Average Error: 0.0 → 0.4
Time: 23.7s
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 r24704 = c;
        double r24705 = sinh(r24704);
        double r24706 = -2.9807307601812193e+165;
        double r24707 = 2.0;
        double r24708 = pow(r24706, r24707);
        double r24709 = r24704 - r24708;
        double r24710 = fmod(r24705, r24709);
        return r24710;
}
↓
double f(double c) {
        double r24711 = c;
        double r24712 = sinh(r24711);
        double r24713 = expm1(r24712);
        double r24714 = log1p(r24713);
        double r24715 = -2.9807307601812193e+165;
        double r24716 = 2.0;
        double r24717 = pow(r24715, r24716);
        double r24718 = r24711 - r24717;
        double r24719 = fmod(r24714, r24718);
        return r24719;
}

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 002"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.98073076018121927e165 2))))