Linear.Projection:perspective from linear-1.19.1.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 2.6s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(x + y) / Float64(x - y))
end

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(x + y) / Float64(x - y))
end

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x + y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(x + y) / Float64(x - y))
end

MATLAB

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

Wolfram

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

Derivation

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

Alternative 2: 72.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+115} \lor \neg \left(y \leq -4.7 \cdot 10^{+73}\right) \land \left(y \leq -3.05 \cdot 10^{-124} \lor \neg \left(y \leq 1.4 \cdot 10^{-6}\right)\right):\\ \;\;\;\;-2 \cdot \frac{x}{y} + -1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8e+115)
         (and (not (<= y -4.7e+73))
              (or (<= y -3.05e-124) (not (<= y 1.4e-6)))))
   (+ (* -2.0 (/ x y)) -1.0)
   1.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8e+115) || (!(y <= -4.7e+73) && ((y <= -3.05e-124) || !(y <= 1.4e-6)))) {
		tmp = (-2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-8d+115)) .or. (.not. (y <= (-4.7d+73))) .and. (y <= (-3.05d-124)) .or. (.not. (y <= 1.4d-6))) then
        tmp = ((-2.0d0) * (x / y)) + (-1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8e+115) || (!(y <= -4.7e+73) && ((y <= -3.05e-124) || !(y <= 1.4e-6)))) {
		tmp = (-2.0 * (x / y)) + -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8e+115) or (not (y <= -4.7e+73) and ((y <= -3.05e-124) or not (y <= 1.4e-6))):
		tmp = (-2.0 * (x / y)) + -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8e+115) || (!(y <= -4.7e+73) && ((y <= -3.05e-124) || !(y <= 1.4e-6))))
		tmp = Float64(Float64(-2.0 * Float64(x / y)) + -1.0);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8e+115) || (~((y <= -4.7e+73)) && ((y <= -3.05e-124) || ~((y <= 1.4e-6)))))
		tmp = (-2.0 * (x / y)) + -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8e+115], And[N[Not[LessEqual[y, -4.7e+73]], $MachinePrecision], Or[LessEqual[y, -3.05e-124], N[Not[LessEqual[y, 1.4e-6]], $MachinePrecision]]]], N[(N[(-2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision], 1.0]

Derivation

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

Alternative 3: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+115}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+90}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -200000:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-59}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -8.4 \cdot 10^{-101}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.5e+115)
   -1.0
   (if (<= y -5e+90)
     1.0
     (if (<= y -200000.0)
       -1.0
       (if (<= y -5e-59)
         1.0
         (if (<= y -8.4e-101) -1.0 (if (<= y 7e-5) 1.0 -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.5e+115) {
		tmp = -1.0;
	} else if (y <= -5e+90) {
		tmp = 1.0;
	} else if (y <= -200000.0) {
		tmp = -1.0;
	} else if (y <= -5e-59) {
		tmp = 1.0;
	} else if (y <= -8.4e-101) {
		tmp = -1.0;
	} else if (y <= 7e-5) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-8.5d+115)) then
        tmp = -1.0d0
    else if (y <= (-5d+90)) then
        tmp = 1.0d0
    else if (y <= (-200000.0d0)) then
        tmp = -1.0d0
    else if (y <= (-5d-59)) then
        tmp = 1.0d0
    else if (y <= (-8.4d-101)) then
        tmp = -1.0d0
    else if (y <= 7d-5) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -8.5e+115) {
		tmp = -1.0;
	} else if (y <= -5e+90) {
		tmp = 1.0;
	} else if (y <= -200000.0) {
		tmp = -1.0;
	} else if (y <= -5e-59) {
		tmp = 1.0;
	} else if (y <= -8.4e-101) {
		tmp = -1.0;
	} else if (y <= 7e-5) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.5e+115:
		tmp = -1.0
	elif y <= -5e+90:
		tmp = 1.0
	elif y <= -200000.0:
		tmp = -1.0
	elif y <= -5e-59:
		tmp = 1.0
	elif y <= -8.4e-101:
		tmp = -1.0
	elif y <= 7e-5:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.5e+115)
		tmp = -1.0;
	elseif (y <= -5e+90)
		tmp = 1.0;
	elseif (y <= -200000.0)
		tmp = -1.0;
	elseif (y <= -5e-59)
		tmp = 1.0;
	elseif (y <= -8.4e-101)
		tmp = -1.0;
	elseif (y <= 7e-5)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8.5e+115)
		tmp = -1.0;
	elseif (y <= -5e+90)
		tmp = 1.0;
	elseif (y <= -200000.0)
		tmp = -1.0;
	elseif (y <= -5e-59)
		tmp = 1.0;
	elseif (y <= -8.4e-101)
		tmp = -1.0;
	elseif (y <= 7e-5)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.5e+115], -1.0, If[LessEqual[y, -5e+90], 1.0, If[LessEqual[y, -200000.0], -1.0, If[LessEqual[y, -5e-59], 1.0, If[LessEqual[y, -8.4e-101], -1.0, If[LessEqual[y, 7e-5], 1.0, -1.0]]]]]]

Derivation

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

Alternative 4: 50.1% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

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

Wolfram

code[x_, y_] := -1.0

Derivation

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

Developer target: 100.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024008 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

  (/ (+ x y) (- x y)))