Average Error: 58.0 → 0.0
Time: 12.6s
Precision: binary64
Cost: 384
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{2 \cdot \sinh x}{2}\]
\frac{e^{x} - e^{-x}}{2}
↓
\frac{2 \cdot \sinh x}{2}
(FPCore (x) :precision binary64 (/ (- (exp x) (exp (- x))) 2.0))
↓
(FPCore (x) :precision binary64 (/ (* 2.0 (sinh x)) 2.0))
double code(double x) {
	return (exp(x) - exp(-x)) / 2.0;
}
↓
double code(double x) {
	return (2.0 * sinh(x)) / 2.0;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs
Alternative 1
Accuracy0.6
Cost1088
\[\frac{2 \cdot \left(x + \left(0.16666666666666666 \cdot {x}^{3} + 0.008333333333333333 \cdot {x}^{5}\right)\right)}{2}\]

Derivation

  1. Initial program 58.0

    \[\frac{e^{x} - e^{-x}}{2}\]
  2. Using strategy rm

  3. Applied sinh-undef_binary64_9530.0

    \[\leadsto \frac{\color{blue}{2 \cdot \sinh x}}{2}\]

  4. Final simplification0.0

    \[\leadsto \frac{2 \cdot \sinh x}{2}\]

Reproduce

herbie shell --seed 2020322 
(FPCore (x)
  :name "Hyperbolic sine"
  :precision binary64
  (/ (- (exp x) (exp (- x))) 2.0))