Average Error: 0.0 → 0.6
Time: 7.6s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r3668 = c;
        double r3669 = sinh(r3668);
        double r3670 = -2.9807307601812193e+165;
        double r3671 = 2.0;
        double r3672 = pow(r3670, r3671);
        double r3673 = r3668 - r3672;
        double r3674 = fmod(r3669, r3673);
        return r3674;
}
↓
double f(double c) {
        double r3675 = 0.16666666666666666;
        double r3676 = c;
        double r3677 = 3.0;
        double r3678 = pow(r3676, r3677);
        double r3679 = 0.008333333333333333;
        double r3680 = 5.0;
        double r3681 = pow(r3676, r3680);
        double r3682 = fma(r3679, r3681, r3676);
        double r3683 = fma(r3675, r3678, r3682);
        double r3684 = -2.9807307601812193e+165;
        double r3685 = 2.0;
        double r3686 = pow(r3684, r3685);
        double r3687 = r3676 - r3686;
        double r3688 = fmod(r3683, r3687);
        return r3688;
}

Error

Bits error versus c

Derivation

  1. Initial program 0.0

    \[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  2. Taylor expanded around 0 0.6

    \[\leadsto \left(\color{blue}{\left(\frac{1}{6} \cdot {c}^{3} + \left(\frac{1}{120} \cdot {c}^{5} + c\right)\right)} \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  3. Simplified0.6

    \[\leadsto \left(\color{blue}{\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right)} \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

  4. Final simplification0.6

    \[\leadsto \left(\left(\mathsf{fma}\left(\frac{1}{6}, {c}^{3}, \mathsf{fma}\left(\frac{1}{120}, {c}^{5}, c\right)\right)\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (c)
  :name "Random Jason Timeout Test 014"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))