Linear.Projection:perspective from linear-1.19.1.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 5.2s

Alternatives: 6

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

1. Initial program 100.0%

   \[\frac{x + y}{x - y} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{y \cdot 2}{x}\\ \mathbf{if}\;x \leq -6 \cdot 10^{-192}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.3 \cdot 10^{+31}:\\ \;\;\;\;-1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (* y 2.0) x))))
   (if (<= x -6e-192) t_0 (if (<= x 7.3e+31) (- -1.0 (/ x y)) t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((y * 2.0) / x);
	double tmp;
	if (x <= -6e-192) {
		tmp = t_0;
	} else if (x <= 7.3e+31) {
		tmp = -1.0 - (x / y);
	} 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 = 1.0d0 + ((y * 2.0d0) / x)
    if (x <= (-6d-192)) then
        tmp = t_0
    else if (x <= 7.3d+31) then
        tmp = (-1.0d0) - (x / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + ((y * 2.0) / x);
	double tmp;
	if (x <= -6e-192) {
		tmp = t_0;
	} else if (x <= 7.3e+31) {
		tmp = -1.0 - (x / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((y * 2.0) / x)
	tmp = 0
	if x <= -6e-192:
		tmp = t_0
	elif x <= 7.3e+31:
		tmp = -1.0 - (x / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(y * 2.0) / x))
	tmp = 0.0
	if (x <= -6e-192)
		tmp = t_0;
	elseif (x <= 7.3e+31)
		tmp = Float64(-1.0 - Float64(x / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((y * 2.0) / x);
	tmp = 0.0;
	if (x <= -6e-192)
		tmp = t_0;
	elseif (x <= 7.3e+31)
		tmp = -1.0 - (x / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(N[(y * 2.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e-192], t$95$0, If[LessEqual[x, 7.3e+31], N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999998e-192 or 7.30000000000000023e31 < x

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\left(1 + \frac{y}{x}\right) - -1 \cdot \frac{y}{x}} \]
   4. Step-by-step derivation

      1. associate--l+ N/A

         \[\leadsto 1 + \color{blue}{\left(\frac{y}{x} - -1 \cdot \frac{y}{x}\right)} \]

      2. *-lft-identity N/A

         \[\leadsto 1 + \left(1 \cdot \frac{y}{x} - \color{blue}{-1} \cdot \frac{y}{x}\right) \]

      3. distribute-rgt-out-- N/A

         \[\leadsto 1 + \frac{y}{x} \cdot \color{blue}{\left(1 - -1\right)} \]

      4. *-rgt-identity N/A

         \[\leadsto 1 + \frac{y \cdot 1}{x} \cdot \left(1 - -1\right) \]

      5. associate-*r/ N/A

         \[\leadsto 1 + \left(y \cdot \frac{1}{x}\right) \cdot \left(\color{blue}{1} - -1\right) \]

      6. metadata-eval N/A

         \[\leadsto 1 + \left(y \cdot \frac{1}{x}\right) \cdot 2 \]

      7. associate-*r* N/A

         \[\leadsto 1 + y \cdot \color{blue}{\left(\frac{1}{x} \cdot 2\right)} \]

      8. *-commutative N/A

         \[\leadsto 1 + y \cdot \left(2 \cdot \color{blue}{\frac{1}{x}}\right) \]

      9. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(1, \color{blue}{\left(y \cdot \left(2 \cdot \frac{1}{x}\right)\right)}\right) \]

      10. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(1, \left(y \cdot \frac{2 \cdot 1}{\color{blue}{x}}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \left(y \cdot \frac{2}{x}\right)\right) \]

      12. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{y \cdot 2}{\color{blue}{x}}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{y \cdot \left(1 - -1\right)}{x}\right)\right) \]

      14. distribute-rgt-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{1 \cdot y - -1 \cdot y}{x}\right)\right) \]

      15. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(1, \left(\frac{y - -1 \cdot y}{x}\right)\right) \]

      16. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y - -1 \cdot y\right), \color{blue}{x}\right)\right) \]

      17. *-lft-identity N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(1 \cdot y - -1 \cdot y\right), x\right)\right) \]

      18. distribute-rgt-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot \left(1 - -1\right)\right), x\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\left(y \cdot 2\right), x\right)\right) \]

      20. *-lowering-*.f64 76.4%

          \[\leadsto \mathsf{+.f64}\left(1, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, 2\right), x\right)\right) \]

   5. Simplified 76.4%

      \[\leadsto \color{blue}{1 + \frac{y \cdot 2}{x}} \]

   if -5.9999999999999998e-192 < x < 7.30000000000000023e31

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{\_.f64}\left(x, y\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 87.5%

      \[\leadsto \frac{\color{blue}{y}}{x - y} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y} - 1} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto -1 \cdot \frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto -1 \cdot \frac{x}{y} + -1 \]

      3. +-commutative N/A

         \[\leadsto -1 + \color{blue}{-1 \cdot \frac{x}{y}} \]

      4. mul-1-neg N/A

         \[\leadsto -1 + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto -1 - \color{blue}{\frac{x}{y}} \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(-1, \color{blue}{\left(\frac{x}{y}\right)}\right) \]

      7. /-lowering-/.f64 87.6%

         \[\leadsto \mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 87.6%

      \[\leadsto \color{blue}{-1 - \frac{x}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 69.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x - y}\\ \mathbf{if}\;x \leq -6 \cdot 10^{-192}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+29}:\\ \;\;\;\;-1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (- x y))))
   (if (<= x -6e-192) t_0 (if (<= x 1.12e+29) (- -1.0 (/ x y)) t_0))))

C

double code(double x, double y) {
	double t_0 = x / (x - y);
	double tmp;
	if (x <= -6e-192) {
		tmp = t_0;
	} else if (x <= 1.12e+29) {
		tmp = -1.0 - (x / y);
	} 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 = x / (x - y)
    if (x <= (-6d-192)) then
        tmp = t_0
    else if (x <= 1.12d+29) then
        tmp = (-1.0d0) - (x / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (x - y);
	double tmp;
	if (x <= -6e-192) {
		tmp = t_0;
	} else if (x <= 1.12e+29) {
		tmp = -1.0 - (x / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (x - y)
	tmp = 0
	if x <= -6e-192:
		tmp = t_0
	elif x <= 1.12e+29:
		tmp = -1.0 - (x / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(x - y))
	tmp = 0.0
	if (x <= -6e-192)
		tmp = t_0;
	elseif (x <= 1.12e+29)
		tmp = Float64(-1.0 - Float64(x / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (x - y);
	tmp = 0.0;
	if (x <= -6e-192)
		tmp = t_0;
	elseif (x <= 1.12e+29)
		tmp = -1.0 - (x / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(x - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6e-192], t$95$0, If[LessEqual[x, 1.12e+29], N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999998e-192 or 1.1200000000000001e29 < x

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, \mathsf{\_.f64}\left(x, y\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 75.6%

      \[\leadsto \frac{\color{blue}{x}}{x - y} \]

   if -5.9999999999999998e-192 < x < 1.1200000000000001e29

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{\_.f64}\left(x, y\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 87.5%

      \[\leadsto \frac{\color{blue}{y}}{x - y} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y} - 1} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto -1 \cdot \frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto -1 \cdot \frac{x}{y} + -1 \]

      3. +-commutative N/A

         \[\leadsto -1 + \color{blue}{-1 \cdot \frac{x}{y}} \]

      4. mul-1-neg N/A

         \[\leadsto -1 + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto -1 - \color{blue}{\frac{x}{y}} \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(-1, \color{blue}{\left(\frac{x}{y}\right)}\right) \]

      7. /-lowering-/.f64 87.6%

         \[\leadsto \mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 87.6%

      \[\leadsto \color{blue}{-1 - \frac{x}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 69.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-192}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+31}:\\ \;\;\;\;-1 - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6e-192) 1.0 (if (<= x 1.3e+31) (- -1.0 (/ x y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6e-192) {
		tmp = 1.0;
	} else if (x <= 1.3e+31) {
		tmp = -1.0 - (x / y);
	} 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 (x <= (-6d-192)) then
        tmp = 1.0d0
    else if (x <= 1.3d+31) then
        tmp = (-1.0d0) - (x / y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6e-192) {
		tmp = 1.0;
	} else if (x <= 1.3e+31) {
		tmp = -1.0 - (x / y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6e-192:
		tmp = 1.0
	elif x <= 1.3e+31:
		tmp = -1.0 - (x / y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6e-192)
		tmp = 1.0;
	elseif (x <= 1.3e+31)
		tmp = Float64(-1.0 - Float64(x / y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6e-192)
		tmp = 1.0;
	elseif (x <= 1.3e+31)
		tmp = -1.0 - (x / y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6e-192], 1.0, If[LessEqual[x, 1.3e+31], N[(-1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999998e-192 or 1.3e31 < x

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 74.9%

      \[\leadsto \color{blue}{1} \]

   if -5.9999999999999998e-192 < x < 1.3e31

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{y}, \mathsf{\_.f64}\left(x, y\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 87.5%

      \[\leadsto \frac{\color{blue}{y}}{x - y} \]

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y} - 1} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto -1 \cdot \frac{x}{y} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)} \]

      2. metadata-eval N/A

         \[\leadsto -1 \cdot \frac{x}{y} + -1 \]

      3. +-commutative N/A

         \[\leadsto -1 + \color{blue}{-1 \cdot \frac{x}{y}} \]

      4. mul-1-neg N/A

         \[\leadsto -1 + \left(\mathsf{neg}\left(\frac{x}{y}\right)\right) \]

      5. sub-neg N/A

         \[\leadsto -1 - \color{blue}{\frac{x}{y}} \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(-1, \color{blue}{\left(\frac{x}{y}\right)}\right) \]

      7. /-lowering-/.f64 87.6%

         \[\leadsto \mathsf{\_.f64}\left(-1, \mathsf{/.f64}\left(x, \color{blue}{y}\right)\right) \]

   8. Simplified 87.6%

      \[\leadsto \color{blue}{-1 - \frac{x}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 69.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-192}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+29}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6e-192) 1.0 (if (<= x 1.55e+29) -1.0 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6e-192) {
		tmp = 1.0;
	} else if (x <= 1.55e+29) {
		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 (x <= (-6d-192)) then
        tmp = 1.0d0
    else if (x <= 1.55d+29) 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 (x <= -6e-192) {
		tmp = 1.0;
	} else if (x <= 1.55e+29) {
		tmp = -1.0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6e-192:
		tmp = 1.0
	elif x <= 1.55e+29:
		tmp = -1.0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6e-192)
		tmp = 1.0;
	elseif (x <= 1.55e+29)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6e-192)
		tmp = 1.0;
	elseif (x <= 1.55e+29)
		tmp = -1.0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6e-192], 1.0, If[LessEqual[x, 1.55e+29], -1.0, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -5.9999999999999998e-192 or 1.5499999999999999e29 < x

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{1} \]
   4. Step-by-step derivation

   5. Simplified 74.9%

      \[\leadsto \color{blue}{1} \]

   if -5.9999999999999998e-192 < x < 1.5499999999999999e29

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{-1} \]
   4. Step-by-step derivation

   5. Simplified 87.2%

      \[\leadsto \color{blue}{-1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 49.3% 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

1. Initial program 100.0%

   \[\frac{x + y}{x - y} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{-1} \]
4. Step-by-step derivation

5. Simplified 49.4%

   \[\leadsto \color{blue}{-1} \]
6. Add Preprocessing

Developer Target 1: 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 2024152 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (/ 1 (- (/ x (+ x y)) (/ y (+ x y)))))

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