Average Error: 0.0 → 0.6
Time: 4.6s
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 r2776 = c;
        double r2777 = sinh(r2776);
        double r2778 = -2.9807307601812193e+165;
        double r2779 = 2.0;
        double r2780 = pow(r2778, r2779);
        double r2781 = r2776 - r2780;
        double r2782 = fmod(r2777, r2781);
        return r2782;
}
↓
double f(double c) {
        double r2783 = 0.16666666666666666;
        double r2784 = c;
        double r2785 = 3.0;
        double r2786 = pow(r2784, r2785);
        double r2787 = r2783 * r2786;
        double r2788 = 0.008333333333333333;
        double r2789 = 5.0;
        double r2790 = pow(r2784, r2789);
        double r2791 = r2788 * r2790;
        double r2792 = r2791 + r2784;
        double r2793 = r2787 + r2792;
        double r2794 = -2.9807307601812193e+165;
        double r2795 = 2.0;
        double r2796 = pow(r2794, r2795);
        double r2797 = r2784 - r2796;
        double r2798 = fmod(r2793, r2797);
        return r2798;
}

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 014"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))