Average Error: 0.0 → 0.6
Time: 23.4s
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 r778538 = c;
        double r778539 = sinh(r778538);
        double r778540 = -2.9807307601812193e+165;
        double r778541 = 2.0;
        double r778542 = pow(r778540, r778541);
        double r778543 = r778538 - r778542;
        double r778544 = fmod(r778539, r778543);
        return r778544;
}
↓
double f(double c) {
        double r778545 = c;
        double r778546 = r778545 * r778545;
        double r778547 = r778545 * r778546;
        double r778548 = 0.16666666666666666;
        double r778549 = r778547 * r778548;
        double r778550 = r778545 + r778549;
        double r778551 = 5.0;
        double r778552 = pow(r778545, r778551);
        double r778553 = 0.008333333333333333;
        double r778554 = r778552 * r778553;
        double r778555 = r778550 + r778554;
        double r778556 = -2.9807307601812193e+165;
        double r778557 = r778556 * r778556;
        double r778558 = r778545 - r778557;
        double r778559 = fmod(r778555, r778558);
        return r778559;
}

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))))