Average Error: 12.5 → 12.5
Time: 27.5s
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\frac{\sin th}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin ky\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\frac{\sin th}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin ky
double f(double kx, double ky, double th) {
        double r36359 = ky;
        double r36360 = sin(r36359);
        double r36361 = kx;
        double r36362 = sin(r36361);
        double r36363 = 2.0;
        double r36364 = pow(r36362, r36363);
        double r36365 = pow(r36360, r36363);
        double r36366 = r36364 + r36365;
        double r36367 = sqrt(r36366);
        double r36368 = r36360 / r36367;
        double r36369 = th;
        double r36370 = sin(r36369);
        double r36371 = r36368 * r36370;
        return r36371;
}
↓
double f(double kx, double ky, double th) {
        double r36372 = th;
        double r36373 = sin(r36372);
        double r36374 = kx;
        double r36375 = sin(r36374);
        double r36376 = 2.0;
        double r36377 = pow(r36375, r36376);
        double r36378 = ky;
        double r36379 = sin(r36378);
        double r36380 = pow(r36379, r36376);
        double r36381 = r36377 + r36380;
        double r36382 = sqrt(r36381);
        double r36383 = r36373 / r36382;
        double r36384 = r36383 * r36379;
        return r36384;
}

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. Using strategy rm

  3. Applied div-inv12.5

    \[\leadsto \color{blue}{\left(\sin ky \cdot \frac{1}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}\right)} \cdot \sin th\]

  4. Applied associate-*l*12.6

    \[\leadsto \color{blue}{\sin ky \cdot \left(\frac{1}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\right)}\]

  5. Simplified12.5

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

  6. Final simplification12.5

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

Reproduce

herbie shell --seed 2019196 
(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)))