Average Error: 58.2 → 1.7
Time: 16.5s
Precision: 64
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
↓
\[x + \left({x}^{5} \cdot \frac{2}{15} - \left(x \cdot x\right) \cdot \left(\frac{1}{3} \cdot x\right)\right)\]
\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}
↓
x + \left({x}^{5} \cdot \frac{2}{15} - \left(x \cdot x\right) \cdot \left(\frac{1}{3} \cdot x\right)\right)
double f(double x) {
        double r1297875 = x;
        double r1297876 = exp(r1297875);
        double r1297877 = -r1297875;
        double r1297878 = exp(r1297877);
        double r1297879 = r1297876 - r1297878;
        double r1297880 = r1297876 + r1297878;
        double r1297881 = r1297879 / r1297880;
        return r1297881;
}
↓
double f(double x) {
        double r1297882 = x;
        double r1297883 = 5.0;
        double r1297884 = pow(r1297882, r1297883);
        double r1297885 = 0.13333333333333333;
        double r1297886 = r1297884 * r1297885;
        double r1297887 = r1297882 * r1297882;
        double r1297888 = 0.3333333333333333;
        double r1297889 = r1297888 * r1297882;
        double r1297890 = r1297887 * r1297889;
        double r1297891 = r1297886 - r1297890;
        double r1297892 = r1297882 + r1297891;
        return r1297892;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.2

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

  2. Taylor expanded around 0 1.7

    \[\leadsto \color{blue}{\left(x + \frac{2}{15} \cdot {x}^{5}\right) - \frac{1}{3} \cdot {x}^{3}}\]

  3. Simplified1.7

    \[\leadsto \color{blue}{x + \left({x}^{5} \cdot \frac{2}{15} - \left(\frac{1}{3} \cdot x\right) \cdot \left(x \cdot x\right)\right)}\]

  4. Final simplification1.7

    \[\leadsto x + \left({x}^{5} \cdot \frac{2}{15} - \left(x \cdot x\right) \cdot \left(\frac{1}{3} \cdot x\right)\right)\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))