Average Error: 0.1 → 0.1
Time: 4.3s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(e^{\log \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(e^{\log \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}\right)
double f(double a, double b) {
        double r19826 = b;
        double r19827 = atan2(r19826, r19826);
        double r19828 = sqrt(r19827);
        double r19829 = a;
        double r19830 = r19826 - r19829;
        double r19831 = pow(r19828, r19830);
        double r19832 = sin(r19831);
        return r19832;
}
↓
double f(double a, double b) {
        double r19833 = b;
        double r19834 = atan2(r19833, r19833);
        double r19835 = sqrt(r19834);
        double r19836 = a;
        double r19837 = r19833 - r19836;
        double r19838 = pow(r19835, r19837);
        double r19839 = log(r19838);
        double r19840 = exp(r19839);
        double r19841 = sin(r19840);
        return r19841;
}

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-exp-log0.1

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

  4. Applied pow-exp0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))