Average Error: 0.0 → 0.6
Time: 17.8s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r14236 = c;
        double r14237 = sinh(r14236);
        double r14238 = -2.9807307601812193e+165;
        double r14239 = 2.0;
        double r14240 = pow(r14238, r14239);
        double r14241 = r14236 - r14240;
        double r14242 = fmod(r14237, r14241);
        return r14242;
}
↓
double f(double c) {
        double r14243 = 0.16666666666666666;
        double r14244 = c;
        double r14245 = 3.0;
        double r14246 = pow(r14244, r14245);
        double r14247 = 0.008333333333333333;
        double r14248 = 5.0;
        double r14249 = pow(r14244, r14248);
        double r14250 = fma(r14247, r14249, r14244);
        double r14251 = fma(r14243, r14246, r14250);
        double r14252 = -2.9807307601812193e+165;
        double r14253 = 2.0;
        double r14254 = pow(r14252, r14253);
        double r14255 = r14244 - r14254;
        double r14256 = fmod(r14251, r14255);
        return r14256;
}

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 0.6

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

  3. Simplified0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 014"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.98073076018121927e165 2))))