Average Error: 0.0 → 0.3
Time: 4.3s
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 r4496 = c;
        double r4497 = sinh(r4496);
        double r4498 = -2.9807307601812193e+165;
        double r4499 = 2.0;
        double r4500 = pow(r4498, r4499);
        double r4501 = r4496 - r4500;
        double r4502 = fmod(r4497, r4501);
        return r4502;
}
↓
double f(double c) {
        double r4503 = c;
        double r4504 = sinh(r4503);
        double r4505 = log1p(r4504);
        double r4506 = expm1(r4505);
        double r4507 = -2.9807307601812193e+165;
        double r4508 = 2.0;
        double r4509 = pow(r4507, r4508);
        double r4510 = r4503 - r4509;
        double r4511 = fmod(r4506, r4510);
        return r4511;
}

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 014"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))