Average Error: 0.0 → 0.5
Time: 12.4s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left({c}^{5}, \frac{1}{120}, c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left({c}^{5}, \frac{1}{120}, c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r16774 = c;
        double r16775 = sinh(r16774);
        double r16776 = -2.9807307601812193e+165;
        double r16777 = 2.0;
        double r16778 = pow(r16776, r16777);
        double r16779 = r16774 - r16778;
        double r16780 = fmod(r16775, r16779);
        return r16780;
}
↓
double f(double c) {
        double r16781 = 0.16666666666666666;
        double r16782 = c;
        double r16783 = 3.0;
        double r16784 = pow(r16782, r16783);
        double r16785 = 5.0;
        double r16786 = pow(r16782, r16785);
        double r16787 = 0.008333333333333333;
        double r16788 = fma(r16786, r16787, r16782);
        double r16789 = fma(r16781, r16784, r16788);
        double r16790 = -2.9807307601812193e+165;
        double r16791 = 2.0;
        double r16792 = pow(r16790, r16791);
        double r16793 = r16782 - r16792;
        double r16794 = fmod(r16789, r16793);
        return r16794;
}

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 0.5

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

  3. Simplified0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2.0))))