Average Error: 12.6 → 13.0
Time: 28.3s
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\sin th \cdot \frac{\sin ky}{\sqrt{e^{\log \left(\sin kx \cdot \sin kx\right)} + \sin ky \cdot \sin ky}}\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\sin th \cdot \frac{\sin ky}{\sqrt{e^{\log \left(\sin kx \cdot \sin kx\right)} + \sin ky \cdot \sin ky}}
double f(double kx, double ky, double th) {
        double r494359 = ky;
        double r494360 = sin(r494359);
        double r494361 = kx;
        double r494362 = sin(r494361);
        double r494363 = 2.0;
        double r494364 = pow(r494362, r494363);
        double r494365 = pow(r494360, r494363);
        double r494366 = r494364 + r494365;
        double r494367 = sqrt(r494366);
        double r494368 = r494360 / r494367;
        double r494369 = th;
        double r494370 = sin(r494369);
        double r494371 = r494368 * r494370;
        return r494371;
}
↓
double f(double kx, double ky, double th) {
        double r494372 = th;
        double r494373 = sin(r494372);
        double r494374 = ky;
        double r494375 = sin(r494374);
        double r494376 = kx;
        double r494377 = sin(r494376);
        double r494378 = r494377 * r494377;
        double r494379 = log(r494378);
        double r494380 = exp(r494379);
        double r494381 = r494375 * r494375;
        double r494382 = r494380 + r494381;
        double r494383 = sqrt(r494382);
        double r494384 = r494375 / r494383;
        double r494385 = r494373 * r494384;
        return r494385;
}

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 12.6

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

  2. Simplified12.6

    \[\leadsto \color{blue}{\sin th \cdot \frac{\sin ky}{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}}\]
  3. Using strategy rm

  4. Applied add-exp-log13.0

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

  5. Final simplification13.0

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

Reproduce

herbie shell --seed 2019153 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))