Average Error: 29.9 → 0.5
Time: 24.1s
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 r114415 = x;
        double r114416 = exp(r114415);
        double r114417 = 2.0;
        double r114418 = r114416 - r114417;
        double r114419 = -r114415;
        double r114420 = exp(r114419);
        double r114421 = r114418 + r114420;
        return r114421;
}
↓
double f(double x) {
        double r114422 = x;
        double r114423 = 2.0;
        double r114424 = pow(r114422, r114423);
        double r114425 = 0.002777777777777778;
        double r114426 = 6.0;
        double r114427 = pow(r114422, r114426);
        double r114428 = r114425 * r114427;
        double r114429 = 0.08333333333333333;
        double r114430 = 4.0;
        double r114431 = pow(r114422, r114430);
        double r114432 = r114429 * r114431;
        double r114433 = r114428 + r114432;
        double r114434 = r114424 + r114433;
        return r114434;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.9
Target0.0
Herbie0.5
\[4 \cdot {\left(\sinh \left(\frac{x}{2}\right)\right)}^{2}\]

Derivation

  1. Initial program 29.9

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

  2. Taylor expanded around 0 0.5

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

  3. Final simplification0.5

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x)
  :name "exp2 (problem 3.3.7)"

  :herbie-target
  (* 4.0 (pow (sinh (/ x 2.0)) 2.0))

  (+ (- (exp x) 2.0) (exp (- x))))