Average Error: 58.1 → 0.6
Time: 13.7s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{x \cdot 2 + \left({x}^{5} \cdot \frac{1}{60} + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{x \cdot 2 + \left({x}^{5} \cdot \frac{1}{60} + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}
double f(double x) {
        double r1064161 = x;
        double r1064162 = exp(r1064161);
        double r1064163 = -r1064161;
        double r1064164 = exp(r1064163);
        double r1064165 = r1064162 - r1064164;
        double r1064166 = 2.0;
        double r1064167 = r1064165 / r1064166;
        return r1064167;
}
↓
double f(double x) {
        double r1064168 = x;
        double r1064169 = 2.0;
        double r1064170 = r1064168 * r1064169;
        double r1064171 = 5.0;
        double r1064172 = pow(r1064168, r1064171);
        double r1064173 = 0.016666666666666666;
        double r1064174 = r1064172 * r1064173;
        double r1064175 = 0.3333333333333333;
        double r1064176 = r1064168 * r1064168;
        double r1064177 = r1064175 * r1064176;
        double r1064178 = r1064177 * r1064168;
        double r1064179 = r1064174 + r1064178;
        double r1064180 = r1064170 + r1064179;
        double r1064181 = r1064180 / r1064169;
        return r1064181;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

    \[\frac{e^{x} - e^{-x}}{2}\]

  2. Taylor expanded around 0 0.6

    \[\leadsto \frac{\color{blue}{2 \cdot x + \left(\frac{1}{3} \cdot {x}^{3} + \frac{1}{60} \cdot {x}^{5}\right)}}{2}\]

  3. Simplified0.6

    \[\leadsto \frac{\color{blue}{x \cdot \left(2 + \frac{1}{3} \cdot \left(x \cdot x\right)\right) + \frac{1}{60} \cdot {x}^{5}}}{2}\]
  4. Using strategy rm

  5. Applied distribute-lft-in0.6

    \[\leadsto \frac{\color{blue}{\left(x \cdot 2 + x \cdot \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right)\right)} + \frac{1}{60} \cdot {x}^{5}}{2}\]

  6. Applied associate-+l+0.6

    \[\leadsto \frac{\color{blue}{x \cdot 2 + \left(x \cdot \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) + \frac{1}{60} \cdot {x}^{5}\right)}}{2}\]

  7. Final simplification0.6

    \[\leadsto \frac{x \cdot 2 + \left({x}^{5} \cdot \frac{1}{60} + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))