Average Error: 58.1 → 0.6
Time: 9.7s
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 r1072504 = x;
        double r1072505 = exp(r1072504);
        double r1072506 = -r1072504;
        double r1072507 = exp(r1072506);
        double r1072508 = r1072505 - r1072507;
        double r1072509 = 2.0;
        double r1072510 = r1072508 / r1072509;
        return r1072510;
}
↓
double f(double x) {
        double r1072511 = 0.016666666666666666;
        double r1072512 = x;
        double r1072513 = 5.0;
        double r1072514 = pow(r1072512, r1072513);
        double r1072515 = r1072511 * r1072514;
        double r1072516 = 2.0;
        double r1072517 = r1072516 * r1072512;
        double r1072518 = 0.3333333333333333;
        double r1072519 = r1072512 * r1072512;
        double r1072520 = r1072518 * r1072519;
        double r1072521 = r1072520 * r1072512;
        double r1072522 = r1072517 + r1072521;
        double r1072523 = r1072515 + r1072522;
        double r1072524 = r1072523 / r1072516;
        return r1072524;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

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

  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-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 2019156 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))