Average Error: 0.0 → 0.1
Time: 30.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \left(\left(\sqrt[3]{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \left(\left(\sqrt[3]{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r174259 = x;
        double r174260 = sin(r174259);
        double r174261 = y;
        double r174262 = sinh(r174261);
        double r174263 = r174262 / r174261;
        double r174264 = r174260 * r174263;
        return r174264;
}
↓
double f(double x, double y) {
        double r174265 = x;
        double r174266 = sin(r174265);
        double r174267 = y;
        double r174268 = sinh(r174267);
        double r174269 = r174268 / r174267;
        double r174270 = sqrt(r174269);
        double r174271 = cbrt(r174270);
        double r174272 = r174271 * r174271;
        double r174273 = r174272 * r174271;
        double r174274 = r174266 * r174273;
        double r174275 = r174274 * r174270;
        return r174275;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

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

  6. Applied add-cube-cbrt0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))