Asymptote B

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 2: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.82 \lor \neg \left(x \leq 0.55\right):\\ \;\;\;\;\frac{x}{x + -1} + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-1}{1 + x} - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.82) (not (<= x 0.55)))
   (+ (/ x (+ x -1.0)) (/ -1.0 x))
   (- (/ -1.0 (+ 1.0 x)) x)))

C

double code(double x) {
	double tmp;
	if ((x <= -1.82) || !(x <= 0.55)) {
		tmp = (x / (x + -1.0)) + (-1.0 / x);
	} else {
		tmp = (-1.0 / (1.0 + x)) - x;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.82d0)) .or. (.not. (x <= 0.55d0))) then
        tmp = (x / (x + (-1.0d0))) + ((-1.0d0) / x)
    else
        tmp = ((-1.0d0) / (1.0d0 + x)) - x
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -1.82) || !(x <= 0.55)) {
		tmp = (x / (x + -1.0)) + (-1.0 / x);
	} else {
		tmp = (-1.0 / (1.0 + x)) - x;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -1.82) or not (x <= 0.55):
		tmp = (x / (x + -1.0)) + (-1.0 / x)
	else:
		tmp = (-1.0 / (1.0 + x)) - x
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -1.82) || !(x <= 0.55))
		tmp = Float64(Float64(x / Float64(x + -1.0)) + Float64(-1.0 / x));
	else
		tmp = Float64(Float64(-1.0 / Float64(1.0 + x)) - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -1.82) || ~((x <= 0.55)))
		tmp = (x / (x + -1.0)) + (-1.0 / x);
	else
		tmp = (-1.0 / (1.0 + x)) - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -1.82], N[Not[LessEqual[x, 0.55]], $MachinePrecision]], N[(N[(x / N[(x + -1.0), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision]]

Derivation

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

Alternative 3: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.82 \lor \neg \left(x \leq 0.55\right):\\ \;\;\;\;\frac{x}{x + -1} + \frac{-1}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(-1 - x\right) - \frac{x}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (or (<= x -1.82) (not (<= x 0.55)))
   (+ (/ x (+ x -1.0)) (/ -1.0 x))
   (- (- -1.0 x) (/ x (- -1.0 x)))))

C

double code(double x) {
	double tmp;
	if ((x <= -1.82) || !(x <= 0.55)) {
		tmp = (x / (x + -1.0)) + (-1.0 / x);
	} else {
		tmp = (-1.0 - x) - (x / (-1.0 - x));
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if ((x <= (-1.82d0)) .or. (.not. (x <= 0.55d0))) then
        tmp = (x / (x + (-1.0d0))) + ((-1.0d0) / x)
    else
        tmp = ((-1.0d0) - x) - (x / ((-1.0d0) - x))
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if ((x <= -1.82) || !(x <= 0.55)) {
		tmp = (x / (x + -1.0)) + (-1.0 / x);
	} else {
		tmp = (-1.0 - x) - (x / (-1.0 - x));
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if (x <= -1.82) or not (x <= 0.55):
		tmp = (x / (x + -1.0)) + (-1.0 / x)
	else:
		tmp = (-1.0 - x) - (x / (-1.0 - x))
	return tmp

Julia

function code(x)
	tmp = 0.0
	if ((x <= -1.82) || !(x <= 0.55))
		tmp = Float64(Float64(x / Float64(x + -1.0)) + Float64(-1.0 / x));
	else
		tmp = Float64(Float64(-1.0 - x) - Float64(x / Float64(-1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if ((x <= -1.82) || ~((x <= 0.55)))
		tmp = (x / (x + -1.0)) + (-1.0 / x);
	else
		tmp = (-1.0 - x) - (x / (-1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[Or[LessEqual[x, -1.82], N[Not[LessEqual[x, 0.55]], $MachinePrecision]], N[(N[(x / N[(x + -1.0), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 - x), $MachinePrecision] - N[(x / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 4: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{-1 - x}\\ \mathbf{if}\;x \leq -0.95:\\ \;\;\;\;\frac{1}{x} - t_0\\ \mathbf{elif}\;x \leq 0.55:\\ \;\;\;\;\left(-1 - x\right) - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + -1} + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (/ x (- -1.0 x))))
   (if (<= x -0.95)
     (- (/ 1.0 x) t_0)
     (if (<= x 0.55) (- (- -1.0 x) t_0) (+ (/ x (+ x -1.0)) (/ -1.0 x))))))

C

double code(double x) {
	double t_0 = x / (-1.0 - x);
	double tmp;
	if (x <= -0.95) {
		tmp = (1.0 / x) - t_0;
	} else if (x <= 0.55) {
		tmp = (-1.0 - x) - t_0;
	} else {
		tmp = (x / (x + -1.0)) + (-1.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / ((-1.0d0) - x)
    if (x <= (-0.95d0)) then
        tmp = (1.0d0 / x) - t_0
    else if (x <= 0.55d0) then
        tmp = ((-1.0d0) - x) - t_0
    else
        tmp = (x / (x + (-1.0d0))) + ((-1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double t_0 = x / (-1.0 - x);
	double tmp;
	if (x <= -0.95) {
		tmp = (1.0 / x) - t_0;
	} else if (x <= 0.55) {
		tmp = (-1.0 - x) - t_0;
	} else {
		tmp = (x / (x + -1.0)) + (-1.0 / x);
	}
	return tmp;
}

Python

def code(x):
	t_0 = x / (-1.0 - x)
	tmp = 0
	if x <= -0.95:
		tmp = (1.0 / x) - t_0
	elif x <= 0.55:
		tmp = (-1.0 - x) - t_0
	else:
		tmp = (x / (x + -1.0)) + (-1.0 / x)
	return tmp

Julia

function code(x)
	t_0 = Float64(x / Float64(-1.0 - x))
	tmp = 0.0
	if (x <= -0.95)
		tmp = Float64(Float64(1.0 / x) - t_0);
	elseif (x <= 0.55)
		tmp = Float64(Float64(-1.0 - x) - t_0);
	else
		tmp = Float64(Float64(x / Float64(x + -1.0)) + Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	t_0 = x / (-1.0 - x);
	tmp = 0.0;
	if (x <= -0.95)
		tmp = (1.0 / x) - t_0;
	elseif (x <= 0.55)
		tmp = (-1.0 - x) - t_0;
	else
		tmp = (x / (x + -1.0)) + (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := Block[{t$95$0 = N[(x / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.95], N[(N[(1.0 / x), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[x, 0.55], N[(N[(-1.0 - x), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(x / N[(x + -1.0), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 5: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\frac{-1}{1 + x} - x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (if (<= x -1.9) 1.0 (if (<= x 1.0) (- (/ -1.0 (+ 1.0 x)) x) 1.0)))

C

double code(double x) {
	double tmp;
	if (x <= -1.9) {
		tmp = 1.0;
	} else if (x <= 1.0) {
		tmp = (-1.0 / (1.0 + x)) - x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    real(8) :: tmp
    if (x <= (-1.9d0)) then
        tmp = 1.0d0
    else if (x <= 1.0d0) then
        tmp = ((-1.0d0) / (1.0d0 + x)) - x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x) {
	double tmp;
	if (x <= -1.9) {
		tmp = 1.0;
	} else if (x <= 1.0) {
		tmp = (-1.0 / (1.0 + x)) - x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x):
	tmp = 0
	if x <= -1.9:
		tmp = 1.0
	elif x <= 1.0:
		tmp = (-1.0 / (1.0 + x)) - x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x)
	tmp = 0.0
	if (x <= -1.9)
		tmp = 1.0;
	elseif (x <= 1.0)
		tmp = Float64(Float64(-1.0 / Float64(1.0 + x)) - x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x)
	tmp = 0.0;
	if (x <= -1.9)
		tmp = 1.0;
	elseif (x <= 1.0)
		tmp = (-1.0 / (1.0 + x)) - x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_] := If[LessEqual[x, -1.9], 1.0, If[LessEqual[x, 1.0], N[(N[(-1.0 / N[(1.0 + x), $MachinePrecision]), $MachinePrecision] - x), $MachinePrecision], 1.0]]

Derivation

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

Alternative 6: 98.9% accurate, 2.1× speedup

Math

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

FPCore

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

C

double code(double x) {
	double tmp;
	if (x <= -1.0) {
		tmp = 1.0;
	} else if (x <= 1.0) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	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 if (x <= 1.0d0) then
        tmp = -1.0d0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 7: 49.8% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 -1.0)

C

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

Fortran

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

Java

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

Python

def code(x):
	return -1.0

Julia

function code(x)
	return -1.0
end

MATLAB

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

Wolfram

code[x_] := -1.0

Derivation

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

Reproduce

herbie shell --seed 2024003 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))