Average Error: 0.1 → 0.1
Time: 4.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\sqrt[3]{{\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}^{3}}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\sqrt[3]{{\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}^{3}}\right)
double f(double a, double b) {
        double r4881 = b;
        double r4882 = atan2(r4881, r4881);
        double r4883 = sqrt(r4882);
        double r4884 = a;
        double r4885 = r4881 - r4884;
        double r4886 = pow(r4883, r4885);
        double r4887 = sin(r4886);
        return r4887;
}
↓
double f(double a, double b) {
        double r4888 = b;
        double r4889 = atan2(r4888, r4888);
        double r4890 = sqrt(r4889);
        double r4891 = a;
        double r4892 = r4888 - r4891;
        double r4893 = pow(r4890, r4892);
        double r4894 = 3.0;
        double r4895 = pow(r4893, r4894);
        double r4896 = cbrt(r4895);
        double r4897 = sin(r4896);
        return r4897;
}

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-cbrt-cube0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020020 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))