Average Error: 0.0 → 0.7
Time: 23.2s
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 r12334 = c;
        double r12335 = sinh(r12334);
        double r12336 = -2.9807307601812193e+165;
        double r12337 = 2.0;
        double r12338 = pow(r12336, r12337);
        double r12339 = r12334 - r12338;
        double r12340 = fmod(r12335, r12339);
        return r12340;
}
↓
double f(double c) {
        double r12341 = 0.16666666666666666;
        double r12342 = c;
        double r12343 = 3.0;
        double r12344 = pow(r12342, r12343);
        double r12345 = r12341 * r12344;
        double r12346 = 0.008333333333333333;
        double r12347 = 5.0;
        double r12348 = pow(r12342, r12347);
        double r12349 = r12346 * r12348;
        double r12350 = r12349 + r12342;
        double r12351 = r12345 + r12350;
        double r12352 = -2.9807307601812193e+165;
        double r12353 = 2.0;
        double r12354 = pow(r12352, r12353);
        double r12355 = r12342 - r12354;
        double r12356 = fmod(r12351, r12355);
        return r12356;
}

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 0.7

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

  3. Final simplification0.7

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

Reproduce

herbie shell --seed 2019303 
(FPCore (c)
  :name "Random Jason Timeout Test 014"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.98073076018121927e165 2))))