Average Error: 0.2 → 0.2
Time: 4.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{1}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt{1}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(2 \cdot \left(b - a\right)\right)}\right)
double f(double a, double b) {
        double r3206 = b;
        double r3207 = atan2(r3206, r3206);
        double r3208 = sqrt(r3207);
        double r3209 = a;
        double r3210 = r3206 - r3209;
        double r3211 = pow(r3208, r3210);
        double r3212 = sin(r3211);
        return r3212;
}
↓
double f(double a, double b) {
        double r3213 = 1.0;
        double r3214 = sqrt(r3213);
        double r3215 = b;
        double r3216 = a;
        double r3217 = r3215 - r3216;
        double r3218 = pow(r3214, r3217);
        double r3219 = atan2(r3215, r3215);
        double r3220 = sqrt(r3219);
        double r3221 = sqrt(r3220);
        double r3222 = 2.0;
        double r3223 = r3222 * r3217;
        double r3224 = pow(r3221, r3223);
        double r3225 = r3218 * r3224;
        double r3226 = sin(r3225);
        return r3226;
}

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-down0.2

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

  7. Applied *-un-lft-identity0.2

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

  8. Applied sqrt-prod0.2

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

  9. Applied unpow-prod-down0.2

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

  10. Applied associate-*l*0.2

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

  11. Simplified0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020002 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))