Average Error: 12.7 → 12.7
Time: 1.2m
Precision: 64
\[\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\]
↓
\[\frac{\sin th}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin ky\]
\frac{\sin ky}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th
↓
\frac{\sin th}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin ky
double f(double kx, double ky, double th) {
        double r1312725 = ky;
        double r1312726 = sin(r1312725);
        double r1312727 = kx;
        double r1312728 = sin(r1312727);
        double r1312729 = 2.0;
        double r1312730 = pow(r1312728, r1312729);
        double r1312731 = pow(r1312726, r1312729);
        double r1312732 = r1312730 + r1312731;
        double r1312733 = sqrt(r1312732);
        double r1312734 = r1312726 / r1312733;
        double r1312735 = th;
        double r1312736 = sin(r1312735);
        double r1312737 = r1312734 * r1312736;
        return r1312737;
}
↓
double f(double kx, double ky, double th) {
        double r1312738 = th;
        double r1312739 = sin(r1312738);
        double r1312740 = kx;
        double r1312741 = sin(r1312740);
        double r1312742 = 2.0;
        double r1312743 = pow(r1312741, r1312742);
        double r1312744 = ky;
        double r1312745 = sin(r1312744);
        double r1312746 = pow(r1312745, r1312742);
        double r1312747 = r1312743 + r1312746;
        double r1312748 = sqrt(r1312747);
        double r1312749 = r1312739 / r1312748;
        double r1312750 = r1312749 * r1312745;
        return r1312750;
}

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. Using strategy rm

  3. Applied div-inv12.8

    \[\leadsto \color{blue}{\left(\sin ky \cdot \frac{1}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}}\right)} \cdot \sin th\]

  4. Applied associate-*l*12.8

    \[\leadsto \color{blue}{\sin ky \cdot \left(\frac{1}{\sqrt{{\left(\sin kx\right)}^{2} + {\left(\sin ky\right)}^{2}}} \cdot \sin th\right)}\]

  5. Simplified12.7

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

  6. Final simplification12.7

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

Reproduce

herbie shell --seed 2019168 
(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)))