Average Error: 0.0 → 0.7
Time: 15.9s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\left(\frac{{c}^{3}}{6} + c\right) + \frac{{c}^{5}}{120}\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\left(\frac{{c}^{3}}{6} + c\right) + \frac{{c}^{5}}{120}\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r12184 = c;
        double r12185 = sinh(r12184);
        double r12186 = -2.9807307601812193e+165;
        double r12187 = 2.0;
        double r12188 = pow(r12186, r12187);
        double r12189 = r12184 - r12188;
        double r12190 = fmod(r12185, r12189);
        return r12190;
}
↓
double f(double c) {
        double r12191 = c;
        double r12192 = 3.0;
        double r12193 = pow(r12191, r12192);
        double r12194 = 6.0;
        double r12195 = r12193 / r12194;
        double r12196 = r12195 + r12191;
        double r12197 = 5.0;
        double r12198 = pow(r12191, r12197);
        double r12199 = 120.0;
        double r12200 = r12198 / r12199;
        double r12201 = r12196 + r12200;
        double r12202 = -2.9807307601812193e+165;
        double r12203 = 2.0;
        double r12204 = pow(r12202, r12203);
        double r12205 = r12191 - r12204;
        double r12206 = fmod(r12201, r12205);
        return r12206;
}

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. Simplified0.7

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

  4. Final simplification0.7

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

Reproduce

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