Average Error: 0.0 → 0.6
Time: 11.2s
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 r14553 = c;
        double r14554 = sinh(r14553);
        double r14555 = -2.9807307601812193e+165;
        double r14556 = 2.0;
        double r14557 = pow(r14555, r14556);
        double r14558 = r14553 - r14557;
        double r14559 = fmod(r14554, r14558);
        return r14559;
}
↓
double f(double c) {
        double r14560 = 0.16666666666666666;
        double r14561 = c;
        double r14562 = 3.0;
        double r14563 = pow(r14561, r14562);
        double r14564 = r14560 * r14563;
        double r14565 = 0.008333333333333333;
        double r14566 = 5.0;
        double r14567 = pow(r14561, r14566);
        double r14568 = r14565 * r14567;
        double r14569 = r14564 + r14568;
        double r14570 = r14569 + r14561;
        double r14571 = -2.9807307601812193e+165;
        double r14572 = 2.0;
        double r14573 = pow(r14571, r14572);
        double r14574 = r14561 - r14573;
        double r14575 = fmod(r14570, r14574);
        return r14575;
}

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 002"
  :precision binary64
  (fmod (sinh c) (- c (pow -2.9807307601812193e+165 2))))