Average Error: 14.8 → 0.3
Time: 16.0s
Precision: 64
\[x \gt y\]
\[\frac{\sin x}{\sin \left(x - y\right)}\]
\[\frac{1}{\cos y - \frac{\sin y}{\sin x} \cdot \cos x}\]
\frac{\sin x}{\sin \left(x - y\right)}
\frac{1}{\cos y - \frac{\sin y}{\sin x} \cdot \cos x}
double f(double x, double y) {
        double r22334283 = x;
        double r22334284 = sin(r22334283);
        double r22334285 = y;
        double r22334286 = r22334283 - r22334285;
        double r22334287 = sin(r22334286);
        double r22334288 = r22334284 / r22334287;
        return r22334288;
}

double f(double x, double y) {
        double r22334289 = 1.0;
        double r22334290 = y;
        double r22334291 = cos(r22334290);
        double r22334292 = sin(r22334290);
        double r22334293 = x;
        double r22334294 = sin(r22334293);
        double r22334295 = r22334292 / r22334294;
        double r22334296 = cos(r22334293);
        double r22334297 = r22334295 * r22334296;
        double r22334298 = r22334291 - r22334297;
        double r22334299 = r22334289 / r22334298;
        return r22334299;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

    \[\frac{\sin x}{\sin \left(x - y\right)}\]
  2. Using strategy rm
  3. Applied sin-diff0.2

    \[\leadsto \frac{\sin x}{\color{blue}{\sin x \cdot \cos y - \cos x \cdot \sin y}}\]
  4. Using strategy rm
  5. Applied clear-num0.3

    \[\leadsto \color{blue}{\frac{1}{\frac{\sin x \cdot \cos y - \cos x \cdot \sin y}{\sin x}}}\]
  6. Simplified0.3

    \[\leadsto \frac{1}{\color{blue}{\cos y - \cos x \cdot \frac{\sin y}{\sin x}}}\]
  7. Final simplification0.3

    \[\leadsto \frac{1}{\cos y - \frac{\sin y}{\sin x} \cdot \cos x}\]

Reproduce

herbie shell --seed 1 
(FPCore (x y)
  :name "sin(x)/sin(x-y)"
  :pre (> x y)
  (/ (sin x) (sin (- x y))))