Average Error: 0.0 → 0.1
Time: 23.4s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \frac{\sqrt[3]{\sinh y} \cdot \sqrt[3]{\sinh y}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{\sinh y}}{\sqrt[3]{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \frac{\sqrt[3]{\sinh y} \cdot \sqrt[3]{\sinh y}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{\sinh y}}{\sqrt[3]{y}}
double f(double x, double y) {
        double r161170 = x;
        double r161171 = sin(r161170);
        double r161172 = y;
        double r161173 = sinh(r161172);
        double r161174 = r161173 / r161172;
        double r161175 = r161171 * r161174;
        return r161175;
}
↓
double f(double x, double y) {
        double r161176 = x;
        double r161177 = sin(r161176);
        double r161178 = y;
        double r161179 = sinh(r161178);
        double r161180 = cbrt(r161179);
        double r161181 = r161180 * r161180;
        double r161182 = cbrt(r161178);
        double r161183 = r161182 * r161182;
        double r161184 = r161181 / r161183;
        double r161185 = r161177 * r161184;
        double r161186 = r161180 / r161182;
        double r161187 = r161185 * r161186;
        return r161187;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied add-cube-cbrt1.6

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied times-frac0.1

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

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))