Average Error: 58.1 → 0.0
Time: 3.6s
Precision: binary64
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}} \]
↓
\[\tanh x \]
\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}
↓
\tanh x

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

Error

Bits error versus x

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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. Applied tanh-undef_binary640.0

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

  3. Final simplification0.0

    \[\leadsto \tanh x \]

Reproduce

herbie shell --seed 2022081 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))