Average Error: 0.0 → 0.7
Time: 21.8s
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 r24985 = c;
        double r24986 = sinh(r24985);
        double r24987 = -2.9807307601812193e+165;
        double r24988 = 2.0;
        double r24989 = pow(r24987, r24988);
        double r24990 = r24985 - r24989;
        double r24991 = fmod(r24986, r24990);
        return r24991;
}
↓
double f(double c) {
        double r24992 = 0.16666666666666666;
        double r24993 = c;
        double r24994 = 3.0;
        double r24995 = pow(r24993, r24994);
        double r24996 = r24992 * r24995;
        double r24997 = 0.008333333333333333;
        double r24998 = 5.0;
        double r24999 = pow(r24993, r24998);
        double r25000 = r24997 * r24999;
        double r25001 = r25000 + r24993;
        double r25002 = r24996 + r25001;
        double r25003 = -2.9807307601812193e+165;
        double r25004 = 2.0;
        double r25005 = pow(r25003, r25004);
        double r25006 = r24993 - r25005;
        double r25007 = fmod(r25002, r25006);
        return r25007;
}

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