Average Error: 58.0 → 0.8
Time: 18.9s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{{x}^{5} \cdot \frac{1}{60} + \left(2 \cdot x + \left(x \cdot \left(x \cdot \frac{1}{3}\right)\right) \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{{x}^{5} \cdot \frac{1}{60} + \left(2 \cdot x + \left(x \cdot \left(x \cdot \frac{1}{3}\right)\right) \cdot x\right)}{2}
double f(double x) {
        double r3780568 = x;
        double r3780569 = exp(r3780568);
        double r3780570 = -r3780568;
        double r3780571 = exp(r3780570);
        double r3780572 = r3780569 - r3780571;
        double r3780573 = 2.0;
        double r3780574 = r3780572 / r3780573;
        return r3780574;
}
↓
double f(double x) {
        double r3780575 = x;
        double r3780576 = 5.0;
        double r3780577 = pow(r3780575, r3780576);
        double r3780578 = 0.016666666666666666;
        double r3780579 = r3780577 * r3780578;
        double r3780580 = 2.0;
        double r3780581 = r3780580 * r3780575;
        double r3780582 = 0.3333333333333333;
        double r3780583 = r3780575 * r3780582;
        double r3780584 = r3780575 * r3780583;
        double r3780585 = r3780584 * r3780575;
        double r3780586 = r3780581 + r3780585;
        double r3780587 = r3780579 + r3780586;
        double r3780588 = r3780587 / r3780580;
        return r3780588;
}

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 0.8

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

  3. Simplified0.8

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

  5. Applied distribute-rgt-in0.8

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

  6. Final simplification0.8

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

Reproduce

herbie shell --seed 2019124 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))