Average Error: 29.1 → 0.0
Time: 3.0s
Precision: binary64
\[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]
↓
\[\frac{\frac{-1}{x} + -3}{x + \frac{-1}{x}} \]
(FPCore (x) :precision binary64 (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))
↓
(FPCore (x) :precision binary64 (/ (+ (/ -1.0 x) -3.0) (+ x (/ -1.0 x))))
double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}
↓
double code(double x) {
	return ((-1.0 / x) + -3.0) / (x + (-1.0 / x));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x / (x + 1.0d0)) - ((x + 1.0d0) / (x - 1.0d0))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = (((-1.0d0) / x) + (-3.0d0)) / (x + ((-1.0d0) / x))
end function

public static double code(double x) {
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
}
↓
public static double code(double x) {
	return ((-1.0 / x) + -3.0) / (x + (-1.0 / x));
}

def code(x):
	return (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0))
↓
def code(x):
	return ((-1.0 / x) + -3.0) / (x + (-1.0 / x))

function code(x)
	return Float64(Float64(x / Float64(x + 1.0)) - Float64(Float64(x + 1.0) / Float64(x - 1.0)))
end
↓
function code(x)
	return Float64(Float64(Float64(-1.0 / x) + -3.0) / Float64(x + Float64(-1.0 / x)))
end

function tmp = code(x)
	tmp = (x / (x + 1.0)) - ((x + 1.0) / (x - 1.0));
end
↓
function tmp = code(x)
	tmp = ((-1.0 / x) + -3.0) / (x + (-1.0 / x));
end

code[x_] := N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(N[(x + 1.0), $MachinePrecision] / N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[(N[(-1.0 / x), $MachinePrecision] + -3.0), $MachinePrecision] / N[(x + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{x}{x + 1} - \frac{x + 1}{x - 1}
↓
\frac{\frac{-1}{x} + -3}{x + \frac{-1}{x}}

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.1

    \[\frac{x}{x + 1} - \frac{x + 1}{x - 1} \]

  2. Applied egg-rr28.7

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

  3. Taylor expanded in x around 0 0.0

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

  4. Simplified0.0

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

  5. Applied egg-rr14.9

    \[\leadsto \frac{\frac{-1}{x} + -3}{\color{blue}{\frac{\mathsf{fma}\left(x, x, -1\right)}{x}}} \]

  6. Taylor expanded in x around 0 0.0

    \[\leadsto \frac{\frac{-1}{x} + -3}{\color{blue}{x - \frac{1}{x}}} \]

  7. Final simplification0.0

    \[\leadsto \frac{\frac{-1}{x} + -3}{x + \frac{-1}{x}} \]

Reproduce

herbie shell --seed 2022204 
(FPCore (x)
  :name "Asymptote C"
  :precision binary64
  (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0))))