Average Error: 0.0 → 0.6
Time: 26.1s
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 r347990 = c;
        double r347991 = sinh(r347990);
        double r347992 = -2.9807307601812193e+165;
        double r347993 = 2.0;
        double r347994 = pow(r347992, r347993);
        double r347995 = r347990 - r347994;
        double r347996 = fmod(r347991, r347995);
        return r347996;
}
↓
double f(double c) {
        double r347997 = c;
        double r347998 = r347997 * r347997;
        double r347999 = r347997 * r347998;
        double r348000 = 0.16666666666666666;
        double r348001 = 0.008333333333333333;
        double r348002 = 5.0;
        double r348003 = pow(r347997, r348002);
        double r348004 = fma(r348001, r348003, r347997);
        double r348005 = fma(r347999, r348000, r348004);
        double r348006 = -2.9807307601812193e+165;
        double r348007 = r348006 * r348006;
        double r348008 = r347997 - r348007;
        double r348009 = fmod(r348005, r348008);
        return r348009;
}

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 014"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))