Average Error: 0.0 → 0.6
Time: 36.4s
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 r717496 = c;
        double r717497 = sinh(r717496);
        double r717498 = -2.9807307601812193e+165;
        double r717499 = 2.0;
        double r717500 = pow(r717498, r717499);
        double r717501 = r717496 - r717500;
        double r717502 = fmod(r717497, r717501);
        return r717502;
}
↓
double f(double c) {
        double r717503 = c;
        double r717504 = r717503 * r717503;
        double r717505 = 0.16666666666666666;
        double r717506 = r717503 * r717505;
        double r717507 = 0.008333333333333333;
        double r717508 = 5.0;
        double r717509 = pow(r717503, r717508);
        double r717510 = fma(r717507, r717509, r717503);
        double r717511 = fma(r717504, r717506, r717510);
        double r717512 = -2.9807307601812193e+165;
        double r717513 = r717512 * r717512;
        double r717514 = r717503 - r717513;
        double r717515 = fmod(r717511, r717514);
        return r717515;
}

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