Average Error: 15.2 → 0.2
Time: 15.0s
Precision: 64
\[\frac{\sin x}{\sin \left(x - y\right)}\]
\[\frac{\sin x}{\cos y \cdot \sin x - \sin y \cdot \cos x}\]
\frac{\sin x}{\sin \left(x - y\right)}
\frac{\sin x}{\cos y \cdot \sin x - \sin y \cdot \cos x}
double f(double x, double y) {
        double r21944252 = x;
        double r21944253 = sin(r21944252);
        double r21944254 = y;
        double r21944255 = r21944252 - r21944254;
        double r21944256 = sin(r21944255);
        double r21944257 = r21944253 / r21944256;
        return r21944257;
}

double f(double x, double y) {
        double r21944258 = x;
        double r21944259 = sin(r21944258);
        double r21944260 = y;
        double r21944261 = cos(r21944260);
        double r21944262 = r21944261 * r21944259;
        double r21944263 = sin(r21944260);
        double r21944264 = cos(r21944258);
        double r21944265 = r21944263 * r21944264;
        double r21944266 = r21944262 - r21944265;
        double r21944267 = r21944259 / r21944266;
        return r21944267;
}

Error

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Bits error versus y

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Results

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Derivation

  1. Initial program 15.2

    \[\frac{\sin x}{\sin \left(x - y\right)}\]
  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. Taylor expanded around inf 0.2

    \[\leadsto \color{blue}{\frac{\sin x}{\cos y \cdot \sin x - \sin y \cdot \cos x}}\]
  5. Final simplification0.2

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

Reproduce

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