Average Error: 0.2 → 0.0
Time: 5.4s
Precision: binary64
Cost: 7232
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
↓
\[6 \cdot \frac{x + -1}{x + \left(1 + 4 \cdot \sqrt{x}\right)} \]
(FPCore (x)
 :precision binary64
 (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))
↓
(FPCore (x)
 :precision binary64
 (* 6.0 (/ (+ x -1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
double code(double x) {
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * sqrt(x)));
}
↓
double code(double x) {
	return 6.0 * ((x + -1.0) / (x + (1.0 + (4.0 * sqrt(x)))));
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (6.0d0 * (x - 1.0d0)) / ((x + 1.0d0) + (4.0d0 * sqrt(x)))
end function
↓
real(8) function code(x)
    real(8), intent (in) :: x
    code = 6.0d0 * ((x + (-1.0d0)) / (x + (1.0d0 + (4.0d0 * sqrt(x)))))
end function

public static double code(double x) {
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * Math.sqrt(x)));
}
↓
public static double code(double x) {
	return 6.0 * ((x + -1.0) / (x + (1.0 + (4.0 * Math.sqrt(x)))));
}

def code(x):
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * math.sqrt(x)))
↓
def code(x):
	return 6.0 * ((x + -1.0) / (x + (1.0 + (4.0 * math.sqrt(x)))))

function code(x)
	return Float64(Float64(6.0 * Float64(x - 1.0)) / Float64(Float64(x + 1.0) + Float64(4.0 * sqrt(x))))
end
↓
function code(x)
	return Float64(6.0 * Float64(Float64(x + -1.0) / Float64(x + Float64(1.0 + Float64(4.0 * sqrt(x))))))
end

function tmp = code(x)
	tmp = (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * sqrt(x)));
end
↓
function tmp = code(x)
	tmp = 6.0 * ((x + -1.0) / (x + (1.0 + (4.0 * sqrt(x)))));
end

code[x_] := N[(N[(6.0 * N[(x - 1.0), $MachinePrecision]), $MachinePrecision] / N[(N[(x + 1.0), $MachinePrecision] + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(6.0 * N[(N[(x + -1.0), $MachinePrecision] / N[(x + N[(1.0 + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
6 \cdot \frac{x + -1}{x + \left(1 + 4 \cdot \sqrt{x}\right)}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.0
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}} \]

Derivation

  1. Initial program 0.2

    \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]

  2. Applied egg-rr0.0

    \[\leadsto \color{blue}{6 \cdot \frac{x + -1}{x + \mathsf{fma}\left(4, \sqrt{x}, 1\right)}} \]

  3. Applied egg-rr0.0

    \[\leadsto 6 \cdot \frac{x + -1}{x + \color{blue}{\left(1 + 4 \cdot \sqrt{x}\right)}} \]

  4. Final simplification0.0

    \[\leadsto 6 \cdot \frac{x + -1}{x + \left(1 + 4 \cdot \sqrt{x}\right)} \]

Alternatives

Alternative 1
Error1.5
Cost7236
\[\begin{array}{l} t_0 := 4 \cdot \sqrt{x}\\ \mathbf{if}\;x \leq 0.39211478482209317:\\ \;\;\;\;\frac{x + -1}{0.16666666666666666 + t_0 \cdot 0.16666666666666666}\\ \mathbf{else}:\\ \;\;\;\;\frac{6 \cdot x}{t_0 + \left(x + 1\right)}\\ \end{array} \]
Alternative 2
Error0.1
Cost7232
\[\left(x + -1\right) \cdot \frac{6}{x + \left(1 + 4 \cdot \sqrt{x}\right)} \]
Alternative 3
Error3.0
Cost576
\[\frac{6}{\frac{x + 1}{x + -1}} \]
Alternative 4
Error3.0
Cost452
\[\begin{array}{l} \mathbf{if}\;x \leq 0.39211478482209317:\\ \;\;\;\;x \cdot 12 + -6\\ \mathbf{else}:\\ \;\;\;\;6\\ \end{array} \]
Alternative 5
Error3.0
Cost452
\[\begin{array}{l} \mathbf{if}\;x \leq 0.39211478482209317:\\ \;\;\;\;x \cdot 12 + -6\\ \mathbf{else}:\\ \;\;\;\;6 + \frac{-12}{x}\\ \end{array} \]
Alternative 6
Error3.0
Cost196
\[\begin{array}{l} \mathbf{if}\;x \leq 0.39211478482209317:\\ \;\;\;\;-6\\ \mathbf{else}:\\ \;\;\;\;6\\ \end{array} \]
Alternative 7
Error33.0
Cost64
\[6 \]

Error

Reproduce

herbie shell --seed 2022228 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"
  :precision binary64

  :herbie-target
  (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

  (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))