Average Error: 57.9 → 0.6
Time: 21.6s
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{{x}^{5} \cdot \frac{1}{60} + \left(2 \cdot x + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{{x}^{5} \cdot \frac{1}{60} + \left(2 \cdot x + \left(\frac{1}{3} \cdot \left(x \cdot x\right)\right) \cdot x\right)}{2}
double f(double x) {
        double r3193048 = x;
        double r3193049 = exp(r3193048);
        double r3193050 = -r3193048;
        double r3193051 = exp(r3193050);
        double r3193052 = r3193049 - r3193051;
        double r3193053 = 2.0;
        double r3193054 = r3193052 / r3193053;
        return r3193054;
}
↓
double f(double x) {
        double r3193055 = x;
        double r3193056 = 5.0;
        double r3193057 = pow(r3193055, r3193056);
        double r3193058 = 0.016666666666666666;
        double r3193059 = r3193057 * r3193058;
        double r3193060 = 2.0;
        double r3193061 = r3193060 * r3193055;
        double r3193062 = 0.3333333333333333;
        double r3193063 = r3193055 * r3193055;
        double r3193064 = r3193062 * r3193063;
        double r3193065 = r3193064 * r3193055;
        double r3193066 = r3193061 + r3193065;
        double r3193067 = r3193059 + r3193066;
        double r3193068 = 2.0;
        double r3193069 = r3193067 / r3193068;
        return r3193069;
}

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 0.6

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

  3. Simplified0.7

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

  5. Applied distribute-lft-in0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2.0))