Average Error: 0.0 → 0.6
Time: 22.0s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\left(c + \left(c \cdot \left(c \cdot c\right)\right) \cdot \frac{1}{6}\right) + {c}^{5} \cdot \frac{1}{120}\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)
↓
\left(\left(\left(c + \left(c \cdot \left(c \cdot c\right)\right) \cdot \frac{1}{6}\right) + {c}^{5} \cdot \frac{1}{120}\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)
double f(double c) {
        double r765152 = c;
        double r765153 = sinh(r765152);
        double r765154 = -2.9807307601812193e+165;
        double r765155 = 2.0;
        double r765156 = pow(r765154, r765155);
        double r765157 = r765152 - r765156;
        double r765158 = fmod(r765153, r765157);
        return r765158;
}
↓
double f(double c) {
        double r765159 = c;
        double r765160 = r765159 * r765159;
        double r765161 = r765159 * r765160;
        double r765162 = 0.16666666666666666;
        double r765163 = r765161 * r765162;
        double r765164 = r765159 + r765163;
        double r765165 = 5.0;
        double r765166 = pow(r765159, r765165);
        double r765167 = 0.008333333333333333;
        double r765168 = r765166 * r765167;
        double r765169 = r765164 + r765168;
        double r765170 = -2.9807307601812193e+165;
        double r765171 = r765170 * r765170;
        double r765172 = r765159 - r765171;
        double r765173 = fmod(r765169, r765172);
        return r765173;
}

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

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019153 
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))