Average Error: 57.9 → 0.7
Time: 12.5s
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 r2343605 = x;
        double r2343606 = exp(r2343605);
        double r2343607 = -r2343605;
        double r2343608 = exp(r2343607);
        double r2343609 = r2343606 - r2343608;
        double r2343610 = 2.0;
        double r2343611 = r2343609 / r2343610;
        return r2343611;
}
↓
double f(double x) {
        double r2343612 = 0.016666666666666666;
        double r2343613 = x;
        double r2343614 = 5.0;
        double r2343615 = pow(r2343613, r2343614);
        double r2343616 = r2343612 * r2343615;
        double r2343617 = 2.0;
        double r2343618 = r2343617 * r2343613;
        double r2343619 = 0.3333333333333333;
        double r2343620 = r2343613 * r2343613;
        double r2343621 = r2343619 * r2343620;
        double r2343622 = r2343621 * r2343613;
        double r2343623 = r2343618 + r2343622;
        double r2343624 = r2343616 + r2343623;
        double r2343625 = r2343624 / r2343617;
        return r2343625;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 57.9

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

  2. Taylor expanded around 0 0.7

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

  3. Simplified0.7

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

  5. Applied distribute-rgt-in0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))