Average Error: 12.7 → 12.7
Time: 35.3s
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\frac{\sin ky}{\sqrt{\sin ky \cdot \sin ky + \sin kx \cdot \sin kx}} \cdot \sin th\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\frac{\sin ky}{\sqrt{\sin ky \cdot \sin ky + \sin kx \cdot \sin kx}} \cdot \sin th
double f(double kx, double ky, double th) {
        double r713909 = ky;
        double r713910 = sin(r713909);
        double r713911 = kx;
        double r713912 = sin(r713911);
        double r713913 = 2.0;
        double r713914 = pow(r713912, r713913);
        double r713915 = pow(r713910, r713913);
        double r713916 = r713914 + r713915;
        double r713917 = sqrt(r713916);
        double r713918 = r713910 / r713917;
        double r713919 = th;
        double r713920 = sin(r713919);
        double r713921 = r713918 * r713920;
        return r713921;
}
↓
double f(double kx, double ky, double th) {
        double r713922 = ky;
        double r713923 = sin(r713922);
        double r713924 = r713923 * r713923;
        double r713925 = kx;
        double r713926 = sin(r713925);
        double r713927 = r713926 * r713926;
        double r713928 = r713924 + r713927;
        double r713929 = sqrt(r713928);
        double r713930 = r713923 / r713929;
        double r713931 = th;
        double r713932 = sin(r713931);
        double r713933 = r713930 * r713932;
        return r713933;
}

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 12.7

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

  2. Simplified12.7

    \[\leadsto \color{blue}{\sin th \cdot \frac{\sin ky}{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}}\]

  3. Taylor expanded around -inf 12.7

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

  4. Simplified12.7

    \[\leadsto \sin th \cdot \frac{\sin ky}{\sqrt{\sin kx \cdot \sin kx + \color{blue}{\sin ky \cdot \sin ky}}}\]

  5. Final simplification12.7

    \[\leadsto \frac{\sin ky}{\sqrt{\sin ky \cdot \sin ky + \sin kx \cdot \sin kx}} \cdot \sin th\]

Reproduce

herbie shell --seed 2019135 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))