Average Error: 0.0 → 0.3
Time: 4.9s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sinh c\right)\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sinh c\right)\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r8169 = c;
        double r8170 = sinh(r8169);
        double r8171 = -2.9807307601812193e+165;
        double r8172 = 2.0;
        double r8173 = pow(r8171, r8172);
        double r8174 = r8169 - r8173;
        double r8175 = fmod(r8170, r8174);
        return r8175;
}
↓
double f(double c) {
        double r8176 = c;
        double r8177 = sinh(r8176);
        double r8178 = log1p(r8177);
        double r8179 = expm1(r8178);
        double r8180 = -2.9807307601812193e+165;
        double r8181 = 2.0;
        double r8182 = pow(r8180, r8181);
        double r8183 = r8176 - r8182;
        double r8184 = fmod(r8179, r8183);
        return r8184;
}

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. Using strategy rm

  3. Applied expm1-log1p-u0.3

    \[\leadsto \left(\color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sinh c\right)\right)\right)} \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  4. Final simplification0.3

    \[\leadsto \left(\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sinh c\right)\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 014"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))