Average Error: 0.0 → 0.0
Time: 26.8s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\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)
double f(double c) {
        double r23808 = c;
        double r23809 = sinh(r23808);
        double r23810 = -2.9807307601812193e+165;
        double r23811 = 2.0;
        double r23812 = pow(r23810, r23811);
        double r23813 = r23808 - r23812;
        double r23814 = fmod(r23809, r23813);
        return r23814;
}
↓
double f(double c) {
        double r23815 = c;
        double r23816 = sinh(r23815);
        double r23817 = -2.9807307601812193e+165;
        double r23818 = 2.0;
        double r23819 = pow(r23817, r23818);
        double r23820 = r23815 - r23819;
        double r23821 = fmod(r23816, r23820);
        return r23821;
}

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. Using strategy rm

  5. Applied log1p-expm10.0

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

  6. Final simplification0.0

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

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))))