Average Error: 58.1 → 1.3
Time: 2.6s
Precision: binary64
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}} \]
↓
\[\frac{\frac{2 \cdot \sinh x}{\cosh x}}{2} \]
\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}
↓
\frac{\frac{2 \cdot \sinh x}{\cosh x}}{2}

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

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.1

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

  3. Applied cosh-undef_binary6458.1

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

  4. Applied sinh-undef_binary641.3

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

  5. Applied times-frac_binary641.3

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

  6. Applied associate-*l/_binary641.3

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

  7. Simplified1.3

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

  8. Final simplification1.3

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

Reproduce

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