Average Error: 12.3 → 12.3
Time: 31.9s
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\frac{\sin ky}{\sqrt{\sin ky \cdot \sin ky + \sin kx \cdot \sin kx}} \cdot \sin th\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\frac{\sin ky}{\sqrt{\sin ky \cdot \sin ky + \sin kx \cdot \sin kx}} \cdot \sin th
double f(double kx, double ky, double th) {
        double r534522 = ky;
        double r534523 = sin(r534522);
        double r534524 = kx;
        double r534525 = sin(r534524);
        double r534526 = 2.0;
        double r534527 = pow(r534525, r534526);
        double r534528 = pow(r534523, r534526);
        double r534529 = r534527 + r534528;
        double r534530 = sqrt(r534529);
        double r534531 = r534523 / r534530;
        double r534532 = th;
        double r534533 = sin(r534532);
        double r534534 = r534531 * r534533;
        return r534534;
}
↓
double f(double kx, double ky, double th) {
        double r534535 = ky;
        double r534536 = sin(r534535);
        double r534537 = r534536 * r534536;
        double r534538 = kx;
        double r534539 = sin(r534538);
        double r534540 = r534539 * r534539;
        double r534541 = r534537 + r534540;
        double r534542 = sqrt(r534541);
        double r534543 = r534536 / r534542;
        double r534544 = th;
        double r534545 = sin(r534544);
        double r534546 = r534543 * r534545;
        return r534546;
}

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. Final simplification12.3

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

Reproduce

herbie shell --seed 2019128 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))