Average Error: 29.4 → 0.8
Time: 6.1s
Precision: binary64
\[\left(e^{x} - 2\right) + e^{-x}\]
↓
\[{x}^{2} + 0.08333333333333333 \cdot {x}^{4}\]
\left(e^{x} - 2\right) + e^{-x}
↓
{x}^{2} + 0.08333333333333333 \cdot {x}^{4}
(FPCore (x) :precision binary64 (+ (- (exp x) 2.0) (exp (- x))))
↓
(FPCore (x)
 :precision binary64
 (+ (pow x 2.0) (* 0.08333333333333333 (pow x 4.0))))
double code(double x) {
	return (exp(x) - 2.0) + exp(-x);
}
↓
double code(double x) {
	return pow(x, 2.0) + (0.08333333333333333 * pow(x, 4.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.4
Target0.0
Herbie0.8
\[4 \cdot {\sinh \left(\frac{x}{2}\right)}^{2}\]

Derivation

  1. Initial program 29.4

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

  2. Taylor expanded around 0 0.8

    \[\leadsto \color{blue}{{x}^{2} + 0.08333333333333333 \cdot {x}^{4}}\]

  3. Final simplification0.8

    \[\leadsto {x}^{2} + 0.08333333333333333 \cdot {x}^{4}\]

Reproduce

herbie shell --seed 2021045 
(FPCore (x)
  :name "exp2 (problem 3.3.7)"
  :precision binary64

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

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