Average Error: 58.3 → 0.6
Time: 9.8s
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 r2636621 = x;
        double r2636622 = exp(r2636621);
        double r2636623 = -r2636621;
        double r2636624 = exp(r2636623);
        double r2636625 = r2636622 - r2636624;
        double r2636626 = 2.0;
        double r2636627 = r2636625 / r2636626;
        return r2636627;
}
↓
double f(double x) {
        double r2636628 = x;
        double r2636629 = 5.0;
        double r2636630 = pow(r2636628, r2636629);
        double r2636631 = 0.016666666666666666;
        double r2636632 = r2636630 * r2636631;
        double r2636633 = 2.0;
        double r2636634 = r2636628 * r2636633;
        double r2636635 = 0.3333333333333333;
        double r2636636 = r2636635 * r2636628;
        double r2636637 = r2636636 * r2636628;
        double r2636638 = r2636637 * r2636628;
        double r2636639 = r2636634 + r2636638;
        double r2636640 = r2636632 + r2636639;
        double r2636641 = 2.0;
        double r2636642 = r2636640 / r2636641;
        return r2636642;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.3

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

  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

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

  5. Applied distribute-lft-in0.6

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

  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 2019171 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2.0))