Average Error: 0.0 → 0.6
Time: 24.5s
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 r393261 = c;
        double r393262 = sinh(r393261);
        double r393263 = -2.9807307601812193e+165;
        double r393264 = 2.0;
        double r393265 = pow(r393263, r393264);
        double r393266 = r393261 - r393265;
        double r393267 = fmod(r393262, r393266);
        return r393267;
}
↓
double f(double c) {
        double r393268 = c;
        double r393269 = r393268 * r393268;
        double r393270 = r393268 * r393269;
        double r393271 = 0.16666666666666666;
        double r393272 = r393270 * r393271;
        double r393273 = r393268 + r393272;
        double r393274 = 5.0;
        double r393275 = pow(r393268, r393274);
        double r393276 = 0.008333333333333333;
        double r393277 = r393275 * r393276;
        double r393278 = r393273 + r393277;
        double r393279 = -2.9807307601812193e+165;
        double r393280 = r393279 * r393279;
        double r393281 = r393268 - r393280;
        double r393282 = fmod(r393278, r393281);
        return r393282;
}

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