Data.Approximate.Numerics:blog from approximate-0.2.2.1

Percentage Accurate: 99.8% → 99.9%

Time: 8.4s

Alternatives: 8

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: 99.8% 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

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

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(6.0 * Float64(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[(6.0 * N[(N[(x + -1.0), $MachinePrecision] / N[(N[(x + 1.0), $MachinePrecision] + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.2:\\ \;\;\;\;6 \cdot \frac{1}{\frac{1}{x + -1}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{6}{1 + \left(x + \sqrt{x \cdot 16}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.2)
   (* 6.0 (/ 1.0 (/ 1.0 (+ x -1.0))))
   (* x (/ 6.0 (+ 1.0 (+ x (sqrt (* x 16.0))))))))

C

double code(double x) {
	double tmp;
	if (x <= 1.2) {
		tmp = 6.0 * (1.0 / (1.0 / (x + -1.0)));
	} else {
		tmp = x * (6.0 / (1.0 + (x + sqrt((x * 16.0)))));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.2d0) then
        tmp = 6.0d0 * (1.0d0 / (1.0d0 / (x + (-1.0d0))))
    else
        tmp = x * (6.0d0 / (1.0d0 + (x + sqrt((x * 16.0d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.2) {
		tmp = 6.0 * (1.0 / (1.0 / (x + -1.0)));
	} else {
		tmp = x * (6.0 / (1.0 + (x + Math.sqrt((x * 16.0)))));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.2:
		tmp = 6.0 * (1.0 / (1.0 / (x + -1.0)))
	else:
		tmp = x * (6.0 / (1.0 + (x + math.sqrt((x * 16.0)))))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.2)
		tmp = Float64(6.0 * Float64(1.0 / Float64(1.0 / Float64(x + -1.0))));
	else
		tmp = Float64(x * Float64(6.0 / Float64(1.0 + Float64(x + sqrt(Float64(x * 16.0))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.2)
		tmp = 6.0 * (1.0 / (1.0 / (x + -1.0)));
	else
		tmp = x * (6.0 / (1.0 + (x + sqrt((x * 16.0)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.2], N[(6.0 * N[(1.0 / N[(1.0 / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(6.0 / N[(1.0 + N[(x + N[Sqrt[N[(x * 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.2:\\ \;\;\;\;6 \cdot \frac{1}{\frac{1}{x + -1}}\\ \mathbf{else}:\\ \;\;\;\;\frac{6 \cdot x}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x 1.2)
   (* 6.0 (/ 1.0 (/ 1.0 (+ x -1.0))))
   (/ (* 6.0 x) (+ (+ x 1.0) (* 4.0 (sqrt x))))))

C

double code(double x) {
	double tmp;
	if (x <= 1.2) {
		tmp = 6.0 * (1.0 / (1.0 / (x + -1.0)));
	} else {
		tmp = (6.0 * x) / ((x + 1.0) + (4.0 * sqrt(x)));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.2d0) then
        tmp = 6.0d0 * (1.0d0 / (1.0d0 / (x + (-1.0d0))))
    else
        tmp = (6.0d0 * x) / ((x + 1.0d0) + (4.0d0 * sqrt(x)))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.2) {
		tmp = 6.0 * (1.0 / (1.0 / (x + -1.0)));
	} else {
		tmp = (6.0 * x) / ((x + 1.0) + (4.0 * Math.sqrt(x)));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.2:
		tmp = 6.0 * (1.0 / (1.0 / (x + -1.0)))
	else:
		tmp = (6.0 * x) / ((x + 1.0) + (4.0 * math.sqrt(x)))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.2)
		tmp = Float64(6.0 * Float64(1.0 / Float64(1.0 / Float64(x + -1.0))));
	else
		tmp = Float64(Float64(6.0 * x) / Float64(Float64(x + 1.0) + Float64(4.0 * sqrt(x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 1.2)
		tmp = 6.0 * (1.0 / (1.0 / (x + -1.0)));
	else
		tmp = (6.0 * x) / ((x + 1.0) + (4.0 * sqrt(x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 1.2], N[(6.0 * N[(1.0 / N[(1.0 / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(6.0 * x), $MachinePrecision] / N[(N[(x + 1.0), $MachinePrecision] + N[(4.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 95.3% accurate, 10.2× speedup

Math

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

FPCore

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

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 6.0 * (1.0 / (1.0 / (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 * (1.0d0 / (1.0d0 / (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 * (1.0 / (1.0 / (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 * (1.0 / (1.0 / (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(1.0 / Float64(1.0 / 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 * (1.0 / (1.0 / (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[(1.0 / N[(1.0 / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 - N[(6.0 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 95.3% accurate, 16.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.5:\\ \;\;\;\;-6\\ \mathbf{else}:\\ \;\;\;\;6 - \frac{6}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 0.5) -6.0 (- 6.0 (/ 6.0 x))))

C

double code(double x) {
	double tmp;
	if (x <= 0.5) {
		tmp = -6.0;
	} 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 <= 0.5d0) then
        tmp = -6.0d0
    else
        tmp = 6.0d0 - (6.0d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.5) {
		tmp = -6.0;
	} else {
		tmp = 6.0 - (6.0 / x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.5:
		tmp = -6.0
	else:
		tmp = 6.0 - (6.0 / x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.5)
		tmp = -6.0;
	else
		tmp = Float64(6.0 - Float64(6.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.5)
		tmp = -6.0;
	else
		tmp = 6.0 - (6.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.5], -6.0, N[(6.0 - N[(6.0 / x), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 95.3% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 95.3% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 48.7% 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

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

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 2023343 
(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)))))