Average Error: 0.0 → 0.6
Time: 12.7s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)
double f(double x, double y) {
        double r106915 = x;
        double r106916 = sin(r106915);
        double r106917 = y;
        double r106918 = sinh(r106917);
        double r106919 = r106918 / r106917;
        double r106920 = r106916 * r106919;
        return r106920;
}
↓
double f(double x, double y) {
        double r106921 = x;
        double r106922 = sin(r106921);
        double r106923 = 0.16666666666666666;
        double r106924 = y;
        double r106925 = 2.0;
        double r106926 = pow(r106924, r106925);
        double r106927 = r106923 * r106926;
        double r106928 = 0.008333333333333333;
        double r106929 = 4.0;
        double r106930 = pow(r106924, r106929);
        double r106931 = r106928 * r106930;
        double r106932 = 1.0;
        double r106933 = r106931 + r106932;
        double r106934 = r106927 + r106933;
        double r106935 = r106922 * r106934;
        return r106935;
}

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

    \[\leadsto \sin x \cdot \color{blue}{\left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)}\]

  3. Final simplification0.6

    \[\leadsto \sin x \cdot \left(\frac{1}{6} \cdot {y}^{2} + \left(\frac{1}{120} \cdot {y}^{4} + 1\right)\right)\]

Reproduce

herbie shell --seed 2019212 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))