Average Error: 4.1 → 4.1
Time: 9.8s
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\frac{1}{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}} \cdot \sin th\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\frac{1}{\frac{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}{\sin ky}} \cdot \sin th
double f(double kx, double ky, double th) {
        double r34458 = ky;
        double r34459 = sin(r34458);
        double r34460 = kx;
        double r34461 = sin(r34460);
        double r34462 = 2.0;
        double r34463 = pow(r34461, r34462);
        double r34464 = pow(r34459, r34462);
        double r34465 = r34463 + r34464;
        double r34466 = sqrt(r34465);
        double r34467 = r34459 / r34466;
        double r34468 = th;
        double r34469 = sin(r34468);
        double r34470 = r34467 * r34469;
        return r34470;
}
↓
double f(double kx, double ky, double th) {
        double r34471 = 1.0;
        double r34472 = kx;
        double r34473 = sin(r34472);
        double r34474 = 2.0;
        double r34475 = pow(r34473, r34474);
        double r34476 = ky;
        double r34477 = sin(r34476);
        double r34478 = pow(r34477, r34474);
        double r34479 = r34475 + r34478;
        double r34480 = sqrt(r34479);
        double r34481 = r34480 / r34477;
        double r34482 = r34471 / r34481;
        double r34483 = th;
        double r34484 = sin(r34483);
        double r34485 = r34482 * r34484;
        return r34485;
}

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 4.1

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

  3. Applied clear-num4.1

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

  4. Final simplification4.1

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

Reproduce

herbie shell --seed 2020062 
(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)))