Average Error: 0.0 → 0.6
Time: 4.0s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
double code(double c) {
	return fmod(sinh(c), (c - pow(-2.9807307601812193e+165, 2.0)));
}
↓
double code(double c) {
	return fmod(((0.16666666666666666 * pow(c, 3.0)) + ((0.008333333333333333 * pow(c, 5.0)) + c)), (c - pow(-2.9807307601812193e+165, 2.0)));
}

Error

Bits error versus c

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  2. Taylor expanded around 0 0.6

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  3. Final simplification0.6

    \[\leadsto \left(\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

Reproduce

herbie shell --seed 2020058 
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))