Average Error: 0.1 → 0.4
Time: 16.9s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\left(\sin y \cdot \left(\sqrt{e^{x} + e^{-x}} \cdot \frac{\frac{\sqrt{\cosh x}}{\sqrt{2}}}{y}\right)\right) \cdot 1\]
\cosh x \cdot \frac{\sin y}{y}
↓
\left(\sin y \cdot \left(\sqrt{e^{x} + e^{-x}} \cdot \frac{\frac{\sqrt{\cosh x}}{\sqrt{2}}}{y}\right)\right) \cdot 1
double f(double x, double y) {
        double r378888 = x;
        double r378889 = cosh(r378888);
        double r378890 = y;
        double r378891 = sin(r378890);
        double r378892 = r378891 / r378890;
        double r378893 = r378889 * r378892;
        return r378893;
}
↓
double f(double x, double y) {
        double r378894 = y;
        double r378895 = sin(r378894);
        double r378896 = x;
        double r378897 = exp(r378896);
        double r378898 = -r378896;
        double r378899 = exp(r378898);
        double r378900 = r378897 + r378899;
        double r378901 = sqrt(r378900);
        double r378902 = cosh(r378896);
        double r378903 = sqrt(r378902);
        double r378904 = 2.0;
        double r378905 = sqrt(r378904);
        double r378906 = r378903 / r378905;
        double r378907 = r378906 / r378894;
        double r378908 = r378901 * r378907;
        double r378909 = r378895 * r378908;
        double r378910 = 1.0;
        double r378911 = r378909 * r378910;
        return r378911;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.4
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

    \[\cosh x \cdot \frac{\sin y}{y}\]
  2. Using strategy rm

  3. Applied associate-*r/0.1

    \[\leadsto \color{blue}{\frac{\cosh x \cdot \sin y}{y}}\]
  4. Using strategy rm

  5. Applied associate-/l*0.2

    \[\leadsto \color{blue}{\frac{\cosh x}{\frac{y}{\sin y}}}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt0.2

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

  8. Applied associate-/l*0.2

    \[\leadsto \color{blue}{\frac{\sqrt{\cosh x}}{\frac{\frac{y}{\sin y}}{\sqrt{\cosh x}}}}\]
  9. Using strategy rm

  10. Applied cosh-def0.2

    \[\leadsto \frac{\sqrt{\cosh x}}{\frac{\frac{y}{\sin y}}{\sqrt{\color{blue}{\frac{e^{x} + e^{-x}}{2}}}}}\]

  11. Applied sqrt-div0.2

    \[\leadsto \frac{\sqrt{\cosh x}}{\frac{\frac{y}{\sin y}}{\color{blue}{\frac{\sqrt{e^{x} + e^{-x}}}{\sqrt{2}}}}}\]

  12. Applied associate-/r/0.3

    \[\leadsto \frac{\sqrt{\cosh x}}{\color{blue}{\frac{\frac{y}{\sin y}}{\sqrt{e^{x} + e^{-x}}} \cdot \sqrt{2}}}\]

  13. Applied *-un-lft-identity0.3

    \[\leadsto \frac{\sqrt{\color{blue}{1 \cdot \cosh x}}}{\frac{\frac{y}{\sin y}}{\sqrt{e^{x} + e^{-x}}} \cdot \sqrt{2}}\]

  14. Applied sqrt-prod0.3

    \[\leadsto \frac{\color{blue}{\sqrt{1} \cdot \sqrt{\cosh x}}}{\frac{\frac{y}{\sin y}}{\sqrt{e^{x} + e^{-x}}} \cdot \sqrt{2}}\]

  15. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{\sqrt{1}}{\frac{\frac{y}{\sin y}}{\sqrt{e^{x} + e^{-x}}}} \cdot \frac{\sqrt{\cosh x}}{\sqrt{2}}}\]

  16. Final simplification0.4

    \[\leadsto \left(\sin y \cdot \left(\sqrt{e^{x} + e^{-x}} \cdot \frac{\frac{\sqrt{\cosh x}}{\sqrt{2}}}{y}\right)\right) \cdot 1\]

Reproduce

herbie shell --seed 2019294 
(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)))