Average Error: 58.2 → 57.6
Time: 2.0s
Precision: binary64
\[\frac{e^{x} - 1}{e^{x}}\]
↓
\[1 - \frac{1}{e^{x}}\]
\frac{e^{x} - 1}{e^{x}}
↓
1 - \frac{1}{e^{x}}
double code(double x) {
	return ((double) (((double) (((double) exp(x)) - 1.0)) / ((double) exp(x))));
}
↓
double code(double x) {
	return ((double) (1.0 - ((double) (1.0 / ((double) exp(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 58.2

    \[\frac{e^{x} - 1}{e^{x}}\]

  2. Simplified57.6

    \[\leadsto \color{blue}{1 - \frac{1}{e^{x}}}\]

  3. Final simplification57.6

    \[\leadsto 1 - \frac{1}{e^{x}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ (- (exp x) 1) (exp x))"
  :precision binary64
  (/ (- (exp x) 1.0) (exp x)))