Average Error: 58.0 → 0.6
Time: 17.4s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{{x}^{5} \cdot \frac{1}{60} + \left(x \cdot 2 + \left(\left(\frac{1}{3} \cdot x\right) \cdot x\right) \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{{x}^{5} \cdot \frac{1}{60} + \left(x \cdot 2 + \left(\left(\frac{1}{3} \cdot x\right) \cdot x\right) \cdot x\right)}{2}
double f(double x) {
        double r2657198 = x;
        double r2657199 = exp(r2657198);
        double r2657200 = -r2657198;
        double r2657201 = exp(r2657200);
        double r2657202 = r2657199 - r2657201;
        double r2657203 = 2.0;
        double r2657204 = r2657202 / r2657203;
        return r2657204;
}
↓
double f(double x) {
        double r2657205 = x;
        double r2657206 = 5.0;
        double r2657207 = pow(r2657205, r2657206);
        double r2657208 = 0.016666666666666666;
        double r2657209 = r2657207 * r2657208;
        double r2657210 = 2.0;
        double r2657211 = r2657205 * r2657210;
        double r2657212 = 0.3333333333333333;
        double r2657213 = r2657212 * r2657205;
        double r2657214 = r2657213 * r2657205;
        double r2657215 = r2657214 * r2657205;
        double r2657216 = r2657211 + r2657215;
        double r2657217 = r2657209 + r2657216;
        double r2657218 = 2.0;
        double r2657219 = r2657217 / r2657218;
        return r2657219;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.0

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

  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

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

  5. Applied distribute-lft-in0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2.0))