Average Error: 0.0 → 0.5
Time: 21.0s
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 r1267895 = c;
        double r1267896 = sinh(r1267895);
        double r1267897 = -2.9807307601812193e+165;
        double r1267898 = 2.0;
        double r1267899 = pow(r1267897, r1267898);
        double r1267900 = r1267895 - r1267899;
        double r1267901 = fmod(r1267896, r1267900);
        return r1267901;
}
↓
double f(double c) {
        double r1267902 = c;
        double r1267903 = r1267902 * r1267902;
        double r1267904 = 0.16666666666666666;
        double r1267905 = r1267902 * r1267904;
        double r1267906 = 0.008333333333333333;
        double r1267907 = 5.0;
        double r1267908 = pow(r1267902, r1267907);
        double r1267909 = fma(r1267906, r1267908, r1267902);
        double r1267910 = fma(r1267903, r1267905, r1267909);
        double r1267911 = -2.9807307601812193e+165;
        double r1267912 = r1267911 * r1267911;
        double r1267913 = r1267902 - r1267912;
        double r1267914 = fmod(r1267910, r1267913);
        return r1267914;
}

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 002"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))