Average Error: 0.0 → 0.1
Time: 15.4s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{{\left(\sqrt{\frac{\sinh y}{y}}\right)}^{3}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{{\left(\sqrt{\frac{\sinh y}{y}}\right)}^{3}}
double f(double x, double y) {
        double r177305 = x;
        double r177306 = sin(r177305);
        double r177307 = y;
        double r177308 = sinh(r177307);
        double r177309 = r177308 / r177307;
        double r177310 = r177306 * r177309;
        return r177310;
}
↓
double f(double x, double y) {
        double r177311 = x;
        double r177312 = sin(r177311);
        double r177313 = y;
        double r177314 = sinh(r177313);
        double r177315 = r177314 / r177313;
        double r177316 = sqrt(r177315);
        double r177317 = r177312 * r177316;
        double r177318 = 3.0;
        double r177319 = pow(r177316, r177318);
        double r177320 = cbrt(r177319);
        double r177321 = r177317 * r177320;
        return r177321;
}

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-cbrt-cube0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))