Average Error: 0.0 → 0.6
Time: 9.6s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\left(\frac{1}{6} \cdot {c}^{3} + \frac{1}{120} \cdot {c}^{5}\right) + c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\left(\frac{1}{6} \cdot {c}^{3} + \frac{1}{120} \cdot {c}^{5}\right) + c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r18723 = c;
        double r18724 = sinh(r18723);
        double r18725 = -2.9807307601812193e+165;
        double r18726 = 2.0;
        double r18727 = pow(r18725, r18726);
        double r18728 = r18723 - r18727;
        double r18729 = fmod(r18724, r18728);
        return r18729;
}
↓
double f(double c) {
        double r18730 = 0.16666666666666666;
        double r18731 = c;
        double r18732 = 3.0;
        double r18733 = pow(r18731, r18732);
        double r18734 = r18730 * r18733;
        double r18735 = 0.008333333333333333;
        double r18736 = 5.0;
        double r18737 = pow(r18731, r18736);
        double r18738 = r18735 * r18737;
        double r18739 = r18734 + r18738;
        double r18740 = r18739 + r18731;
        double r18741 = -2.9807307601812193e+165;
        double r18742 = 2.0;
        double r18743 = pow(r18741, r18742);
        double r18744 = r18731 - r18743;
        double r18745 = fmod(r18740, r18744);
        return r18745;
}

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. Using strategy rm

  4. Applied associate-+r+0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2020046 
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))