Average Error: 0.1 → 0.1
Time: 16.0s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left({\left(\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)}\right)
double f(double a, double b) {
        double r31195 = b;
        double r31196 = atan2(r31195, r31195);
        double r31197 = sqrt(r31196);
        double r31198 = a;
        double r31199 = r31195 - r31198;
        double r31200 = pow(r31197, r31199);
        double r31201 = sin(r31200);
        return r31201;
}
↓
double f(double a, double b) {
        double r31202 = b;
        double r31203 = atan2(r31202, r31202);
        double r31204 = sqrt(r31203);
        double r31205 = a;
        double r31206 = r31202 - r31205;
        double r31207 = cbrt(r31206);
        double r31208 = r31207 * r31207;
        double r31209 = pow(r31204, r31208);
        double r31210 = pow(r31209, r31207);
        double r31211 = sin(r31210);
        return r31211;
}

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-cube-cbrt0.1

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

  4. Applied pow-unpow0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019298 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))