Average Error: 29.1 → 0.6
Time: 29.4s
Precision: 64
\[\left(e^{x} - 2\right) + e^{-x}\]
↓
\[\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) \cdot \frac{1}{360} + \left(\frac{1}{12} \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + x \cdot x\right)\]
\left(e^{x} - 2\right) + e^{-x}
↓
\left(\left(\left(x \cdot x\right) \cdot x\right) \cdot \left(\left(x \cdot x\right) \cdot x\right)\right) \cdot \frac{1}{360} + \left(\frac{1}{12} \cdot \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right)\right) + x \cdot x\right)
double f(double x) {
        double r2992900 = x;
        double r2992901 = exp(r2992900);
        double r2992902 = 2.0;
        double r2992903 = r2992901 - r2992902;
        double r2992904 = -r2992900;
        double r2992905 = exp(r2992904);
        double r2992906 = r2992903 + r2992905;
        return r2992906;
}
↓
double f(double x) {
        double r2992907 = x;
        double r2992908 = r2992907 * r2992907;
        double r2992909 = r2992908 * r2992907;
        double r2992910 = r2992909 * r2992909;
        double r2992911 = 0.002777777777777778;
        double r2992912 = r2992910 * r2992911;
        double r2992913 = 0.08333333333333333;
        double r2992914 = r2992908 * r2992908;
        double r2992915 = r2992913 * r2992914;
        double r2992916 = r2992915 + r2992908;
        double r2992917 = r2992912 + r2992916;
        return r2992917;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.1
Target0.0
Herbie0.6
\[4 \cdot {\left(\sinh \left(\frac{x}{2}\right)\right)}^{2}\]

Derivation

  1. Initial program 29.1

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

  2. Taylor expanded around 0 0.6

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

  3. Simplified0.6

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

  4. Final simplification0.6

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

Reproduce

herbie shell --seed 2019141 
(FPCore (x)
  :name "exp2 (problem 3.3.7)"

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

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