Average Error: 0.0 → 0.6
Time: 3.8s
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 code(double x, double y) {
	return ((double) (((double) sin(x)) * ((double) (((double) sinh(y)) / y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) sin(x)) * ((double) (((double) (0.16666666666666666 * ((double) pow(y, 2.0)))) + ((double) (((double) (0.008333333333333333 * ((double) pow(y, 4.0)))) + 1.0))))));
}

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. 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 2020121 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))