Average Error: 0.1 → 0.6
Time: 20.3s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot \frac{1}{120} + \frac{1}{6}\right)\right) \cdot \sin x + \sin x\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot \frac{1}{120} + \frac{1}{6}\right)\right) \cdot \sin x + \sin x
double f(double x, double y) {
        double r8492126 = x;
        double r8492127 = sin(r8492126);
        double r8492128 = y;
        double r8492129 = sinh(r8492128);
        double r8492130 = r8492129 / r8492128;
        double r8492131 = r8492127 * r8492130;
        return r8492131;
}
↓
double f(double x, double y) {
        double r8492132 = y;
        double r8492133 = r8492132 * r8492132;
        double r8492134 = 0.008333333333333333;
        double r8492135 = r8492133 * r8492134;
        double r8492136 = 0.16666666666666666;
        double r8492137 = r8492135 + r8492136;
        double r8492138 = r8492133 * r8492137;
        double r8492139 = x;
        double r8492140 = sin(r8492139);
        double r8492141 = r8492138 * r8492140;
        double r8492142 = r8492141 + r8492140;
        return r8492142;
}

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 0.1

    \[\sin x \cdot \frac{\sinh y}{y}\]

  2. Taylor expanded around 0 0.6

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

  3. Simplified0.6

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

  4. Taylor expanded around inf 0.6

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

  5. Simplified0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))