Average Error: 0.0 → 0.7
Time: 21.8s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r25018 = c;
        double r25019 = sinh(r25018);
        double r25020 = -2.9807307601812193e+165;
        double r25021 = 2.0;
        double r25022 = pow(r25020, r25021);
        double r25023 = r25018 - r25022;
        double r25024 = fmod(r25019, r25023);
        return r25024;
}
↓
double f(double c) {
        double r25025 = 0.16666666666666666;
        double r25026 = c;
        double r25027 = 3.0;
        double r25028 = pow(r25026, r25027);
        double r25029 = r25025 * r25028;
        double r25030 = 0.008333333333333333;
        double r25031 = 5.0;
        double r25032 = pow(r25026, r25031);
        double r25033 = r25030 * r25032;
        double r25034 = r25033 + r25026;
        double r25035 = r25029 + r25034;
        double r25036 = -2.9807307601812193e+165;
        double r25037 = 2.0;
        double r25038 = pow(r25036, r25037);
        double r25039 = r25026 - r25038;
        double r25040 = fmod(r25035, r25039);
        return r25040;
}

Error

Bits error versus c

Derivation

  1. Initial program 0.0

    \[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

  2. Taylor expanded around 0 0.7

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

  3. Final simplification0.7

    \[\leadsto \left(\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

Reproduce

herbie shell --seed 2019303 
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.98073076018121927e165 2))))