Average Error: 14.3 → 0.5
Time: 30.7s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\left(\sinh y \cdot \frac{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot \frac{\sqrt[3]{\sin x}}{\sqrt[3]{x}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\left(\sinh y \cdot \frac{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot \frac{\sqrt[3]{\sin x}}{\sqrt[3]{x}}
double f(double x, double y) {
        double r359724 = x;
        double r359725 = sin(r359724);
        double r359726 = y;
        double r359727 = sinh(r359726);
        double r359728 = r359725 * r359727;
        double r359729 = r359728 / r359724;
        return r359729;
}
↓
double f(double x, double y) {
        double r359730 = y;
        double r359731 = sinh(r359730);
        double r359732 = x;
        double r359733 = sin(r359732);
        double r359734 = cbrt(r359733);
        double r359735 = r359734 * r359734;
        double r359736 = cbrt(r359732);
        double r359737 = r359736 * r359736;
        double r359738 = r359735 / r359737;
        double r359739 = r359731 * r359738;
        double r359740 = r359734 / r359736;
        double r359741 = r359739 * r359740;
        return r359741;
}

Error

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Results

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Target

Original14.3
Target0.2
Herbie0.5
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.3

    \[\frac{\sin x \cdot \sinh y}{x}\]

  2. Taylor expanded around inf 43.7

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

  3. Simplified0.2

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

  5. Applied div-inv0.3

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

  6. Applied associate-*l*0.2

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

  7. Simplified0.1

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

  9. Applied add-cube-cbrt1.1

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

  10. Applied add-cube-cbrt0.5

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

  11. Applied times-frac0.5

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

  12. Applied associate-*r*0.5

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

  13. Final simplification0.5

    \[\leadsto \left(\sinh y \cdot \frac{\sqrt[3]{\sin x} \cdot \sqrt[3]{\sin x}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot \frac{\sqrt[3]{\sin x}}{\sqrt[3]{x}}\]

Reproduce

herbie shell --seed 2019325 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

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

  (/ (* (sin x) (sinh y)) x))