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 r386568 = c;
        double r386569 = sinh(r386568);
        double r386570 = -2.9807307601812193e+165;
        double r386571 = 2.0;
        double r386572 = pow(r386570, r386571);
        double r386573 = r386568 - r386572;
        double r386574 = fmod(r386569, r386573);
        return r386574;
}
↓
double f(double c) {
        double r386575 = c;
        double r386576 = r386575 * r386575;
        double r386577 = r386575 * r386576;
        double r386578 = 0.16666666666666666;
        double r386579 = r386577 * r386578;
        double r386580 = r386575 + r386579;
        double r386581 = 5.0;
        double r386582 = pow(r386575, r386581);
        double r386583 = 0.008333333333333333;
        double r386584 = r386582 * r386583;
        double r386585 = r386580 + r386584;
        double r386586 = -2.9807307601812193e+165;
        double r386587 = r386586 * r386586;
        double r386588 = r386575 - r386587;
        double r386589 = fmod(r386585, r386588);
        return r386589;
}

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))))