Average Error: 58.0 → 0.7
Time: 28.5s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{{x}^{5} \cdot \frac{1}{60} + \left(x \cdot 2 + x \cdot \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right)\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{{x}^{5} \cdot \frac{1}{60} + \left(x \cdot 2 + x \cdot \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right)\right)}{2}
double f(double x) {
        double r2356738 = x;
        double r2356739 = exp(r2356738);
        double r2356740 = -r2356738;
        double r2356741 = exp(r2356740);
        double r2356742 = r2356739 - r2356741;
        double r2356743 = 2.0;
        double r2356744 = r2356742 / r2356743;
        return r2356744;
}
↓
double f(double x) {
        double r2356745 = x;
        double r2356746 = 5.0;
        double r2356747 = pow(r2356745, r2356746);
        double r2356748 = 0.016666666666666666;
        double r2356749 = r2356747 * r2356748;
        double r2356750 = 2.0;
        double r2356751 = r2356745 * r2356750;
        double r2356752 = 0.3333333333333333;
        double r2356753 = r2356745 * r2356745;
        double r2356754 = r2356752 * r2356753;
        double r2356755 = r2356745 * r2356754;
        double r2356756 = r2356751 + r2356755;
        double r2356757 = r2356749 + r2356756;
        double r2356758 = 2.0;
        double r2356759 = r2356757 / r2356758;
        return r2356759;
}

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 0.7

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

  3. Simplified0.7

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

  5. Applied distribute-lft-in0.7

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

  6. Final simplification0.7

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2.0))