Average Error: 12.8 → 12.8
Time: 19.1s
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 r37438 = ky;
        double r37439 = sin(r37438);
        double r37440 = kx;
        double r37441 = sin(r37440);
        double r37442 = 2.0;
        double r37443 = pow(r37441, r37442);
        double r37444 = pow(r37439, r37442);
        double r37445 = r37443 + r37444;
        double r37446 = sqrt(r37445);
        double r37447 = r37439 / r37446;
        double r37448 = th;
        double r37449 = sin(r37448);
        double r37450 = r37447 * r37449;
        return r37450;
}
↓
double f(double kx, double ky, double th) {
        double r37451 = th;
        double r37452 = sin(r37451);
        double r37453 = ky;
        double r37454 = sin(r37453);
        double r37455 = kx;
        double r37456 = sin(r37455);
        double r37457 = 2.0;
        double r37458 = pow(r37456, r37457);
        double r37459 = pow(r37454, r37457);
        double r37460 = r37458 + r37459;
        double r37461 = sqrt(r37460);
        double r37462 = r37454 / r37461;
        double r37463 = r37452 * r37462;
        return r37463;
}

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 12.8

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

  3. Applied *-commutative12.8

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

  4. Final simplification12.8

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

Reproduce

herbie shell --seed 2019350 
(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)))