Average Error: 4.3 → 4.3
Time: 12.2s
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\frac{1}{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}} \cdot \sin th\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\frac{1}{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}} \cdot \sin th
double f(double kx, double ky, double th) {
        double r44038 = ky;
        double r44039 = sin(r44038);
        double r44040 = kx;
        double r44041 = sin(r44040);
        double r44042 = 2.0;
        double r44043 = pow(r44041, r44042);
        double r44044 = pow(r44039, r44042);
        double r44045 = r44043 + r44044;
        double r44046 = sqrt(r44045);
        double r44047 = r44039 / r44046;
        double r44048 = th;
        double r44049 = sin(r44048);
        double r44050 = r44047 * r44049;
        return r44050;
}
↓
double f(double kx, double ky, double th) {
        double r44051 = 1.0;
        double r44052 = kx;
        double r44053 = sin(r44052);
        double r44054 = 2.0;
        double r44055 = pow(r44053, r44054);
        double r44056 = ky;
        double r44057 = sin(r44056);
        double r44058 = pow(r44057, r44054);
        double r44059 = r44055 + r44058;
        double r44060 = sqrt(r44059);
        double r44061 = r44060 / r44057;
        double r44062 = r44051 / r44061;
        double r44063 = th;
        double r44064 = sin(r44063);
        double r44065 = r44062 * r44064;
        return r44065;
}

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 4.3

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

  3. Applied clear-num4.3

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}}} \cdot \sin th\]

  4. Final simplification4.3

    \[\leadsto \frac{1}{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}} \cdot \sin th\]

Reproduce

herbie shell --seed 2020064 
(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)))