Average Error: 0.0 → 0.6
Time: 29.1s
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 r1650991 = c;
        double r1650992 = sinh(r1650991);
        double r1650993 = -2.9807307601812193e+165;
        double r1650994 = 2.0;
        double r1650995 = pow(r1650993, r1650994);
        double r1650996 = r1650991 - r1650995;
        double r1650997 = fmod(r1650992, r1650996);
        return r1650997;
}
↓
double f(double c) {
        double r1650998 = c;
        double r1650999 = 0.008333333333333333;
        double r1651000 = 5.0;
        double r1651001 = pow(r1650998, r1651000);
        double r1651002 = r1650999 * r1651001;
        double r1651003 = 0.16666666666666666;
        double r1651004 = r1650998 * r1651003;
        double r1651005 = r1650998 * r1650998;
        double r1651006 = r1651004 * r1651005;
        double r1651007 = r1651002 + r1651006;
        double r1651008 = r1650998 + r1651007;
        double r1651009 = -2.9807307601812193e+165;
        double r1651010 = r1651009 * r1651009;
        double r1651011 = r1650998 - r1651010;
        double r1651012 = fmod(r1651008, r1651011);
        return r1651012;
}

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))))