Average Error: 0.0 → 0.4
Time: 20.7s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\sinh c\right)\right)\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\sinh c\right)\right)\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)
double f(double c) {
        double r975671 = c;
        double r975672 = sinh(r975671);
        double r975673 = -2.9807307601812193e+165;
        double r975674 = 2.0;
        double r975675 = pow(r975673, r975674);
        double r975676 = r975671 - r975675;
        double r975677 = fmod(r975672, r975676);
        return r975677;
}
↓
double f(double c) {
        double r975678 = c;
        double r975679 = sinh(r975678);
        double r975680 = expm1(r975679);
        double r975681 = log1p(r975680);
        double r975682 = -2.9807307601812193e+165;
        double r975683 = r975682 * r975682;
        double r975684 = r975678 - r975683;
        double r975685 = fmod(r975681, r975684);
        return r975685;
}

Error

Bits error versus c

Derivation

  1. Initial program 0.0

    \[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(\left(\sinh c\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)}\]
  3. Using strategy rm

  4. Applied log1p-expm1-u0.4

    \[\leadsto \left(\color{blue}{\left(\mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\sinh c\right)\right)\right)\right)\right)} \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

  5. Final simplification0.4

    \[\leadsto \left(\left(\mathsf{log1p}\left(\left(\mathsf{expm1}\left(\left(\sinh c\right)\right)\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))