Average Error: 9.3 → 9.3
Time: 10.7s
Precision: binary64
Cost: 960
\[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1} \]
↓
\[\left(\frac{1}{1 + x} + \frac{-2}{x}\right) + \frac{1}{x + -1} \]
(FPCore (x)
 :precision binary64
 (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (+ (+ (/ 1.0 (+ 1.0 x)) (/ -2.0 x)) (/ 1.0 (+ x -1.0))))
double code(double x) {
	return ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0));
}
↓
double code(double x) {
	return ((1.0 / (1.0 + x)) + (-2.0 / x)) + (1.0 / (x + -1.0));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = ((1.0d0 / (x + 1.0d0)) - (2.0d0 / x)) + (1.0d0 / (x - 1.0d0))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = ((1.0d0 / (1.0d0 + x)) + ((-2.0d0) / x)) + (1.0d0 / (x + (-1.0d0)))
end function

public static double code(double x) {
	return ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0));
}
↓
public static double code(double x) {
	return ((1.0 / (1.0 + x)) + (-2.0 / x)) + (1.0 / (x + -1.0));
}

def code(x):
	return ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0))
↓
def code(x):
	return ((1.0 / (1.0 + x)) + (-2.0 / x)) + (1.0 / (x + -1.0))

function code(x)
	return Float64(Float64(Float64(1.0 / Float64(x + 1.0)) - Float64(2.0 / x)) + Float64(1.0 / Float64(x - 1.0)))
end
↓
function code(x)
	return Float64(Float64(Float64(1.0 / Float64(1.0 + x)) + Float64(-2.0 / x)) + Float64(1.0 / Float64(x + -1.0)))
end

function tmp = code(x)
	tmp = ((1.0 / (x + 1.0)) - (2.0 / x)) + (1.0 / (x - 1.0));
end
↓
function tmp = code(x)
	tmp = ((1.0 / (1.0 + x)) + (-2.0 / x)) + (1.0 / (x + -1.0));
end

code[x_] := N[(N[(N[(1.0 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] - N[(2.0 / x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x - 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[(N[(1.0 / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] + N[(-2.0 / x), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1}
↓
\left(\frac{1}{1 + x} + \frac{-2}{x}\right) + \frac{1}{x + -1}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original9.3
Target0.2
Herbie9.3
\[\frac{2}{x \cdot \left(x \cdot x - 1\right)} \]

Derivation

  1. Initial program 9.3

    \[\left(\frac{1}{x + 1} - \frac{2}{x}\right) + \frac{1}{x - 1} \]

  2. Final simplification9.3

    \[\leadsto \left(\frac{1}{1 + x} + \frac{-2}{x}\right) + \frac{1}{x + -1} \]

Reproduce

herbie shell --seed 2022334 
(FPCore (x)
  :name "3frac (problem 3.3.3)"
  :precision binary64

  :herbie-target
  (/ 2.0 (* x (- (* x x) 1.0)))

  (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0))))