Average Error: 0.0 → 0.2
Time: 23.9s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \sqrt[3]{\frac{\sinh y}{y} \cdot \left(\frac{\sinh y}{y} \cdot \frac{\sinh y}{y}\right)}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \sqrt[3]{\frac{\sinh y}{y} \cdot \left(\frac{\sinh y}{y} \cdot \frac{\sinh y}{y}\right)}
double f(double x, double y) {
        double r6710441 = x;
        double r6710442 = sin(r6710441);
        double r6710443 = y;
        double r6710444 = sinh(r6710443);
        double r6710445 = r6710444 / r6710443;
        double r6710446 = r6710442 * r6710445;
        return r6710446;
}
↓
double f(double x, double y) {
        double r6710447 = x;
        double r6710448 = sin(r6710447);
        double r6710449 = y;
        double r6710450 = sinh(r6710449);
        double r6710451 = r6710450 / r6710449;
        double r6710452 = r6710451 * r6710451;
        double r6710453 = r6710451 * r6710452;
        double r6710454 = cbrt(r6710453);
        double r6710455 = r6710448 * r6710454;
        return r6710455;
}

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-cbrt-cube41.1

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

  4. Applied add-cbrt-cube41.0

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

  5. Applied cbrt-undiv41.0

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))