Average Error: 0.1 → 0.1
Time: 4.8s
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 r20952 = b;
        double r20953 = atan2(r20952, r20952);
        double r20954 = sqrt(r20953);
        double r20955 = a;
        double r20956 = r20952 - r20955;
        double r20957 = pow(r20954, r20956);
        double r20958 = sin(r20957);
        return r20958;
}
↓
double f(double a, double b) {
        double r20959 = b;
        double r20960 = atan2(r20959, r20959);
        double r20961 = sqrt(r20960);
        double r20962 = a;
        double r20963 = r20959 - r20962;
        double r20964 = pow(r20961, r20963);
        double r20965 = log(r20964);
        double r20966 = exp(r20965);
        double r20967 = sin(r20966);
        return r20967;
}

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 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))