Average Error: 12.2 → 12.7
Time: 27.8s
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\left(\left(\left(\sqrt[3]{\sqrt[3]{\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}}} \cdot \sqrt[3]{\sqrt[3]{\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}}}\right) \cdot \left(\sqrt[3]{\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}} \cdot \sqrt[3]{\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}}\right)\right) \cdot \sin th\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\left(\left(\left(\sqrt[3]{\sqrt[3]{\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}}} \cdot \sqrt[3]{\sqrt[3]{\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}}}\right) \cdot \sqrt[3]{\sqrt[3]{\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}}}\right) \cdot \left(\sqrt[3]{\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}} \cdot \sqrt[3]{\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}}\right)\right) \cdot \sin th
double f(double kx, double ky, double th) {
        double r32579 = ky;
        double r32580 = sin(r32579);
        double r32581 = kx;
        double r32582 = sin(r32581);
        double r32583 = 2.0;
        double r32584 = pow(r32582, r32583);
        double r32585 = pow(r32580, r32583);
        double r32586 = r32584 + r32585;
        double r32587 = sqrt(r32586);
        double r32588 = r32580 / r32587;
        double r32589 = th;
        double r32590 = sin(r32589);
        double r32591 = r32588 * r32590;
        return r32591;
}
↓
double f(double kx, double ky, double th) {
        double r32592 = ky;
        double r32593 = sin(r32592);
        double r32594 = kx;
        double r32595 = sin(r32594);
        double r32596 = 2.0;
        double r32597 = pow(r32595, r32596);
        double r32598 = pow(r32593, r32596);
        double r32599 = r32597 + r32598;
        double r32600 = sqrt(r32599);
        double r32601 = r32593 / r32600;
        double r32602 = cbrt(r32601);
        double r32603 = cbrt(r32602);
        double r32604 = r32603 * r32603;
        double r32605 = r32604 * r32603;
        double r32606 = r32602 * r32602;
        double r32607 = r32605 * r32606;
        double r32608 = th;
        double r32609 = sin(r32608);
        double r32610 = r32607 * r32609;
        return r32610;
}

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 12.2

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

  3. Applied add-cube-cbrt12.6

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

  5. Applied add-cube-cbrt12.7

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

  6. Final simplification12.7

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

Reproduce

herbie shell --seed 2019194 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))