Data.Approximate.Numerics:blog from approximate-0.2.2.1

Percentage Accurate: 99.7% → 99.9%

Time: 7.5s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))

C

double code(double x) {
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * sqrt(x)));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))

C

double code(double x) {
	return (6.0 * (x - 1.0)) / ((x + 1.0) + (4.0 * sqrt(x)));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (/ 6.0 (/ (+ (* 4.0 (sqrt x)) (+ x 1.0)) (+ x -1.0))))

C

double code(double x) {
	return 6.0 / (((4.0 * sqrt(x)) + (x + 1.0)) / (x + -1.0));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

   \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
2. Step-by-step derivation

   1. associate-/l* 99.9%

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

   2. sub-neg 99.9%

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

   3. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (* -6.0 (/ (+ x -1.0) (+ (* (sqrt x) -4.0) (- -1.0 x)))))

C

double code(double x) {
	return -6.0 * ((x + -1.0) / ((sqrt(x) * -4.0) + (-1.0 - x)));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

   \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
2. Step-by-step derivation

   1. associate-/l* 99.9%

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

   2. sub-neg 99.9%

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

   3. metadata-eval 99.9%

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

3. Simplified 99.9%

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

   1. frac-2neg 99.9%

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

   2. metadata-eval 99.9%

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

   3. div-inv 99.9%

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

   4. distribute-neg-frac 99.9%

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

   5. +-commutative 99.9%

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

   6. fma-def 99.9%

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

5. Applied egg-rr 99.9%

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

   1. associate-/r/ 99.8%

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

   2. associate-*l/ 99.9%

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

   3. *-lft-identity 99.9%

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

   4. +-commutative 99.9%

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

   5. fma-udef 99.9%

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

   6. distribute-neg-in 99.9%

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

   7. sub-neg 99.9%

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

   8. *-commutative 99.9%

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

   9. distribute-rgt-neg-in 99.9%

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

   10. metadata-eval 99.9%

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

   11. +-commutative 99.9%

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

7. Simplified 99.9%

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

8. Final simplification 99.9%

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

Alternative 3: 95.3% accurate, 12.6× speedup

Math

\[\begin{array}{l} \\ \left(x + -1\right) \cdot \frac{6}{x + 1} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (+ x -1.0) (/ 6.0 (+ x 1.0))))

C

double code(double x) {
	return (x + -1.0) * (6.0 / (x + 1.0));
}

Fortran

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

Java

public static double code(double x) {
	return (x + -1.0) * (6.0 / (x + 1.0));
}

Python

def code(x):
	return (x + -1.0) * (6.0 / (x + 1.0))

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

   \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
2. Step-by-step derivation

   1. associate-/l* 99.9%

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

   2. sub-neg 99.9%

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

   3. metadata-eval 99.9%

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

3. Simplified 99.9%

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

   1. associate-/r/ 99.9%

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

   2. +-commutative 99.9%

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

   3. fma-def 99.9%

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

5. Applied egg-rr 99.9%

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

   1. fma-udef 99.9%

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

   2. associate-+r+ 99.9%

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

   3. add-sqr-sqrt 99.9%

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

   4. sqrt-unprod 99.5%

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

   5. *-commutative 99.5%

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

   6. *-commutative 99.5%

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

   7. swap-sqr 99.5%

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

   8. metadata-eval 99.5%

      \[\leadsto \frac{6}{\left(\sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{16}} + x\right) + 1} \cdot \left(x + -1\right) \]

   9. metadata-eval 99.5%

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

   10. swap-sqr 99.5%

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

   11. sqrt-unprod 0.0%

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

   12. add-sqr-sqrt 95.6%

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

   13. add-sqr-sqrt 0.0%

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

   14. sqrt-unprod 99.5%

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

   15. swap-sqr 99.5%

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

   16. add-sqr-sqrt 99.5%

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

   17. metadata-eval 99.5%

       \[\leadsto \frac{6}{\left(\sqrt{x \cdot \color{blue}{16}} + x\right) + 1} \cdot \left(x + -1\right) \]

7. Applied egg-rr 99.5%

   \[\leadsto \frac{6}{\color{blue}{\left(\sqrt{x \cdot 16} + x\right) + 1}} \cdot \left(x + -1\right) \]

8. Taylor expanded in x around inf 95.8%

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

9. Final simplification 95.8%

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

Alternative 4: 95.4% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;6 \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;6\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 2.0) (* 6.0 (+ x -1.0)) 6.0))

C

double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = 6.0 * (x + -1.0);
	} else {
		tmp = 6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 2.0d0) then
        tmp = 6.0d0 * (x + (-1.0d0))
    else
        tmp = 6.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 2.0) {
		tmp = 6.0 * (x + -1.0);
	} else {
		tmp = 6.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 2.0:
		tmp = 6.0 * (x + -1.0)
	else:
		tmp = 6.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 2.0)
		tmp = Float64(6.0 * Float64(x + -1.0));
	else
		tmp = 6.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 2.0)
		tmp = 6.0 * (x + -1.0);
	else
		tmp = 6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 2.0], N[(6.0 * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], 6.0]

Derivation

1. Split input into 2 regimes

2. if x < 2

   1. Initial program 99.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-def 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-+r+ 99.9%

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

      3. add-sqr-sqrt 99.9%

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

      4. sqrt-unprod 99.9%

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

      5. *-commutative 99.9%

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

      6. *-commutative 99.9%

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

      7. swap-sqr 99.9%

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

      8. metadata-eval 99.9%

         \[\leadsto \frac{6}{\left(\sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{16}} + x\right) + 1} \cdot \left(x + -1\right) \]

      9. metadata-eval 99.9%

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

      10. swap-sqr 99.9%

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

      11. sqrt-unprod 0.0%

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

      12. add-sqr-sqrt 94.1%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 99.9%

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

      15. swap-sqr 99.9%

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

      16. add-sqr-sqrt 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \frac{6}{\left(\sqrt{x \cdot \color{blue}{16}} + x\right) + 1} \cdot \left(x + -1\right) \]

   7. Applied egg-rr 99.9%

      \[\leadsto \frac{6}{\color{blue}{\left(\sqrt{x \cdot 16} + x\right) + 1}} \cdot \left(x + -1\right) \]

   8. Taylor expanded in x around 0 94.5%

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

   if 2 < x

   1. Initial program 99.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 97.2%

      \[\leadsto \color{blue}{6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2:\\ \;\;\;\;6 \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;6\\ \end{array} \]

Alternative 5: 95.4% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;6 \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;6 + \frac{-6}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.0) (* 6.0 (+ x -1.0)) (+ 6.0 (/ -6.0 x))))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 6.0 * (x + -1.0);
	} else {
		tmp = 6.0 + (-6.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.0d0) then
        tmp = 6.0d0 * (x + (-1.0d0))
    else
        tmp = 6.0d0 + ((-6.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 6.0 * (x + -1.0);
	} else {
		tmp = 6.0 + (-6.0 / x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = 6.0 * (x + -1.0)
	else:
		tmp = 6.0 + (-6.0 / x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.0)
		tmp = Float64(6.0 * Float64(x + -1.0));
	else
		tmp = Float64(6.0 + Float64(-6.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.0)
		tmp = 6.0 * (x + -1.0);
	else
		tmp = 6.0 + (-6.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.0], N[(6.0 * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], N[(6.0 + N[(-6.0 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 99.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

      2. +-commutative 99.9%

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

      3. fma-def 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. fma-udef 99.9%

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

      2. associate-+r+ 99.9%

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

      3. add-sqr-sqrt 99.9%

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

      4. sqrt-unprod 99.9%

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

      5. *-commutative 99.9%

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

      6. *-commutative 99.9%

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

      7. swap-sqr 99.9%

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

      8. metadata-eval 99.9%

         \[\leadsto \frac{6}{\left(\sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{16}} + x\right) + 1} \cdot \left(x + -1\right) \]

      9. metadata-eval 99.9%

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

      10. swap-sqr 99.9%

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

      11. sqrt-unprod 0.0%

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

      12. add-sqr-sqrt 94.1%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 99.9%

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

      15. swap-sqr 99.9%

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

      16. add-sqr-sqrt 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \frac{6}{\left(\sqrt{x \cdot \color{blue}{16}} + x\right) + 1} \cdot \left(x + -1\right) \]

   7. Applied egg-rr 99.9%

      \[\leadsto \frac{6}{\color{blue}{\left(\sqrt{x \cdot 16} + x\right) + 1}} \cdot \left(x + -1\right) \]

   8. Taylor expanded in x around 0 94.5%

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

   if 1 < x

   1. Initial program 99.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 97.2%

      \[\leadsto \frac{6}{\frac{\color{blue}{x}}{x + -1}} \]

   5. Taylor expanded in x around 0 97.2%

      \[\leadsto \color{blue}{6 - 6 \cdot \frac{1}{x}} \]
   6. Step-by-step derivation

      1. associate-*r/ 97.2%

         \[\leadsto 6 - \color{blue}{\frac{6 \cdot 1}{x}} \]

      2. metadata-eval 97.2%

         \[\leadsto 6 - \frac{\color{blue}{6}}{x} \]

      3. sub-neg 97.2%

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

      4. distribute-neg-frac 97.2%

         \[\leadsto 6 + \color{blue}{\frac{-6}{x}} \]

      5. metadata-eval 97.2%

         \[\leadsto 6 + \frac{\color{blue}{-6}}{x} \]

   7. Simplified 97.2%

      \[\leadsto \color{blue}{6 + \frac{-6}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;6 \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;6 + \frac{-6}{x}\\ \end{array} \]

Alternative 6: 95.4% accurate, 36.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;-6\\ \mathbf{else}:\\ \;\;\;\;6\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 1.0) -6.0 6.0))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = -6.0;
	} else {
		tmp = 6.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.0d0) then
        tmp = -6.0d0
    else
        tmp = 6.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = -6.0;
	} else {
		tmp = 6.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = -6.0
	else:
		tmp = 6.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.0)
		tmp = -6.0;
	else
		tmp = 6.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.0)
		tmp = -6.0;
	else
		tmp = 6.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.0], -6.0, 6.0]

Derivation

1. Split input into 2 regimes

2. if x < 1

   1. Initial program 99.9%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. sub-neg 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 94.5%

      \[\leadsto \color{blue}{-6} \]

   if 1 < x

   1. Initial program 99.0%

      \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. sub-neg 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 97.2%

      \[\leadsto \color{blue}{6} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;-6\\ \mathbf{else}:\\ \;\;\;\;6\\ \end{array} \]

Alternative 7: 48.3% accurate, 113.0× speedup

Math

\[\begin{array}{l} \\ -6 \end{array} \]

FPCore

(FPCore (x) :precision binary64 -6.0)

C

double code(double x) {
	return -6.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = -6.0d0
end function

Java

public static double code(double x) {
	return -6.0;
}

Python

def code(x):
	return -6.0

Julia

function code(x)
	return -6.0
end

MATLAB

function tmp = code(x)
	tmp = -6.0;
end

Wolfram

code[x_] := -6.0

Derivation

1. Initial program 99.4%

   \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}} \]
2. Step-by-step derivation

   1. associate-/l* 99.9%

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

   2. sub-neg 99.9%

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

   3. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 46.6%

   \[\leadsto \color{blue}{-6} \]

5. Final simplification 46.6%

   \[\leadsto -6 \]

Developer target: 99.9% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x)
 :precision binary64
 (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0))))

C

double code(double x) {
	return 6.0 / (((x + 1.0) + (4.0 * sqrt(x))) / (x - 1.0));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023318 
(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)))))