Average Error: 58.2 → 0.0
Time: 3.0s
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 (((double) (((double) exp(x)) - ((double) exp(((double) -(x)))))) / ((double) (((double) exp(x)) + ((double) exp(((double) -(x)))))));
}
↓
double code(double x) {
	return ((double) tanh(x));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 58.2 bits

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

  3. Applied tanh-undefError: 0.0 bits

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

  4. Final simplificationError: 0.0 bits

    \[\leadsto \tanh x\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x)
  :name "Hyperbolic tangent"
  :precision binary64
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))