Average Error: 0.2 → 0.2
Time: 10.1s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\cosh x}{\frac{y}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\cosh x}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r361695 = x;
        double r361696 = cosh(r361695);
        double r361697 = y;
        double r361698 = sin(r361697);
        double r361699 = r361698 / r361697;
        double r361700 = r361696 * r361699;
        return r361700;
}
↓
double f(double x, double y) {
        double r361701 = x;
        double r361702 = cosh(r361701);
        double r361703 = y;
        double r361704 = sin(r361703);
        double r361705 = r361703 / r361704;
        double r361706 = r361702 / r361705;
        return r361706;
}

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

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

Reproduce

herbie shell --seed 2019304 
(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)))