Average Error: 0.0 → 0.6
Time: 11.4s
Precision: 64
\[\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
↓
\[\left(\left(\left(\frac{1}{6} \cdot {c}^{3} + \frac{1}{120} \cdot {c}^{5}\right) + c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)\]
\left(\left(\sinh c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
↓
\left(\left(\left(\frac{1}{6} \cdot {c}^{3} + \frac{1}{120} \cdot {c}^{5}\right) + c\right) \bmod \left(c - {\left( -2.98073076018121927 \cdot 10^{165} \right)}^{2}\right)\right)
double f(double c) {
        double r6275 = c;
        double r6276 = sinh(r6275);
        double r6277 = -2.9807307601812193e+165;
        double r6278 = 2.0;
        double r6279 = pow(r6277, r6278);
        double r6280 = r6275 - r6279;
        double r6281 = fmod(r6276, r6280);
        return r6281;
}
↓
double f(double c) {
        double r6282 = 0.16666666666666666;
        double r6283 = c;
        double r6284 = 3.0;
        double r6285 = pow(r6283, r6284);
        double r6286 = r6282 * r6285;
        double r6287 = 0.008333333333333333;
        double r6288 = 5.0;
        double r6289 = pow(r6283, r6288);
        double r6290 = r6287 * r6289;
        double r6291 = r6286 + r6290;
        double r6292 = r6291 + r6283;
        double r6293 = -2.9807307601812193e+165;
        double r6294 = 2.0;
        double r6295 = pow(r6293, r6294);
        double r6296 = r6283 - r6295;
        double r6297 = fmod(r6292, r6296);
        return r6297;
}

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. Using strategy rm

  4. Applied associate-+r+0.6

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

  5. Final simplification0.6

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

Reproduce

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