Average Error: 58.2 → 0.5
Time: 9.9s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{\left(x + x\right) + \left({x}^{3} \cdot \frac{1}{3} + {x}^{5} \cdot \frac{1}{60}\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{\left(x + x\right) + \left({x}^{3} \cdot \frac{1}{3} + {x}^{5} \cdot \frac{1}{60}\right)}{2}
double f(double x) {
        double r30376 = x;
        double r30377 = exp(r30376);
        double r30378 = -r30376;
        double r30379 = exp(r30378);
        double r30380 = r30377 - r30379;
        double r30381 = 2.0;
        double r30382 = r30380 / r30381;
        return r30382;
}
↓
double f(double x) {
        double r30383 = x;
        double r30384 = r30383 + r30383;
        double r30385 = 3.0;
        double r30386 = pow(r30383, r30385);
        double r30387 = 0.3333333333333333;
        double r30388 = r30386 * r30387;
        double r30389 = 5.0;
        double r30390 = pow(r30383, r30389);
        double r30391 = 0.016666666666666666;
        double r30392 = r30390 * r30391;
        double r30393 = r30388 + r30392;
        double r30394 = r30384 + r30393;
        double r30395 = 2.0;
        double r30396 = r30394 / r30395;
        return r30396;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.2

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

  2. Taylor expanded around 0 0.5

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

  3. Simplified0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2.0))