Average Error: 0.1 → 0.2
Time: 16.6s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{1}{\frac{y}{\sin y}} \cdot \cosh x\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{1}{\frac{y}{\sin y}} \cdot \cosh x
double f(double x, double y) {
        double r22206755 = x;
        double r22206756 = cosh(r22206755);
        double r22206757 = y;
        double r22206758 = sin(r22206757);
        double r22206759 = r22206758 / r22206757;
        double r22206760 = r22206756 * r22206759;
        return r22206760;
}
↓
double f(double x, double y) {
        double r22206761 = 1.0;
        double r22206762 = y;
        double r22206763 = sin(r22206762);
        double r22206764 = r22206762 / r22206763;
        double r22206765 = r22206761 / r22206764;
        double r22206766 = x;
        double r22206767 = cosh(r22206766);
        double r22206768 = r22206765 * r22206767;
        return r22206768;
}

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

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

Reproduce

herbie shell --seed 2019192 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"

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

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