Average Error: 12.5 → 12.5
Time: 36.1s
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 r1350536 = ky;
        double r1350537 = sin(r1350536);
        double r1350538 = kx;
        double r1350539 = sin(r1350538);
        double r1350540 = 2.0;
        double r1350541 = pow(r1350539, r1350540);
        double r1350542 = pow(r1350537, r1350540);
        double r1350543 = r1350541 + r1350542;
        double r1350544 = sqrt(r1350543);
        double r1350545 = r1350537 / r1350544;
        double r1350546 = th;
        double r1350547 = sin(r1350546);
        double r1350548 = r1350545 * r1350547;
        return r1350548;
}
↓
double f(double kx, double ky, double th) {
        double r1350549 = th;
        double r1350550 = sin(r1350549);
        double r1350551 = ky;
        double r1350552 = sin(r1350551);
        double r1350553 = kx;
        double r1350554 = sin(r1350553);
        double r1350555 = 2.0;
        double r1350556 = pow(r1350554, r1350555);
        double r1350557 = pow(r1350552, r1350555);
        double r1350558 = r1350556 + r1350557;
        double r1350559 = sqrt(r1350558);
        double r1350560 = r1350552 / r1350559;
        double r1350561 = r1350550 * r1350560;
        return r1350561;
}

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. 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 2019158 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))