Average Error: 0.2 → 0.3
Time: 27.9s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}
double f(double x, double y) {
        double r316855 = x;
        double r316856 = cosh(r316855);
        double r316857 = y;
        double r316858 = sin(r316857);
        double r316859 = r316858 / r316857;
        double r316860 = r316856 * r316859;
        return r316860;
}
↓
double f(double x, double y) {
        double r316861 = x;
        double r316862 = cosh(r316861);
        double r316863 = 1.0;
        double r316864 = y;
        double r316865 = r316863 / r316864;
        double r316866 = sin(r316864);
        double r316867 = r316863 / r316866;
        double r316868 = r316865 / r316867;
        double r316869 = r316862 * r316868;
        return r316869;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.3
\[\frac{\cosh x \cdot \sin y}{y}\]

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. Using strategy rm

  5. Applied div-inv0.4

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

  6. Applied associate-/r*0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019303 
(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)))