Average Error: 12.7 → 12.8
Time: 2.2m
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 r3752786 = ky;
        double r3752787 = sin(r3752786);
        double r3752788 = kx;
        double r3752789 = sin(r3752788);
        double r3752790 = 2.0;
        double r3752791 = pow(r3752789, r3752790);
        double r3752792 = pow(r3752787, r3752790);
        double r3752793 = r3752791 + r3752792;
        double r3752794 = sqrt(r3752793);
        double r3752795 = r3752787 / r3752794;
        double r3752796 = th;
        double r3752797 = sin(r3752796);
        double r3752798 = r3752795 * r3752797;
        return r3752798;
}
↓
double f(double kx, double ky, double th) {
        double r3752799 = th;
        double r3752800 = sin(r3752799);
        double r3752801 = 1.0;
        double r3752802 = kx;
        double r3752803 = sin(r3752802);
        double r3752804 = r3752803 * r3752803;
        double r3752805 = ky;
        double r3752806 = sin(r3752805);
        double r3752807 = r3752806 * r3752806;
        double r3752808 = r3752804 + r3752807;
        double r3752809 = sqrt(r3752808);
        double r3752810 = r3752809 / r3752806;
        double r3752811 = r3752801 / r3752810;
        double r3752812 = r3752800 * r3752811;
        return r3752812;
}

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. Using strategy rm

  4. Applied clear-num12.8

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

  5. Final simplification12.8

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

Reproduce

herbie shell --seed 2019112 
(FPCore (kx ky th)
  :name "Toniolo and Linder, Equation (3b), real"
  (* (/ (sin ky) (sqrt (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin th)))