Average Error: 0.0 → 0.6
Time: 9.7s
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 r7958 = c;
        double r7959 = sinh(r7958);
        double r7960 = -2.9807307601812193e+165;
        double r7961 = 2.0;
        double r7962 = pow(r7960, r7961);
        double r7963 = r7958 - r7962;
        double r7964 = fmod(r7959, r7963);
        return r7964;
}
↓
double f(double c) {
        double r7965 = 0.16666666666666666;
        double r7966 = c;
        double r7967 = 3.0;
        double r7968 = pow(r7966, r7967);
        double r7969 = r7965 * r7968;
        double r7970 = 0.008333333333333333;
        double r7971 = 5.0;
        double r7972 = pow(r7966, r7971);
        double r7973 = r7970 * r7972;
        double r7974 = r7969 + r7973;
        double r7975 = r7974 + r7966;
        double r7976 = -2.9807307601812193e+165;
        double r7977 = 2.0;
        double r7978 = pow(r7976, r7977);
        double r7979 = r7966 - r7978;
        double r7980 = fmod(r7975, r7979);
        return r7980;
}

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))))