Average Error: 0.0 → 0.3
Time: 4.0s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sinh c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{expm1}\left(\mathsf{log1p}\left(\sinh c\right)\right)\right) \bmod \left(c - {\left( -2.980730760181219266293799099291950778447 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r25148 = c;
        double r25149 = sinh(r25148);
        double r25150 = -2.9807307601812193e+165;
        double r25151 = 2.0;
        double r25152 = pow(r25150, r25151);
        double r25153 = r25148 - r25152;
        double r25154 = fmod(r25149, r25153);
        return r25154;
}
↓
double f(double c) {
        double r25155 = c;
        double r25156 = sinh(r25155);
        double r25157 = log1p(r25156);
        double r25158 = expm1(r25157);
        double r25159 = -2.9807307601812193e+165;
        double r25160 = 2.0;
        double r25161 = pow(r25159, r25160);
        double r25162 = r25155 - r25161;
        double r25163 = fmod(r25158, r25162);
        return r25163;
}

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 expm1-log1p-u0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))