Average Error: 0.0 → 0.6
Time: 4.2s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \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( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r10489 = c;
        double r10490 = sinh(r10489);
        double r10491 = -2.9807307601812193e+165;
        double r10492 = 2.0;
        double r10493 = pow(r10491, r10492);
        double r10494 = r10489 - r10493;
        double r10495 = fmod(r10490, r10494);
        return r10495;
}
↓
double f(double c) {
        double r10496 = 0.16666666666666666;
        double r10497 = c;
        double r10498 = 3.0;
        double r10499 = pow(r10497, r10498);
        double r10500 = r10496 * r10499;
        double r10501 = 0.008333333333333333;
        double r10502 = 5.0;
        double r10503 = pow(r10497, r10502);
        double r10504 = r10501 * r10503;
        double r10505 = r10504 + r10497;
        double r10506 = r10500 + r10505;
        double r10507 = -2.9807307601812193e+165;
        double r10508 = 2.0;
        double r10509 = pow(r10507, r10508);
        double r10510 = r10497 - r10509;
        double r10511 = fmod(r10506, r10510);
        return r10511;
}

Error

Bits error versus c

Derivation

  1. Initial program 0.0

    \[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  2. Taylor expanded around 0 0.6

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  3. Final simplification0.6

    \[\leadsto \left(\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

Reproduce

herbie shell --seed 2020021 
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))