Average Error: 0.0 → 0.6
Time: 7.6s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r14806 = c;
        double r14807 = sinh(r14806);
        double r14808 = -2.9807307601812193e+165;
        double r14809 = 2.0;
        double r14810 = pow(r14808, r14809);
        double r14811 = r14806 - r14810;
        double r14812 = fmod(r14807, r14811);
        return r14812;
}
↓
double f(double c) {
        double r14813 = 0.16666666666666666;
        double r14814 = c;
        double r14815 = 3.0;
        double r14816 = pow(r14814, r14815);
        double r14817 = 0.008333333333333333;
        double r14818 = 5.0;
        double r14819 = pow(r14814, r14818);
        double r14820 = fma(r14817, r14819, r14814);
        double r14821 = fma(r14813, r14816, r14820);
        double r14822 = -2.9807307601812193e+165;
        double r14823 = 2.0;
        double r14824 = pow(r14822, r14823);
        double r14825 = r14814 - r14824;
        double r14826 = fmod(r14821, r14825);
        return r14826;
}

Error

Bits error versus c

Derivation

  1. Initial program 0.0

    \[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  2. Taylor expanded around 0 0.6

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  3. Simplified0.6

    \[\leadsto \left(\color{blue}{\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right)} \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  4. Final simplification0.6

    \[\leadsto \left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))