Average Error: 0.0 → 0.6
Time: 4.1s
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 r1012 = c;
        double r1013 = sinh(r1012);
        double r1014 = -2.9807307601812193e+165;
        double r1015 = 2.0;
        double r1016 = pow(r1014, r1015);
        double r1017 = r1012 - r1016;
        double r1018 = fmod(r1013, r1017);
        return r1018;
}
↓
double f(double c) {
        double r1019 = 0.16666666666666666;
        double r1020 = c;
        double r1021 = 3.0;
        double r1022 = pow(r1020, r1021);
        double r1023 = 0.008333333333333333;
        double r1024 = 5.0;
        double r1025 = pow(r1020, r1024);
        double r1026 = fma(r1023, r1025, r1020);
        double r1027 = fma(r1019, r1022, r1026);
        double r1028 = -2.9807307601812193e+165;
        double r1029 = 2.0;
        double r1030 = pow(r1028, r1029);
        double r1031 = r1020 - r1030;
        double r1032 = fmod(r1027, r1031);
        return r1032;
}

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 2020025 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 014"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))