Average Error: 12.3 → 12.4
Time: 1.2m
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2.0} + {\left(\sin ky\right)}^{2.0}}} \cdot \sin th\]
↓
\[\frac{1}{\frac{\sqrt{{\left(\sin ky\right)}^{2.0} + {\left(\sin kx\right)}^{2.0}}}{\sin ky}} \cdot \sin th\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2.0} + {\left(\sin ky\right)}^{2.0}}} \cdot \sin th
↓
\frac{1}{\frac{\sqrt{{\left(\sin ky\right)}^{2.0} + {\left(\sin kx\right)}^{2.0}}}{\sin ky}} \cdot \sin th
double f(double kx, double ky, double th) {
        double r1276821 = ky;
        double r1276822 = sin(r1276821);
        double r1276823 = kx;
        double r1276824 = sin(r1276823);
        double r1276825 = 2.0;
        double r1276826 = pow(r1276824, r1276825);
        double r1276827 = pow(r1276822, r1276825);
        double r1276828 = r1276826 + r1276827;
        double r1276829 = sqrt(r1276828);
        double r1276830 = r1276822 / r1276829;
        double r1276831 = th;
        double r1276832 = sin(r1276831);
        double r1276833 = r1276830 * r1276832;
        return r1276833;
}
↓
double f(double kx, double ky, double th) {
        double r1276834 = 1.0;
        double r1276835 = ky;
        double r1276836 = sin(r1276835);
        double r1276837 = 2.0;
        double r1276838 = pow(r1276836, r1276837);
        double r1276839 = kx;
        double r1276840 = sin(r1276839);
        double r1276841 = pow(r1276840, r1276837);
        double r1276842 = r1276838 + r1276841;
        double r1276843 = sqrt(r1276842);
        double r1276844 = r1276843 / r1276836;
        double r1276845 = r1276834 / r1276844;
        double r1276846 = th;
        double r1276847 = sin(r1276846);
        double r1276848 = r1276845 * r1276847;
        return r1276848;
}

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 12.3

    \[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2.0} + {\left(\sin ky\right)}^{2.0}}} \cdot \sin th\]
  2. Using strategy rm

  3. Applied clear-num12.4

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt{{\left(\sin kx\right)}^{2.0} + {\left(\sin ky\right)}^{2.0}}}{\sin ky}}} \cdot \sin th\]

  4. Final simplification12.4

    \[\leadsto \frac{1}{\frac{\sqrt{{\left(\sin ky\right)}^{2.0} + {\left(\sin kx\right)}^{2.0}}}{\sin ky}} \cdot \sin th\]

Reproduce

herbie shell --seed 2019165 
(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)))