Average Error: 0.0 → 0.5
Time: 21.3s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{fma}\left(c \cdot c, c \cdot \frac{1}{6}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{fma}\left(c \cdot c, c \cdot \frac{1}{6}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, 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 r577147 = c;
        double r577148 = sinh(r577147);
        double r577149 = -2.9807307601812193e+165;
        double r577150 = 2.0;
        double r577151 = pow(r577149, r577150);
        double r577152 = r577147 - r577151;
        double r577153 = fmod(r577148, r577152);
        return r577153;
}
↓
double f(double c) {
        double r577154 = c;
        double r577155 = r577154 * r577154;
        double r577156 = 0.16666666666666666;
        double r577157 = r577154 * r577156;
        double r577158 = 0.008333333333333333;
        double r577159 = 5.0;
        double r577160 = pow(r577154, r577159);
        double r577161 = fma(r577158, r577160, r577154);
        double r577162 = fma(r577155, r577157, r577161);
        double r577163 = -2.9807307601812193e+165;
        double r577164 = r577163 * r577163;
        double r577165 = r577154 - r577164;
        double r577166 = fmod(r577162, r577165);
        return r577166;
}

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 0.5

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

  4. Simplified0.5

    \[\leadsto \left(\color{blue}{\left(\mathsf{fma}\left(c \cdot c, c \cdot \frac{1}{6}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right)} \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

  5. Final simplification0.5

    \[\leadsto \left(\left(\mathsf{fma}\left(c \cdot c, c \cdot \frac{1}{6}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

Reproduce

herbie shell --seed 2019149 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 014"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))