Average Error: 57.8 → 0.7
Time: 18.1s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{\left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x + \left({x}^{5} \cdot \frac{1}{60} + 2 \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{\left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x + \left({x}^{5} \cdot \frac{1}{60} + 2 \cdot x\right)}{2}
double f(double x) {
        double r3462940 = x;
        double r3462941 = exp(r3462940);
        double r3462942 = -r3462940;
        double r3462943 = exp(r3462942);
        double r3462944 = r3462941 - r3462943;
        double r3462945 = 2.0;
        double r3462946 = r3462944 / r3462945;
        return r3462946;
}
↓
double f(double x) {
        double r3462947 = 0.3333333333333333;
        double r3462948 = x;
        double r3462949 = r3462948 * r3462948;
        double r3462950 = r3462947 * r3462949;
        double r3462951 = r3462950 * r3462948;
        double r3462952 = 5.0;
        double r3462953 = pow(r3462948, r3462952);
        double r3462954 = 0.016666666666666666;
        double r3462955 = r3462953 * r3462954;
        double r3462956 = 2.0;
        double r3462957 = r3462956 * r3462948;
        double r3462958 = r3462955 + r3462957;
        double r3462959 = r3462951 + r3462958;
        double r3462960 = r3462959 / r3462956;
        return r3462960;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 57.8

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

  2. Taylor expanded around 0 0.7

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

  3. Simplified0.7

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

  5. Applied distribute-rgt-in0.7

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

  6. Applied associate-+l+0.7

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

  7. Final simplification0.7

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

Reproduce

herbie shell --seed 2019163 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))