Average Error: 0.0 → 0.6
Time: 31.1s
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 r845901 = c;
        double r845902 = sinh(r845901);
        double r845903 = -2.9807307601812193e+165;
        double r845904 = 2.0;
        double r845905 = pow(r845903, r845904);
        double r845906 = r845901 - r845905;
        double r845907 = fmod(r845902, r845906);
        return r845907;
}
↓
double f(double c) {
        double r845908 = c;
        double r845909 = 0.008333333333333333;
        double r845910 = 5.0;
        double r845911 = pow(r845908, r845910);
        double r845912 = r845909 * r845911;
        double r845913 = 0.16666666666666666;
        double r845914 = r845908 * r845913;
        double r845915 = r845908 * r845908;
        double r845916 = r845914 * r845915;
        double r845917 = r845912 + r845916;
        double r845918 = r845908 + r845917;
        double r845919 = -2.9807307601812193e+165;
        double r845920 = r845919 * r845919;
        double r845921 = r845908 - r845920;
        double r845922 = fmod(r845918, r845921);
        return r845922;
}

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))))