Average Error: 0.0 → 0.6
Time: 24.7s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{fma}\left(c \cdot \left(c \cdot c\right), \frac{1}{6}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]
\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 \left(c \cdot c\right), \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 r853104 = c;
        double r853105 = sinh(r853104);
        double r853106 = -2.9807307601812193e+165;
        double r853107 = 2.0;
        double r853108 = pow(r853106, r853107);
        double r853109 = r853104 - r853108;
        double r853110 = fmod(r853105, r853109);
        return r853110;
}
↓
double f(double c) {
        double r853111 = c;
        double r853112 = r853111 * r853111;
        double r853113 = r853111 * r853112;
        double r853114 = 0.16666666666666666;
        double r853115 = 0.008333333333333333;
        double r853116 = 5.0;
        double r853117 = pow(r853111, r853116);
        double r853118 = fma(r853115, r853117, r853111);
        double r853119 = fma(r853113, r853114, r853118);
        double r853120 = -2.9807307601812193e+165;
        double r853121 = r853120 * r853120;
        double r853122 = r853111 - r853121;
        double r853123 = fmod(r853119, r853122);
        return r853123;
}

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

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))