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 r33984 = ky;
        double r33985 = sin(r33984);
        double r33986 = kx;
        double r33987 = sin(r33986);
        double r33988 = 2.0;
        double r33989 = pow(r33987, r33988);
        double r33990 = pow(r33985, r33988);
        double r33991 = r33989 + r33990;
        double r33992 = sqrt(r33991);
        double r33993 = r33985 / r33992;
        double r33994 = th;
        double r33995 = sin(r33994);
        double r33996 = r33993 * r33995;
        return r33996;
}
↓
double f(double kx, double ky, double th) {
        double r33997 = 1.0;
        double r33998 = kx;
        double r33999 = sin(r33998);
        double r34000 = 2.0;
        double r34001 = pow(r33999, r34000);
        double r34002 = ky;
        double r34003 = sin(r34002);
        double r34004 = pow(r34003, r34000);
        double r34005 = r34001 + r34004;
        double r34006 = sqrt(r34005);
        double r34007 = r34006 / r34003;
        double r34008 = r33997 / r34007;
        double r34009 = th;
        double r34010 = sin(r34009);
        double r34011 = r34008 * r34010;
        return r34011;
}

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)))