Average Error: 0.0 → 0.6
Time: 4.4s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \frac{\frac{1}{6} \cdot {y}^{3} + \left(\frac{1}{120} \cdot {y}^{5} + y\right)}{y}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \frac{\frac{1}{6} \cdot {y}^{3} + \left(\frac{1}{120} \cdot {y}^{5} + y\right)}{y}
double f(double x, double y) {
        double r144740 = x;
        double r144741 = sin(r144740);
        double r144742 = y;
        double r144743 = sinh(r144742);
        double r144744 = r144743 / r144742;
        double r144745 = r144741 * r144744;
        return r144745;
}
↓
double f(double x, double y) {
        double r144746 = x;
        double r144747 = sin(r144746);
        double r144748 = 0.16666666666666666;
        double r144749 = y;
        double r144750 = 3.0;
        double r144751 = pow(r144749, r144750);
        double r144752 = r144748 * r144751;
        double r144753 = 0.008333333333333333;
        double r144754 = 5.0;
        double r144755 = pow(r144749, r144754);
        double r144756 = r144753 * r144755;
        double r144757 = r144756 + r144749;
        double r144758 = r144752 + r144757;
        double r144759 = r144758 / r144749;
        double r144760 = r144747 * r144759;
        return r144760;
}

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. Taylor expanded around 0 0.6

    \[\leadsto \sin x \cdot \frac{\color{blue}{\frac{1}{6} \cdot {y}^{3} + \left(\frac{1}{120} \cdot {y}^{5} + y\right)}}{y}\]

  3. Final simplification0.6

    \[\leadsto \sin x \cdot \frac{\frac{1}{6} \cdot {y}^{3} + \left(\frac{1}{120} \cdot {y}^{5} + y\right)}{y}\]

Reproduce

herbie shell --seed 2020025 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))