Average Error: 0.0 → 0.4
Time: 24.5s
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 r14087 = c;
        double r14088 = sinh(r14087);
        double r14089 = -2.9807307601812193e+165;
        double r14090 = 2.0;
        double r14091 = pow(r14089, r14090);
        double r14092 = r14087 - r14091;
        double r14093 = fmod(r14088, r14092);
        return r14093;
}
↓
double f(double c) {
        double r14094 = c;
        double r14095 = sinh(r14094);
        double r14096 = expm1(r14095);
        double r14097 = log1p(r14096);
        double r14098 = -2.9807307601812193e+165;
        double r14099 = 2.0;
        double r14100 = pow(r14098, r14099);
        double r14101 = r14094 - r14100;
        double r14102 = fmod(r14097, r14101);
        return r14102;
}

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))))