Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\sqrt[3]{{\left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}\right)}^{\left(\sqrt{\frac{3}{2}}\right)}\right)}^{\left(\sqrt{\frac{3}{2}}\right)}}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\sqrt[3]{{\left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}\right)}^{\left(\sqrt{\frac{3}{2}}\right)}\right)}^{\left(\sqrt{\frac{3}{2}}\right)}}\right)
double f(double a, double b) {
        double r14942 = b;
        double r14943 = atan2(r14942, r14942);
        double r14944 = sqrt(r14943);
        double r14945 = a;
        double r14946 = r14942 - r14945;
        double r14947 = pow(r14944, r14946);
        double r14948 = sin(r14947);
        return r14948;
}
↓
double f(double a, double b) {
        double r14949 = b;
        double r14950 = atan2(r14949, r14949);
        double r14951 = a;
        double r14952 = r14949 - r14951;
        double r14953 = pow(r14950, r14952);
        double r14954 = 1.5;
        double r14955 = sqrt(r14954);
        double r14956 = pow(r14953, r14955);
        double r14957 = pow(r14956, r14955);
        double r14958 = cbrt(r14957);
        double r14959 = sin(r14958);
        return r14959;
}

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 pow1/20.1

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

  4. Applied pow-pow0.1

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

  6. Applied add-cbrt-cube0.1

    \[\leadsto \sin \color{blue}{\left(\sqrt[3]{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right) \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}}\right)}\]

  7. Simplified0.1

    \[\leadsto \sin \left(\sqrt[3]{\color{blue}{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}\right)}^{\frac{3}{2}}}}\right)\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.1

    \[\leadsto \sin \left(\sqrt[3]{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}\right)}^{\color{blue}{\left(\sqrt{\frac{3}{2}} \cdot \sqrt{\frac{3}{2}}\right)}}}\right)\]

  10. Applied pow-unpow0.1

    \[\leadsto \sin \left(\sqrt[3]{\color{blue}{{\left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}\right)}^{\left(\sqrt{\frac{3}{2}}\right)}\right)}^{\left(\sqrt{\frac{3}{2}}\right)}}}\right)\]

  11. Final simplification0.1

    \[\leadsto \sin \left(\sqrt[3]{{\left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(b - a\right)}\right)}^{\left(\sqrt{\frac{3}{2}}\right)}\right)}^{\left(\sqrt{\frac{3}{2}}\right)}}\right)\]

Reproduce

herbie shell --seed 2020033 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))