Average Error: 58.0 → 0.0
Time: 2.5s
Precision: binary64
Cost: 6720
\[\frac{e^{x} - e^{-x}}{2}\]
↓
\[\frac{2 \cdot \sinh x}{2}\]
\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

Alternatives

Alternative 1
Error0.8
Cost832
\[\frac{\left(x + x\right) + x \cdot \left(0.3333333333333333 \cdot \left(x \cdot x\right)\right)}{2}\]
Alternative 2
Error1.2
Cost320
\[\frac{x + x}{2}\]
Alternative 3
Error60.6
Cost64
\[0\]
Alternative 4
Error61.5
Cost64
\[1\]

Error

Derivation

  1. Initial program 58.0

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

  3. Applied sinh-undef_binary64_23170.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Hyperbolic sine"
  :precision binary64
  (/ (- (exp x) (exp (- x))) 2.0))