Average Error: 0.1 → 0.1
Time: 5.2s
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 r9143 = b;
        double r9144 = atan2(r9143, r9143);
        double r9145 = sqrt(r9144);
        double r9146 = a;
        double r9147 = r9143 - r9146;
        double r9148 = pow(r9145, r9147);
        double r9149 = sin(r9148);
        return r9149;
}
↓
double f(double a, double b) {
        double r9150 = b;
        double r9151 = atan2(r9150, r9150);
        double r9152 = sqrt(r9151);
        double r9153 = a;
        double r9154 = r9150 - r9153;
        double r9155 = cbrt(r9154);
        double r9156 = r9155 * r9155;
        double r9157 = pow(r9152, r9156);
        double r9158 = pow(r9157, r9155);
        double r9159 = sin(r9158);
        return r9159;
}

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 2020001 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))