Average Error: 0.2 → 0.0
Time: 6.1s
Precision: binary64
Cost: 7232
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
↓
\[6 \cdot \frac{x + -1}{\left(x + 4 \cdot \sqrt{x}\right) + 1} \]
(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 (* 4.0 (sqrt x))) 1.0))))
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 + (4.0 * sqrt(x))) + 1.0));
}

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 + (4.0d0 * sqrt(x))) + 1.0d0))
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 + (4.0 * Math.sqrt(x))) + 1.0));
}

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 + (4.0 * math.sqrt(x))) + 1.0))

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(Float64(x + Float64(4.0 * sqrt(x))) + 1.0)))
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 + (4.0 * sqrt(x))) + 1.0));
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[(N[(x + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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

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

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

  3. Applied egg-rr0.0

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

  4. Final simplification0.0

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

Alternatives

Alternative 1
Error2.3
Cost7368
\[\begin{array}{l} \mathbf{if}\;x \leq 0.07676580519094359:\\ \;\;\;\;x \cdot 12 + -6\\ \mathbf{elif}\;x \leq 6.246879111149029 \cdot 10^{+31}:\\ \;\;\;\;\frac{6 \cdot x}{4 \cdot \sqrt{x} + \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;6\\ \end{array} \]
Alternative 2
Error0.2
Cost7232
\[\frac{6 \cdot x + -6}{x - \left(-1 + \sqrt{x} \cdot -4\right)} \]
Alternative 3
Error0.1
Cost7232
\[\frac{6}{\frac{4 \cdot \sqrt{x} + \left(x + 1\right)}{x + -1}} \]
Alternative 4
Error3.1
Cost704
\[6 \cdot \frac{1}{\frac{x + 1}{x + -1}} \]
Alternative 5
Error3.3
Cost576
\[\frac{6 + x \cdot -6}{-1 - x} \]
Alternative 6
Error3.1
Cost452
\[\begin{array}{l} \mathbf{if}\;x \leq 0.07676580519094359:\\ \;\;\;\;x \cdot 12 + -6\\ \mathbf{else}:\\ \;\;\;\;6\\ \end{array} \]
Alternative 7
Error3.1
Cost452
\[\begin{array}{l} \mathbf{if}\;x \leq 0.07676580519094359:\\ \;\;\;\;x \cdot 12 + -6\\ \mathbf{else}:\\ \;\;\;\;6 + \frac{-12}{x}\\ \end{array} \]
Alternative 8
Error3.1
Cost196
\[\begin{array}{l} \mathbf{if}\;x \leq 0.07676580519094359:\\ \;\;\;\;-6\\ \mathbf{else}:\\ \;\;\;\;6\\ \end{array} \]
Alternative 9
Error32.8
Cost64
\[-6 \]

Error

Reproduce

herbie shell --seed 2022294 
(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)))))