Average Error: 0.0 → 0.1
Time: 12.3s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right)
double f(double x, double y) {
        double r108017 = x;
        double r108018 = sin(r108017);
        double r108019 = y;
        double r108020 = sinh(r108019);
        double r108021 = r108020 / r108019;
        double r108022 = r108018 * r108021;
        return r108022;
}
↓
double f(double x, double y) {
        double r108023 = x;
        double r108024 = sin(r108023);
        double r108025 = y;
        double r108026 = sinh(r108025);
        double r108027 = r108026 / r108025;
        double r108028 = cbrt(r108027);
        double r108029 = r108028 * r108028;
        double r108030 = r108028 * r108029;
        double r108031 = r108024 * r108030;
        return r108031;
}

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-cbrt0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))