Average Error: 58.0 → 0.6
Time: 15.4s
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 r2291555 = x;
        double r2291556 = exp(r2291555);
        double r2291557 = -r2291555;
        double r2291558 = exp(r2291557);
        double r2291559 = r2291556 - r2291558;
        double r2291560 = 2.0;
        double r2291561 = r2291559 / r2291560;
        return r2291561;
}
↓
double f(double x) {
        double r2291562 = 0.016666666666666666;
        double r2291563 = x;
        double r2291564 = 5.0;
        double r2291565 = pow(r2291563, r2291564);
        double r2291566 = r2291562 * r2291565;
        double r2291567 = 2.0;
        double r2291568 = r2291567 * r2291563;
        double r2291569 = 0.3333333333333333;
        double r2291570 = r2291563 * r2291563;
        double r2291571 = r2291569 * r2291570;
        double r2291572 = r2291571 * r2291563;
        double r2291573 = r2291568 + r2291572;
        double r2291574 = r2291566 + r2291573;
        double r2291575 = r2291574 / r2291567;
        return r2291575;
}

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

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

  5. Applied distribute-rgt-in0.6

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

  6. 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 2019158 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))