Average Error: 12.9 → 13.0
Time: 34.9s
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\frac{\sin ky}{\sqrt{\left(\sqrt[3]{{\left(\sin kx\right)}^{2}} \cdot \sqrt[3]{{\left(\sin kx\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\sin kx\right)}^{2}} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\frac{\sin ky}{\sqrt{\left(\sqrt[3]{{\left(\sin kx\right)}^{2}} \cdot \sqrt[3]{{\left(\sin kx\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\sin kx\right)}^{2}} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
double f(double kx, double ky, double th) {
        double r1266990 = ky;
        double r1266991 = sin(r1266990);
        double r1266992 = kx;
        double r1266993 = sin(r1266992);
        double r1266994 = 2.0;
        double r1266995 = pow(r1266993, r1266994);
        double r1266996 = pow(r1266991, r1266994);
        double r1266997 = r1266995 + r1266996;
        double r1266998 = sqrt(r1266997);
        double r1266999 = r1266991 / r1266998;
        double r1267000 = th;
        double r1267001 = sin(r1267000);
        double r1267002 = r1266999 * r1267001;
        return r1267002;
}
↓
double f(double kx, double ky, double th) {
        double r1267003 = ky;
        double r1267004 = sin(r1267003);
        double r1267005 = kx;
        double r1267006 = sin(r1267005);
        double r1267007 = 2.0;
        double r1267008 = pow(r1267006, r1267007);
        double r1267009 = cbrt(r1267008);
        double r1267010 = r1267009 * r1267009;
        double r1267011 = r1267010 * r1267009;
        double r1267012 = pow(r1267004, r1267007);
        double r1267013 = r1267011 + r1267012;
        double r1267014 = sqrt(r1267013);
        double r1267015 = r1267004 / r1267014;
        double r1267016 = th;
        double r1267017 = sin(r1267016);
        double r1267018 = r1267015 * r1267017;
        return r1267018;
}

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 12.9

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

  3. Applied add-cube-cbrt13.0

    \[\leadsto \frac{\sin ky}{\sqrt{\color{blue}{\left(\sqrt[3]{{\left(\sin kx\right)}^{2}} \cdot \sqrt[3]{{\left(\sin kx\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\sin kx\right)}^{2}}} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]

  4. Final simplification13.0

    \[\leadsto \frac{\sin ky}{\sqrt{\left(\sqrt[3]{{\left(\sin kx\right)}^{2}} \cdot \sqrt[3]{{\left(\sin kx\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\sin kx\right)}^{2}} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]

Reproduce

herbie shell --seed 2019164 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))