Average Error: 0.2 → 0.2
Time: 29.7s
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 r357568 = x;
        double r357569 = cosh(r357568);
        double r357570 = y;
        double r357571 = sin(r357570);
        double r357572 = r357571 / r357570;
        double r357573 = r357569 * r357572;
        return r357573;
}
↓
double f(double x, double y) {
        double r357574 = x;
        double r357575 = cosh(r357574);
        double r357576 = 1.0;
        double r357577 = y;
        double r357578 = sin(r357577);
        double r357579 = r357577 / r357578;
        double r357580 = r357576 / r357579;
        double r357581 = r357575 * r357580;
        return r357581;
}

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 2019304 +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)))