Average Error: 57.9 → 0.6
Time: 9.4s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{\frac{1}{60} \cdot {x}^{5} + \left(2 \cdot x + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{\frac{1}{60} \cdot {x}^{5} + \left(2 \cdot x + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}
double f(double x) {
        double r937200 = x;
        double r937201 = exp(r937200);
        double r937202 = -r937200;
        double r937203 = exp(r937202);
        double r937204 = r937201 - r937203;
        double r937205 = 2.0;
        double r937206 = r937204 / r937205;
        return r937206;
}
↓
double f(double x) {
        double r937207 = 0.016666666666666666;
        double r937208 = x;
        double r937209 = 5.0;
        double r937210 = pow(r937208, r937209);
        double r937211 = r937207 * r937210;
        double r937212 = 2.0;
        double r937213 = r937212 * r937208;
        double r937214 = 0.3333333333333333;
        double r937215 = r937208 * r937208;
        double r937216 = r937214 * r937215;
        double r937217 = r937216 * r937208;
        double r937218 = r937213 + r937217;
        double r937219 = r937211 + r937218;
        double r937220 = r937219 / r937212;
        return r937220;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 57.9

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

  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-rgt-in0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019154 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))