Average Error: 58.0 → 0.0
Time: 2.6s
Precision: binary64
\[\frac{e^{x} - e^{-x}}{2} \]
↓
\[\sinh x \]
\frac{e^{x} - e^{-x}}{2}
↓
\sinh x

(FPCore (x) :precision binary64 (/ (- (exp x) (exp (- x))) 2.0))
↓
(FPCore (x) :precision binary64 (sinh x))
double code(double x) {
	return (exp(x) - exp(-x)) / 2.0;
}
↓
double code(double x) {
	return sinh(x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.0

    \[\frac{e^{x} - e^{-x}}{2} \]

  2. Taylor expanded in x around inf 58.0

    \[\leadsto \frac{\color{blue}{e^{x} - e^{-x}}}{2} \]

  3. Simplified0.0

    \[\leadsto \color{blue}{\sinh x} \]

  4. Final simplification0.0

    \[\leadsto \sinh x \]

Reproduce

herbie shell --seed 2021211 
(FPCore (x)
  :name "Hyperbolic sine"
  :precision binary64
  (/ (- (exp x) (exp (- x))) 2.0))