Average Error: 12.3 → 12.3
Time: 3.7m
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\sin th \cdot \frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\sin th \cdot \frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}
double f(double kx, double ky, double th) {
        double r6572114 = ky;
        double r6572115 = sin(r6572114);
        double r6572116 = kx;
        double r6572117 = sin(r6572116);
        double r6572118 = 2.0;
        double r6572119 = pow(r6572117, r6572118);
        double r6572120 = pow(r6572115, r6572118);
        double r6572121 = r6572119 + r6572120;
        double r6572122 = sqrt(r6572121);
        double r6572123 = r6572115 / r6572122;
        double r6572124 = th;
        double r6572125 = sin(r6572124);
        double r6572126 = r6572123 * r6572125;
        return r6572126;
}
↓
double f(double kx, double ky, double th) {
        double r6572127 = th;
        double r6572128 = sin(r6572127);
        double r6572129 = 1.0;
        double r6572130 = kx;
        double r6572131 = sin(r6572130);
        double r6572132 = r6572131 * r6572131;
        double r6572133 = ky;
        double r6572134 = sin(r6572133);
        double r6572135 = r6572134 * r6572134;
        double r6572136 = r6572132 + r6572135;
        double r6572137 = sqrt(r6572136);
        double r6572138 = r6572137 / r6572134;
        double r6572139 = r6572129 / r6572138;
        double r6572140 = r6572128 * r6572139;
        return r6572140;
}

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

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

  2. Simplified12.3

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

  4. Applied clear-num12.3

    \[\leadsto \sin th \cdot \color{blue}{\frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}}\]

  5. Final simplification12.3

    \[\leadsto \sin th \cdot \frac{1}{\frac{\sqrt{\sin kx \cdot \sin kx + \sin ky \cdot \sin ky}}{\sin ky}}\]

Reproduce

herbie shell --seed 2019119 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))