Average Error: 0.0 → 0.7
Time: 14.0s
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 r33617 = c;
        double r33618 = sinh(r33617);
        double r33619 = -2.9807307601812193e+165;
        double r33620 = 2.0;
        double r33621 = pow(r33619, r33620);
        double r33622 = r33617 - r33621;
        double r33623 = fmod(r33618, r33622);
        return r33623;
}
↓
double f(double c) {
        double r33624 = c;
        double r33625 = 3.0;
        double r33626 = pow(r33624, r33625);
        double r33627 = 6.0;
        double r33628 = r33626 / r33627;
        double r33629 = r33628 + r33624;
        double r33630 = 5.0;
        double r33631 = pow(r33624, r33630);
        double r33632 = 120.0;
        double r33633 = r33631 / r33632;
        double r33634 = r33629 + r33633;
        double r33635 = -2.9807307601812193e+165;
        double r33636 = 2.0;
        double r33637 = pow(r33635, r33636);
        double r33638 = r33624 - r33637;
        double r33639 = fmod(r33634, r33638);
        return r33639;
}

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 002"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.98073076018121927e165 2))))