?

Average Error: 0.0 → 0.0
Time: 3.0s
Precision: binary64
Cost: 576

?

\[0 \leq x \land x \leq 1000\]
\[\frac{1}{1 + x} \]
\[\frac{1 - x}{1 - x \cdot x} \]
(FPCore (x) :precision binary64 (/ 1.0 (+ 1.0 x)))
(FPCore (x) :precision binary64 (/ (- 1.0 x) (- 1.0 (* x x))))
double code(double x) {
	return 1.0 / (1.0 + x);
}
double code(double x) {
	return (1.0 - x) / (1.0 - (x * x));
}
real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0 / (1.0d0 + x)
end function
real(8) function code(x)
    real(8), intent (in) :: x
    code = (1.0d0 - x) / (1.0d0 - (x * x))
end function
public static double code(double x) {
	return 1.0 / (1.0 + x);
}
public static double code(double x) {
	return (1.0 - x) / (1.0 - (x * x));
}
def code(x):
	return 1.0 / (1.0 + x)
def code(x):
	return (1.0 - x) / (1.0 - (x * x))
function code(x)
	return Float64(1.0 / Float64(1.0 + x))
end
function code(x)
	return Float64(Float64(1.0 - x) / Float64(1.0 - Float64(x * x)))
end
function tmp = code(x)
	tmp = 1.0 / (1.0 + x);
end
function tmp = code(x)
	tmp = (1.0 - x) / (1.0 - (x * x));
end
code[x_] := N[(1.0 / N[(1.0 + x), $MachinePrecision]), $MachinePrecision]
code[x_] := N[(N[(1.0 - x), $MachinePrecision] / N[(1.0 - N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\frac{1}{1 + x}
\frac{1 - x}{1 - x \cdot x}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.0

    \[\frac{1}{1 + x} \]
  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{\frac{1}{1 - x \cdot x} \cdot \left(1 - x\right)} \]
  3. Simplified0.0

    \[\leadsto \color{blue}{\frac{1 - x}{1 - x \cdot x}} \]
    Proof

    [Start]0.0

    \[ \frac{1}{1 - x \cdot x} \cdot \left(1 - x\right) \]

    associate-*l/ [=>]0.0

    \[ \color{blue}{\frac{1 \cdot \left(1 - x\right)}{1 - x \cdot x}} \]

    *-lft-identity [=>]0.0

    \[ \frac{\color{blue}{1 - x}}{1 - x \cdot x} \]
  4. Final simplification0.0

    \[\leadsto \frac{1 - x}{1 - x \cdot x} \]

Alternatives

Alternative 1
Error0.0
Cost320
\[\frac{1}{1 + x} \]
Alternative 2
Error1.4
Cost192
\[1 - x \]
Alternative 3
Error1.9
Cost64
\[1 \]

Error

Reproduce?

herbie shell --seed 1 
(FPCore (x)
  :name "1.0/(1+x)"
  :precision binary64
  :pre (and (<= 0.0 x) (<= x 1000.0))
  (/ 1.0 (+ 1.0 x)))