Average Error: 12.5 → 12.5
Time: 30.8s
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\sin th \cdot \frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\sin th \cdot \frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}
double f(double kx, double ky, double th) {
        double r33892 = ky;
        double r33893 = sin(r33892);
        double r33894 = kx;
        double r33895 = sin(r33894);
        double r33896 = 2.0;
        double r33897 = pow(r33895, r33896);
        double r33898 = pow(r33893, r33896);
        double r33899 = r33897 + r33898;
        double r33900 = sqrt(r33899);
        double r33901 = r33893 / r33900;
        double r33902 = th;
        double r33903 = sin(r33902);
        double r33904 = r33901 * r33903;
        return r33904;
}
↓
double f(double kx, double ky, double th) {
        double r33905 = th;
        double r33906 = sin(r33905);
        double r33907 = ky;
        double r33908 = sin(r33907);
        double r33909 = kx;
        double r33910 = sin(r33909);
        double r33911 = 2.0;
        double r33912 = pow(r33910, r33911);
        double r33913 = pow(r33908, r33911);
        double r33914 = r33912 + r33913;
        double r33915 = sqrt(r33914);
        double r33916 = r33908 / r33915;
        double r33917 = r33906 * r33916;
        return r33917;
}

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 12.5

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

  3. Applied *-commutative12.5

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

  4. Final simplification12.5

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

Reproduce

herbie shell --seed 2019305 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  :precision binary64
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))