Average Error: 0.0 → 0.4
Time: 21.7s
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 r975639 = c;
        double r975640 = sinh(r975639);
        double r975641 = -2.9807307601812193e+165;
        double r975642 = 2.0;
        double r975643 = pow(r975641, r975642);
        double r975644 = r975639 - r975643;
        double r975645 = fmod(r975640, r975644);
        return r975645;
}
↓
double f(double c) {
        double r975646 = c;
        double r975647 = sinh(r975646);
        double r975648 = expm1(r975647);
        double r975649 = log1p(r975648);
        double r975650 = -2.9807307601812193e+165;
        double r975651 = r975650 * r975650;
        double r975652 = r975646 - r975651;
        double r975653 = fmod(r975649, r975652);
        return r975653;
}

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