Average Error: 0.0 → 0.6
Time: 14.7s
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 r26377 = c;
        double r26378 = sinh(r26377);
        double r26379 = -2.9807307601812193e+165;
        double r26380 = 2.0;
        double r26381 = pow(r26379, r26380);
        double r26382 = r26377 - r26381;
        double r26383 = fmod(r26378, r26382);
        return r26383;
}
↓
double f(double c) {
        double r26384 = 0.16666666666666666;
        double r26385 = c;
        double r26386 = 3.0;
        double r26387 = pow(r26385, r26386);
        double r26388 = r26384 * r26387;
        double r26389 = 0.008333333333333333;
        double r26390 = 5.0;
        double r26391 = pow(r26385, r26390);
        double r26392 = r26389 * r26391;
        double r26393 = r26392 + r26385;
        double r26394 = r26388 + r26393;
        double r26395 = -2.9807307601812193e+165;
        double r26396 = 2.0;
        double r26397 = pow(r26395, r26396);
        double r26398 = r26385 - r26397;
        double r26399 = fmod(r26394, r26398);
        return r26399;
}

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 0.6

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

  3. Final simplification0.6

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

Reproduce

herbie shell --seed 2019208 
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.98073076018121927e165 2))))