Average Error: 0.0 → 0.0
Time: 8.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)
double f(double x, double y) {
        double r184496 = x;
        double r184497 = sin(r184496);
        double r184498 = y;
        double r184499 = sinh(r184498);
        double r184500 = r184499 / r184498;
        double r184501 = r184497 * r184500;
        return r184501;
}
↓
double f(double x, double y) {
        double r184502 = x;
        double r184503 = sin(r184502);
        double r184504 = y;
        double r184505 = sinh(r184504);
        double r184506 = r184505 / r184504;
        double r184507 = cbrt(r184506);
        double r184508 = r184507 * r184507;
        double r184509 = r184508 * r184507;
        double r184510 = r184503 * r184509;
        return r184510;
}

Error

Bits error versus x

Bits error versus y

Try it out

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-cbrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))