3276018);
        double r3276020 = sin(r3276019);
        return r3276020;
}
↓
double f(double a, double b) {
        double r3276021 = b;
        double r3276022 = atan2(r3276021, r3276021);
        double r3276023 = sqrt(r3276022);
        double r3276024 = sqrt(r3276023);
        double r3276025 = a;
        double r3276026 = r3276021 - r3276025;
        double r3276027 = cbrt(r3276026);
        double r3276028 = r3276027 * r3276027;
        double r3276029 = pow(r3276024, r3276028);
        double r3276030 = pow(r3276029, r3276027);
        double r3276031 = 4.0;
        double r3276032 = r3276026 / r3276031;
        double r3276033 = pow(r3276022, r3276032);
        double r3276034 = r3276030 * r3276033;
        double r3276035 = sin(r3276034);
        return r3276035;
}

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 0.2

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

  3. Applied add-sqr-sqrt0.2

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

  4. Applied sqrt-prod0.2

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

  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 pow1/20.1

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

  8. Applied sqrt-pow10.1

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

  9. Applied pow-pow0.1

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

  10. Simplified0.1

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

  12. Applied add-cube-cbrt0.1

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

  13. Applied pow-unpow0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))