Average Error: 0.1 → 0.3
Time: 6.4s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\left(\sqrt[3]{e^{x} + e^{-x}} \cdot \sqrt[3]{e^{x} + e^{-x}}\right) \cdot \sqrt[3]{\cosh x}}{\left(\sqrt[3]{2} \cdot \sqrt[3]{2}\right) \cdot \frac{y}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\left(\sqrt[3]{e^{x} + e^{-x}} \cdot \sqrt[3]{e^{x} + e^{-x}}\right) \cdot \sqrt[3]{\cosh x}}{\left(\sqrt[3]{2} \cdot \sqrt[3]{2}\right) \cdot \frac{y}{\sin y}}
double f(double x, double y) {
        double r509111 = x;
        double r509112 = cosh(r509111);
        double r509113 = y;
        double r509114 = sin(r509113);
        double r509115 = r509114 / r509113;
        double r509116 = r509112 * r509115;
        return r509116;
}
↓
double f(double x, double y) {
        double r509117 = x;
        double r509118 = exp(r509117);
        double r509119 = -r509117;
        double r509120 = exp(r509119);
        double r509121 = r509118 + r509120;
        double r509122 = cbrt(r509121);
        double r509123 = r509122 * r509122;
        double r509124 = cosh(r509117);
        double r509125 = cbrt(r509124);
        double r509126 = r509123 * r509125;
        double r509127 = 2.0;
        double r509128 = cbrt(r509127);
        double r509129 = r509128 * r509128;
        double r509130 = y;
        double r509131 = sin(r509130);
        double r509132 = r509130 / r509131;
        double r509133 = r509129 * r509132;
        double r509134 = r509126 / r509133;
        return r509134;
}

Error

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Results

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Target

Original0.1
Target0.1
Herbie0.3
\[\frac{\cosh x \cdot \sin y}{y}\]

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. Using strategy rm

  5. Applied add-cube-cbrt0.2

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\cosh x} \cdot \sqrt[3]{\cosh x}\right) \cdot \sqrt[3]{\cosh x}\right)} \cdot \frac{1}{\frac{y}{\sin y}}\]

  6. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\left(\sqrt[3]{\cosh x} \cdot \sqrt[3]{\cosh x}\right) \cdot \left(\sqrt[3]{\cosh x} \cdot \frac{1}{\frac{y}{\sin y}}\right)}\]

  7. Simplified0.2

    \[\leadsto \left(\sqrt[3]{\cosh x} \cdot \sqrt[3]{\cosh x}\right) \cdot \color{blue}{\frac{\sqrt[3]{\cosh x}}{\frac{y}{\sin y}}}\]
  8. Using strategy rm

  9. Applied cosh-def0.2

    \[\leadsto \left(\sqrt[3]{\cosh x} \cdot \sqrt[3]{\color{blue}{\frac{e^{x} + e^{-x}}{2}}}\right) \cdot \frac{\sqrt[3]{\cosh x}}{\frac{y}{\sin y}}\]

  10. Applied cbrt-div0.2

    \[\leadsto \left(\sqrt[3]{\cosh x} \cdot \color{blue}{\frac{\sqrt[3]{e^{x} + e^{-x}}}{\sqrt[3]{2}}}\right) \cdot \frac{\sqrt[3]{\cosh x}}{\frac{y}{\sin y}}\]

  11. Applied cosh-def0.2

    \[\leadsto \left(\sqrt[3]{\color{blue}{\frac{e^{x} + e^{-x}}{2}}} \cdot \frac{\sqrt[3]{e^{x} + e^{-x}}}{\sqrt[3]{2}}\right) \cdot \frac{\sqrt[3]{\cosh x}}{\frac{y}{\sin y}}\]

  12. Applied cbrt-div0.2

    \[\leadsto \left(\color{blue}{\frac{\sqrt[3]{e^{x} + e^{-x}}}{\sqrt[3]{2}}} \cdot \frac{\sqrt[3]{e^{x} + e^{-x}}}{\sqrt[3]{2}}\right) \cdot \frac{\sqrt[3]{\cosh x}}{\frac{y}{\sin y}}\]

  13. Applied frac-times0.2

    \[\leadsto \color{blue}{\frac{\sqrt[3]{e^{x} + e^{-x}} \cdot \sqrt[3]{e^{x} + e^{-x}}}{\sqrt[3]{2} \cdot \sqrt[3]{2}}} \cdot \frac{\sqrt[3]{\cosh x}}{\frac{y}{\sin y}}\]

  14. Applied frac-times0.3

    \[\leadsto \color{blue}{\frac{\left(\sqrt[3]{e^{x} + e^{-x}} \cdot \sqrt[3]{e^{x} + e^{-x}}\right) \cdot \sqrt[3]{\cosh x}}{\left(\sqrt[3]{2} \cdot \sqrt[3]{2}\right) \cdot \frac{y}{\sin y}}}\]

  15. Final simplification0.3

    \[\leadsto \frac{\left(\sqrt[3]{e^{x} + e^{-x}} \cdot \sqrt[3]{e^{x} + e^{-x}}\right) \cdot \sqrt[3]{\cosh x}}{\left(\sqrt[3]{2} \cdot \sqrt[3]{2}\right) \cdot \frac{y}{\sin y}}\]

Reproduce

herbie shell --seed 2020100 
(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)))