Average Error: 58.1 → 0.5
Time: 1.4m
Precision: 64
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{\left(x \cdot \left(x \cdot \frac{1}{3}\right)\right) \cdot x + \left(\frac{1}{60} \cdot {x}^{5} + 2 \cdot x\right)}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{\left(x \cdot \left(x \cdot \frac{1}{3}\right)\right) \cdot x + \left(\frac{1}{60} \cdot {x}^{5} + 2 \cdot x\right)}{2}
double f(double x) {
        double r9806179 = x;
        double r9806180 = exp(r9806179);
        double r9806181 = -r9806179;
        double r9806182 = exp(r9806181);
        double r9806183 = r9806180 - r9806182;
        double r9806184 = 2.0;
        double r9806185 = r9806183 / r9806184;
        return r9806185;
}
↓
double f(double x) {
        double r9806186 = x;
        double r9806187 = 0.3333333333333333;
        double r9806188 = r9806186 * r9806187;
        double r9806189 = r9806186 * r9806188;
        double r9806190 = r9806189 * r9806186;
        double r9806191 = 0.016666666666666666;
        double r9806192 = 5.0;
        double r9806193 = pow(r9806186, r9806192);
        double r9806194 = r9806191 * r9806193;
        double r9806195 = 2.0;
        double r9806196 = r9806195 * r9806186;
        double r9806197 = r9806194 + r9806196;
        double r9806198 = r9806190 + r9806197;
        double r9806199 = r9806198 / r9806195;
        return r9806199;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

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

  2. Taylor expanded around 0 0.5

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

  3. Simplified0.5

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

  5. Applied distribute-rgt-in0.5

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

  6. Applied associate-+l+0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2019119 
(FPCore (x)
  :name "Hyperbolic sine"
  (/ (- (exp x) (exp (- x))) 2))