Linear.Projection:perspective from linear-1.19.1.3, A

Percentage Accurate: 100.0% → 99.9%

Time: 5.7s

Alternatives: 7

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: 99.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 2: 73.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -2 \cdot \frac{x}{y} + -1\\ \mathbf{if}\;y \leq -9.5 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+30}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+49}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (* -2.0 (/ x y)) -1.0)))
   (if (<= y -9.5e+101)
     t_0
     (if (<= y 1.9e+30)
       (+ 1.0 (* 2.0 (/ y x)))
       (if (<= y 4e+49) -1.0 (if (<= y 1.5e+61) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = (-2.0 * (x / y)) + -1.0;
	double tmp;
	if (y <= -9.5e+101) {
		tmp = t_0;
	} else if (y <= 1.9e+30) {
		tmp = 1.0 + (2.0 * (y / x));
	} else if (y <= 4e+49) {
		tmp = -1.0;
	} else if (y <= 1.5e+61) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((-2.0d0) * (x / y)) + (-1.0d0)
    if (y <= (-9.5d+101)) then
        tmp = t_0
    else if (y <= 1.9d+30) then
        tmp = 1.0d0 + (2.0d0 * (y / x))
    else if (y <= 4d+49) then
        tmp = -1.0d0
    else if (y <= 1.5d+61) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (-2.0 * (x / y)) + -1.0;
	double tmp;
	if (y <= -9.5e+101) {
		tmp = t_0;
	} else if (y <= 1.9e+30) {
		tmp = 1.0 + (2.0 * (y / x));
	} else if (y <= 4e+49) {
		tmp = -1.0;
	} else if (y <= 1.5e+61) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (-2.0 * (x / y)) + -1.0
	tmp = 0
	if y <= -9.5e+101:
		tmp = t_0
	elif y <= 1.9e+30:
		tmp = 1.0 + (2.0 * (y / x))
	elif y <= 4e+49:
		tmp = -1.0
	elif y <= 1.5e+61:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(-2.0 * Float64(x / y)) + -1.0)
	tmp = 0.0
	if (y <= -9.5e+101)
		tmp = t_0;
	elseif (y <= 1.9e+30)
		tmp = Float64(1.0 + Float64(2.0 * Float64(y / x)));
	elseif (y <= 4e+49)
		tmp = -1.0;
	elseif (y <= 1.5e+61)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (-2.0 * (x / y)) + -1.0;
	tmp = 0.0;
	if (y <= -9.5e+101)
		tmp = t_0;
	elseif (y <= 1.9e+30)
		tmp = 1.0 + (2.0 * (y / x));
	elseif (y <= 4e+49)
		tmp = -1.0;
	elseif (y <= 1.5e+61)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(-2.0 * N[(x / y), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]}, If[LessEqual[y, -9.5e+101], t$95$0, If[LessEqual[y, 1.9e+30], N[(1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+49], -1.0, If[LessEqual[y, 1.5e+61], 1.0, t$95$0]]]]]

Derivation

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

Alternative 3: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+101}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+29}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 10^{+48}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9.5e+101)
   -1.0
   (if (<= y 1.26e+29)
     (+ 1.0 (* 2.0 (/ y x)))
     (if (<= y 1e+48) -1.0 (if (<= y 1.2e+61) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9.5e+101) {
		tmp = -1.0;
	} else if (y <= 1.26e+29) {
		tmp = 1.0 + (2.0 * (y / x));
	} else if (y <= 1e+48) {
		tmp = -1.0;
	} else if (y <= 1.2e+61) {
		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 <= (-9.5d+101)) then
        tmp = -1.0d0
    else if (y <= 1.26d+29) then
        tmp = 1.0d0 + (2.0d0 * (y / x))
    else if (y <= 1d+48) then
        tmp = -1.0d0
    else if (y <= 1.2d+61) 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 <= -9.5e+101) {
		tmp = -1.0;
	} else if (y <= 1.26e+29) {
		tmp = 1.0 + (2.0 * (y / x));
	} else if (y <= 1e+48) {
		tmp = -1.0;
	} else if (y <= 1.2e+61) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9.5e+101:
		tmp = -1.0
	elif y <= 1.26e+29:
		tmp = 1.0 + (2.0 * (y / x))
	elif y <= 1e+48:
		tmp = -1.0
	elif y <= 1.2e+61:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9.5e+101)
		tmp = -1.0;
	elseif (y <= 1.26e+29)
		tmp = Float64(1.0 + Float64(2.0 * Float64(y / x)));
	elseif (y <= 1e+48)
		tmp = -1.0;
	elseif (y <= 1.2e+61)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9.5e+101)
		tmp = -1.0;
	elseif (y <= 1.26e+29)
		tmp = 1.0 + (2.0 * (y / x));
	elseif (y <= 1e+48)
		tmp = -1.0;
	elseif (y <= 1.2e+61)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9.5e+101], -1.0, If[LessEqual[y, 1.26e+29], N[(1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+48], -1.0, If[LessEqual[y, 1.2e+61], 1.0, -1.0]]]]

Derivation

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

Alternative 4: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+101}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+49}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+61}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9.5e+101)
   -1.0
   (if (<= y 9.5e+22)
     1.0
     (if (<= y 4e+49) -1.0 (if (<= y 1.3e+61) 1.0 -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9.5e+101) {
		tmp = -1.0;
	} else if (y <= 9.5e+22) {
		tmp = 1.0;
	} else if (y <= 4e+49) {
		tmp = -1.0;
	} else if (y <= 1.3e+61) {
		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 <= (-9.5d+101)) then
        tmp = -1.0d0
    else if (y <= 9.5d+22) then
        tmp = 1.0d0
    else if (y <= 4d+49) then
        tmp = -1.0d0
    else if (y <= 1.3d+61) 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 <= -9.5e+101) {
		tmp = -1.0;
	} else if (y <= 9.5e+22) {
		tmp = 1.0;
	} else if (y <= 4e+49) {
		tmp = -1.0;
	} else if (y <= 1.3e+61) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9.5e+101:
		tmp = -1.0
	elif y <= 9.5e+22:
		tmp = 1.0
	elif y <= 4e+49:
		tmp = -1.0
	elif y <= 1.3e+61:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9.5e+101)
		tmp = -1.0;
	elseif (y <= 9.5e+22)
		tmp = 1.0;
	elseif (y <= 4e+49)
		tmp = -1.0;
	elseif (y <= 1.3e+61)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9.5e+101)
		tmp = -1.0;
	elseif (y <= 9.5e+22)
		tmp = 1.0;
	elseif (y <= 4e+49)
		tmp = -1.0;
	elseif (y <= 1.3e+61)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9.5e+101], -1.0, If[LessEqual[y, 9.5e+22], 1.0, If[LessEqual[y, 4e+49], -1.0, If[LessEqual[y, 1.3e+61], 1.0, -1.0]]]]

Derivation

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

Alternative 5: 100.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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

Alternative 6: 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 7: 49.7% 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 2023343 
(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)))