Average Error: 0.0 → 0.5
Time: 12.6s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\left(c + {c}^{5} \cdot \frac{1}{120}\right) + \frac{1}{6} \cdot {c}^{3}\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\left(c + {c}^{5} \cdot \frac{1}{120}\right) + \frac{1}{6} \cdot {c}^{3}\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r17187 = c;
        double r17188 = sinh(r17187);
        double r17189 = -2.9807307601812193e+165;
        double r17190 = 2.0;
        double r17191 = pow(r17189, r17190);
        double r17192 = r17187 - r17191;
        double r17193 = fmod(r17188, r17192);
        return r17193;
}
↓
double f(double c) {
        double r17194 = c;
        double r17195 = 5.0;
        double r17196 = pow(r17194, r17195);
        double r17197 = 0.008333333333333333;
        double r17198 = r17196 * r17197;
        double r17199 = r17194 + r17198;
        double r17200 = 0.16666666666666666;
        double r17201 = 3.0;
        double r17202 = pow(r17194, r17201);
        double r17203 = r17200 * r17202;
        double r17204 = r17199 + r17203;
        double r17205 = -2.9807307601812193e+165;
        double r17206 = 2.0;
        double r17207 = pow(r17205, r17206);
        double r17208 = r17194 - r17207;
        double r17209 = fmod(r17204, r17208);
        return r17209;
}

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 0.5

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

  3. Simplified0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2019196 
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2.0))))