Average Error: 29.9 → 0.6
Time: 21.2s
Precision: 64
\[\left(e^{x} - 2\right) + e^{-x}\]
↓
\[{x}^{2} + \left(\frac{1}{360} \cdot {x}^{6} + \frac{1}{12} \cdot {x}^{4}\right)\]
\left(e^{x} - 2\right) + e^{-x}
↓
{x}^{2} + \left(\frac{1}{360} \cdot {x}^{6} + \frac{1}{12} \cdot {x}^{4}\right)
double f(double x) {
        double r95167 = x;
        double r95168 = exp(r95167);
        double r95169 = 2.0;
        double r95170 = r95168 - r95169;
        double r95171 = -r95167;
        double r95172 = exp(r95171);
        double r95173 = r95170 + r95172;
        return r95173;
}
↓
double f(double x) {
        double r95174 = x;
        double r95175 = 2.0;
        double r95176 = pow(r95174, r95175);
        double r95177 = 0.002777777777777778;
        double r95178 = 6.0;
        double r95179 = pow(r95174, r95178);
        double r95180 = r95177 * r95179;
        double r95181 = 0.08333333333333333;
        double r95182 = 4.0;
        double r95183 = pow(r95174, r95182);
        double r95184 = r95181 * r95183;
        double r95185 = r95180 + r95184;
        double r95186 = r95176 + r95185;
        return r95186;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.9
Target0.1
Herbie0.6
\[4 \cdot {\left(\sinh \left(\frac{x}{2}\right)\right)}^{2}\]

Derivation

  1. Initial program 29.9

    \[\left(e^{x} - 2\right) + e^{-x}\]

  2. Taylor expanded around 0 0.6

    \[\leadsto \color{blue}{{x}^{2} + \left(\frac{1}{360} \cdot {x}^{6} + \frac{1}{12} \cdot {x}^{4}\right)}\]

  3. Final simplification0.6

    \[\leadsto {x}^{2} + \left(\frac{1}{360} \cdot {x}^{6} + \frac{1}{12} \cdot {x}^{4}\right)\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x)
  :name "exp2 (problem 3.3.7)"
  :precision binary64

  :herbie-target
  (* 4 (pow (sinh (/ x 2)) 2))

  (+ (- (exp x) 2) (exp (- x))))