Average Error: 0.1 → 0.2
Time: 17.2s
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 r520673 = x;
        double r520674 = cosh(r520673);
        double r520675 = y;
        double r520676 = sin(r520675);
        double r520677 = r520676 / r520675;
        double r520678 = r520674 * r520677;
        return r520678;
}
↓
double f(double x, double y) {
        double r520679 = x;
        double r520680 = cosh(r520679);
        double r520681 = 1.0;
        double r520682 = y;
        double r520683 = sin(r520682);
        double r520684 = r520682 / r520683;
        double r520685 = r520681 / r520684;
        double r520686 = r520680 * r520685;
        return r520686;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

    \[\cosh x \cdot \frac{\sin y}{y}\]
  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 2020045 +o rules:numerics
(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)))