Average Error: 0.0 → 0.6
Time: 31.2s
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 r829489 = c;
        double r829490 = sinh(r829489);
        double r829491 = -2.9807307601812193e+165;
        double r829492 = 2.0;
        double r829493 = pow(r829491, r829492);
        double r829494 = r829489 - r829493;
        double r829495 = fmod(r829490, r829494);
        return r829495;
}
↓
double f(double c) {
        double r829496 = c;
        double r829497 = 0.008333333333333333;
        double r829498 = 5.0;
        double r829499 = pow(r829496, r829498);
        double r829500 = r829497 * r829499;
        double r829501 = 0.16666666666666666;
        double r829502 = r829496 * r829501;
        double r829503 = r829496 * r829496;
        double r829504 = r829502 * r829503;
        double r829505 = r829500 + r829504;
        double r829506 = r829496 + r829505;
        double r829507 = -2.9807307601812193e+165;
        double r829508 = r829507 * r829507;
        double r829509 = r829496 - r829508;
        double r829510 = fmod(r829506, r829509);
        return r829510;
}

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