Average Error: 12.3 → 12.4
Time: 39.6s
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\sin th \cdot \frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\sin th \cdot \frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}
double f(double kx, double ky, double th) {
        double r699852 = ky;
        double r699853 = sin(r699852);
        double r699854 = kx;
        double r699855 = sin(r699854);
        double r699856 = 2.0;
        double r699857 = pow(r699855, r699856);
        double r699858 = pow(r699853, r699856);
        double r699859 = r699857 + r699858;
        double r699860 = sqrt(r699859);
        double r699861 = r699853 / r699860;
        double r699862 = th;
        double r699863 = sin(r699862);
        double r699864 = r699861 * r699863;
        return r699864;
}
↓
double f(double kx, double ky, double th) {
        double r699865 = th;
        double r699866 = sin(r699865);
        double r699867 = 1.0;
        double r699868 = kx;
        double r699869 = sin(r699868);
        double r699870 = r699869 * r699869;
        double r699871 = ky;
        double r699872 = sin(r699871);
        double r699873 = r699872 * r699872;
        double r699874 = r699870 + r699873;
        double r699875 = sqrt(r699874);
        double r699876 = r699875 / r699872;
        double r699877 = r699867 / r699876;
        double r699878 = r699866 * r699877;
        return r699878;
}

Error

Bits error versus kx

Bits error versus ky

Bits error versus th

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.3

    \[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]

  2. Simplified12.3

    \[\leadsto \color{blue}{\sin th \cdot \frac{\sin ky}{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}}\]
  3. Using strategy rm

  4. Applied clear-num12.4

    \[\leadsto \sin th \cdot \color{blue}{\frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}}\]

  5. Final simplification12.4

    \[\leadsto \sin th \cdot \frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}\]

Reproduce

herbie shell --seed 2019142 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))