Asymptote A

Percentage Accurate: 76.9% → 99.9%

Time: 6.3s

Alternatives: 10

Speedup: 1.2×

Specification

Math

\[\begin{array}{l} \\ \frac{1}{x + 1} - \frac{1}{x - 1} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{x + 1} - \frac{1}{x - 1} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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1. Add Preprocessing

Alternative 2: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{-2}{1 - x} \cdot \frac{1}{-1 - x} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* (/ -2.0 (- 1.0 x)) (/ 1.0 (- -1.0 x))))

C

double code(double x) {
	return (-2.0 / (1.0 - x)) * (1.0 / (-1.0 - x));
}

Fortran

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

Java

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

Python

def code(x):
	return (-2.0 / (1.0 - x)) * (1.0 / (-1.0 - x))

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 3: 74.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.76:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{x \cdot \left(1 - x\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 0.76) 2.0 (/ 2.0 (* x (- 1.0 x)))))

C

double code(double x) {
	double tmp;
	if (x <= 0.76) {
		tmp = 2.0;
	} else {
		tmp = 2.0 / (x * (1.0 - x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 0.76d0) then
        tmp = 2.0d0
    else
        tmp = 2.0d0 / (x * (1.0d0 - x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.76) {
		tmp = 2.0;
	} else {
		tmp = 2.0 / (x * (1.0 - x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.76:
		tmp = 2.0
	else:
		tmp = 2.0 / (x * (1.0 - x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.76)
		tmp = 2.0;
	else
		tmp = Float64(2.0 / Float64(x * Float64(1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.76)
		tmp = 2.0;
	else
		tmp = 2.0 / (x * (1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.76], 2.0, N[(2.0 / N[(x * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 4: 75.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.76:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{x}}{1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 0.76) 2.0 (/ (/ 2.0 x) (- 1.0 x))))

C

double code(double x) {
	double tmp;
	if (x <= 0.76) {
		tmp = 2.0;
	} else {
		tmp = (2.0 / x) / (1.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 0.76d0) then
        tmp = 2.0d0
    else
        tmp = (2.0d0 / x) / (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 0.76) {
		tmp = 2.0;
	} else {
		tmp = (2.0 / x) / (1.0 - x);
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 0.76:
		tmp = 2.0
	else:
		tmp = (2.0 / x) / (1.0 - x)
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 0.76)
		tmp = 2.0;
	else
		tmp = Float64(Float64(2.0 / x) / Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 0.76)
		tmp = 2.0;
	else
		tmp = (2.0 / x) / (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 0.76], 2.0, N[(N[(2.0 / x), $MachinePrecision] / N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

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1. Add Preprocessing

Alternative 5: 99.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \frac{-2}{\left(-1 + x\right) \cdot \left(x - -1\right)} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (/ -2.0 (* (+ -1.0 x) (- x -1.0))))

C

double code(double x) {
	return -2.0 / ((-1.0 + x) * (x - -1.0));
}

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 6: 63.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.5 \cdot 10^{+102}:\\ \;\;\;\;\frac{-2}{-1 + x}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 5.5e+102) (/ -2.0 (+ -1.0 x)) 0.0))

C

double code(double x) {
	double tmp;
	if (x <= 5.5e+102) {
		tmp = -2.0 / (-1.0 + x);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 5.5d+102) then
        tmp = (-2.0d0) / ((-1.0d0) + x)
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 5.5e+102) {
		tmp = -2.0 / (-1.0 + x);
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 5.5e+102:
		tmp = -2.0 / (-1.0 + x)
	else:
		tmp = 0.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 5.5e+102)
		tmp = Float64(-2.0 / Float64(-1.0 + x));
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= 5.5e+102)
		tmp = -2.0 / (-1.0 + x);
	else
		tmp = 0.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, 5.5e+102], N[(-2.0 / N[(-1.0 + x), $MachinePrecision]), $MachinePrecision], 0.0]

Derivation

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

Alternative 7: 23.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 1.0) 1.0 0.0))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = 1.0
	else:
		tmp = 0.0
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_] := If[LessEqual[x, 1.0], 1.0, 0.0]

Derivation

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

Alternative 8: 63.2% accurate, 3.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1:\\ \;\;\;\;2\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (if (<= x 1.0) 2.0 0.0))

C

double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= 1.0d0) then
        tmp = 2.0d0
    else
        tmp = 0.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= 1.0) {
		tmp = 2.0;
	} else {
		tmp = 0.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= 1.0:
		tmp = 2.0
	else:
		tmp = 0.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= 1.0)
		tmp = 2.0;
	else
		tmp = 0.0;
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_] := If[LessEqual[x, 1.0], 2.0, 0.0]

Derivation

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

Alternative 9: 2.9% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ -0.125 \end{array} \]

FPCore

(FPCore (x) :precision binary64 -0.125)

C

double code(double x) {
	return -0.125;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = -0.125d0
end function

Java

public static double code(double x) {
	return -0.125;
}

Python

def code(x):
	return -0.125

Julia

function code(x)
	return -0.125
end

MATLAB

function tmp = code(x)
	tmp = -0.125;
end

Wolfram

code[x_] := -0.125

Derivation

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

Alternative 10: 27.1% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x) :precision binary64 0.0)

C

double code(double x) {
	return 0.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.0d0
end function

Java

public static double code(double x) {
	return 0.0;
}

Python

def code(x):
	return 0.0

Julia

function code(x)
	return 0.0
end

MATLAB

function tmp = code(x)
	tmp = 0.0;
end

Wolfram

code[x_] := 0.0

Derivation

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

Reproduce

herbie shell --seed 2023348 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0))))