Average Error: 29.4 → 29.4
Time: 5.8s
Precision: binary64
Cost: 13184
\[\left(e^{x} - 2\right) + e^{-x}\]
↓
\[\left(e^{x} - 2\right) + e^{-x}\]
\left(e^{x} - 2\right) + e^{-x}
↓
\left(e^{x} - 2\right) + e^{-x}
(FPCore (x) :precision binary64 (+ (- (exp x) 2.0) (exp (- x))))
↓
(FPCore (x) :precision binary64 (+ (- (exp x) 2.0) (exp (- x))))
double code(double x) {
	return (exp(x) - 2.0) + exp(-x);
}
↓
double code(double x) {
	return (exp(x) - 2.0) + exp(-x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.4
Target0.0
Herbie29.4
\[4 \cdot {\sinh \left(\frac{x}{2}\right)}^{2}\]

Derivation

  1. Initial program 29.4

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

  2. Simplified29.4

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

  3. Final simplification29.4

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

Reproduce

herbie shell --seed 2021023 
(FPCore (x)
  :name "exp2 (problem 3.3.7)"
  :precision binary64
  :herbie-expected 1.5

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

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