Average Error: 0.0 → 0.7
Time: 21.7s
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 r12351 = c;
        double r12352 = sinh(r12351);
        double r12353 = -2.9807307601812193e+165;
        double r12354 = 2.0;
        double r12355 = pow(r12353, r12354);
        double r12356 = r12351 - r12355;
        double r12357 = fmod(r12352, r12356);
        return r12357;
}
↓
double f(double c) {
        double r12358 = 0.16666666666666666;
        double r12359 = c;
        double r12360 = 3.0;
        double r12361 = pow(r12359, r12360);
        double r12362 = r12358 * r12361;
        double r12363 = 0.008333333333333333;
        double r12364 = 5.0;
        double r12365 = pow(r12359, r12364);
        double r12366 = r12363 * r12365;
        double r12367 = r12366 + r12359;
        double r12368 = r12362 + r12367;
        double r12369 = -2.9807307601812193e+165;
        double r12370 = 2.0;
        double r12371 = pow(r12369, r12370);
        double r12372 = r12359 - r12371;
        double r12373 = fmod(r12368, r12372);
        return r12373;
}

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))))