Average Error: 0.0 → 0.6
Time: 28.7s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(c + \left(\frac{1}{120} \cdot {c}^{5} + \left(c \cdot \frac{1}{6}\right) \cdot \left(c \cdot c\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)
↓
\left(\left(c + \left(\frac{1}{120} \cdot {c}^{5} + \left(c \cdot \frac{1}{6}\right) \cdot \left(c \cdot c\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)
double f(double c) {
        double r1683818 = c;
        double r1683819 = sinh(r1683818);
        double r1683820 = -2.9807307601812193e+165;
        double r1683821 = 2.0;
        double r1683822 = pow(r1683820, r1683821);
        double r1683823 = r1683818 - r1683822;
        double r1683824 = fmod(r1683819, r1683823);
        return r1683824;
}
↓
double f(double c) {
        double r1683825 = c;
        double r1683826 = 0.008333333333333333;
        double r1683827 = 5.0;
        double r1683828 = pow(r1683825, r1683827);
        double r1683829 = r1683826 * r1683828;
        double r1683830 = 0.16666666666666666;
        double r1683831 = r1683825 * r1683830;
        double r1683832 = r1683825 * r1683825;
        double r1683833 = r1683831 * r1683832;
        double r1683834 = r1683829 + r1683833;
        double r1683835 = r1683825 + r1683834;
        double r1683836 = -2.9807307601812193e+165;
        double r1683837 = r1683836 * r1683836;
        double r1683838 = r1683825 - r1683837;
        double r1683839 = fmod(r1683835, r1683838);
        return r1683839;
}

Error

Bits error versus c

Derivation

  1. Initial program 0.0

    \[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\left(\sinh c\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)}\]

  3. Taylor expanded around 0 0.6

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

  4. Simplified0.6

    \[\leadsto \left(\color{blue}{\left(\left(\left(c \cdot \frac{1}{6}\right) \cdot \left(c \cdot c\right) + {c}^{5} \cdot \frac{1}{120}\right) + c\right)} \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

  5. Final simplification0.6

    \[\leadsto \left(\left(c + \left(\frac{1}{120} \cdot {c}^{5} + \left(c \cdot \frac{1}{6}\right) \cdot \left(c \cdot c\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

Reproduce

herbie shell --seed 2019158 
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))