Average Error: 0.0 → 0.6
Time: 32.0s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{fma}\left(c \cdot c, c \cdot \frac{1}{6}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.9807307601812193 \cdot 10^{+165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{fma}\left(c \cdot c, c \cdot \frac{1}{6}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)
double f(double c) {
        double r1426998 = c;
        double r1426999 = sinh(r1426998);
        double r1427000 = -2.9807307601812193e+165;
        double r1427001 = 2.0;
        double r1427002 = pow(r1427000, r1427001);
        double r1427003 = r1426998 - r1427002;
        double r1427004 = fmod(r1426999, r1427003);
        return r1427004;
}
↓
double f(double c) {
        double r1427005 = c;
        double r1427006 = r1427005 * r1427005;
        double r1427007 = 0.16666666666666666;
        double r1427008 = r1427005 * r1427007;
        double r1427009 = 0.008333333333333333;
        double r1427010 = 5.0;
        double r1427011 = pow(r1427005, r1427010);
        double r1427012 = fma(r1427009, r1427011, r1427005);
        double r1427013 = fma(r1427006, r1427008, r1427012);
        double r1427014 = -2.9807307601812193e+165;
        double r1427015 = r1427014 * r1427014;
        double r1427016 = r1427005 - r1427015;
        double r1427017 = fmod(r1427013, r1427016);
        return r1427017;
}

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. Taylor expanded around 0 0.6

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

  4. Simplified0.6

    \[\leadsto \left(\color{blue}{\left(\mathsf{fma}\left(c \cdot c, \frac{1}{6} \cdot c, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right)} \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

  5. Final simplification0.6

    \[\leadsto \left(\left(\mathsf{fma}\left(c \cdot c, c \cdot \frac{1}{6}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - -2.9807307601812193 \cdot 10^{+165} \cdot -2.9807307601812193 \cdot 10^{+165}\right)\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 002"
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))