Average Error: 0.0 → 0.4
Time: 29.5s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{log1p}\left(\mathsf{expm1}\left(\sinh c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{log1p}\left(\mathsf{expm1}\left(\sinh c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r15897 = c;
        double r15898 = sinh(r15897);
        double r15899 = -2.9807307601812193e+165;
        double r15900 = 2.0;
        double r15901 = pow(r15899, r15900);
        double r15902 = r15897 - r15901;
        double r15903 = fmod(r15898, r15902);
        return r15903;
}
↓
double f(double c) {
        double r15904 = c;
        double r15905 = sinh(r15904);
        double r15906 = expm1(r15905);
        double r15907 = log1p(r15906);
        double r15908 = -2.9807307601812193e+165;
        double r15909 = 2.0;
        double r15910 = pow(r15908, r15909);
        double r15911 = r15904 - r15910;
        double r15912 = fmod(r15907, r15911);
        return r15912;
}

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. Using strategy rm

  3. Applied log1p-expm1-u0.4

    \[\leadsto \left(\color{blue}{\left(\mathsf{log1p}\left(\mathsf{expm1}\left(\sinh c\right)\right)\right)} \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

  4. Final simplification0.4

    \[\leadsto \left(\left(\mathsf{log1p}\left(\mathsf{expm1}\left(\sinh c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 014"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.98073076018121927e165 2))))