Average Error: 0.1 → 0.2
Time: 15.4s
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 r359812 = x;
        double r359813 = cosh(r359812);
        double r359814 = y;
        double r359815 = sin(r359814);
        double r359816 = r359815 / r359814;
        double r359817 = r359813 * r359816;
        return r359817;
}
↓
double f(double x, double y) {
        double r359818 = 1.0;
        double r359819 = y;
        double r359820 = sin(r359819);
        double r359821 = r359819 / r359820;
        double r359822 = r359818 / r359821;
        double r359823 = x;
        double r359824 = cosh(r359823);
        double r359825 = r359822 * r359824;
        return r359825;
}

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 *-un-lft-identity0.1

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

  4. Applied *-un-lft-identity0.1

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

  5. Applied times-frac0.1

    \[\leadsto \cosh x \cdot \color{blue}{\left(\frac{1}{1} \cdot \frac{\sin y}{y}\right)}\]

  6. Simplified0.1

    \[\leadsto \cosh x \cdot \left(\color{blue}{1} \cdot \frac{\sin y}{y}\right)\]
  7. Using strategy rm

  8. Applied clear-num0.2

    \[\leadsto \cosh x \cdot \left(1 \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\right)\]

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019235 +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)))