Average Error: 0.2 → 0.2
Time: 5.1s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{1}{\frac{y}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{1}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r472172 = x;
        double r472173 = cosh(r472172);
        double r472174 = y;
        double r472175 = sin(r472174);
        double r472176 = r472175 / r472174;
        double r472177 = r472173 * r472176;
        return r472177;
}
↓
double f(double x, double y) {
        double r472178 = x;
        double r472179 = cosh(r472178);
        double r472180 = 1.0;
        double r472181 = y;
        double r472182 = sin(r472181);
        double r472183 = r472181 / r472182;
        double r472184 = r472180 / r472183;
        double r472185 = r472179 * r472184;
        return r472185;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.2

    \[\cosh x \cdot \frac{\sin y}{y}\]
  2. Using strategy rm

  3. Applied clear-num0.2

    \[\leadsto \cosh x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\]

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))