Average Error: 0.0 → 0.6
Time: 16.5s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \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( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r16981 = c;
        double r16982 = sinh(r16981);
        double r16983 = -2.9807307601812193e+165;
        double r16984 = 2.0;
        double r16985 = pow(r16983, r16984);
        double r16986 = r16981 - r16985;
        double r16987 = fmod(r16982, r16986);
        return r16987;
}
↓
double f(double c) {
        double r16988 = 0.16666666666666666;
        double r16989 = c;
        double r16990 = 3.0;
        double r16991 = pow(r16989, r16990);
        double r16992 = r16988 * r16991;
        double r16993 = 0.008333333333333333;
        double r16994 = 5.0;
        double r16995 = pow(r16989, r16994);
        double r16996 = r16993 * r16995;
        double r16997 = r16996 + r16989;
        double r16998 = r16992 + r16997;
        double r16999 = -2.9807307601812193e+165;
        double r17000 = 2.0;
        double r17001 = pow(r16999, r17000);
        double r17002 = r16989 - r17001;
        double r17003 = fmod(r16998, r17002);
        return r17003;
}

Error

Bits error versus c

Derivation

  1. Initial program 0.0

    \[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

  2. Taylor expanded around 0 0.6

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

  3. Final simplification0.6

    \[\leadsto \left(\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

Reproduce

herbie shell --seed 2019208 
(FPCore (c)
  :name "Random Jason Timeout Test 014"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.98073076018121927e165 2))))