Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.5% → 98.9%

Time: 2.2s

Alternatives: 4

Speedup: 0.7×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+128} \lor \neg \left(y \leq 3.8 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \frac{2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.25e+128) (not (<= y 3.8e-33)))
   (* x (/ 2.0 (/ (- x y) y)))
   (* y (/ (* x 2.0) (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.25e+128) || !(y <= 3.8e-33)) {
		tmp = x * (2.0 / ((x - y) / y));
	} else {
		tmp = y * ((x * 2.0) / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.25d+128)) .or. (.not. (y <= 3.8d-33))) then
        tmp = x * (2.0d0 / ((x - y) / y))
    else
        tmp = y * ((x * 2.0d0) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.25e+128) || !(y <= 3.8e-33)) {
		tmp = x * (2.0 / ((x - y) / y));
	} else {
		tmp = y * ((x * 2.0) / (x - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.25e+128) or not (y <= 3.8e-33):
		tmp = x * (2.0 / ((x - y) / y))
	else:
		tmp = y * ((x * 2.0) / (x - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.25e+128) || !(y <= 3.8e-33))
		tmp = Float64(x * Float64(2.0 / Float64(Float64(x - y) / y)));
	else
		tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.25e+128) || ~((y <= 3.8e-33)))
		tmp = x * (2.0 / ((x - y) / y));
	else
		tmp = y * ((x * 2.0) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.25e+128], N[Not[LessEqual[y, 3.8e-33]], $MachinePrecision]], N[(x * N[(2.0 / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e128 or 3.79999999999999994e-33 < y

   1. Initial program 77.3%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. associate-*r/ 99.9%

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

   3. Simplified 99.9%

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

   if -1.25e128 < y < 3.79999999999999994e-33

   1. Initial program 78.1%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+128} \lor \neg \left(y \leq 3.8 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \frac{2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \]

Alternative 2: 93.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+132}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 1.03 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \frac{2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.85e+132)
   (* y 2.0)
   (if (<= x 1.03e+183) (* x (/ 2.0 (/ (- x y) y))) (* y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.85e+132) {
		tmp = y * 2.0;
	} else if (x <= 1.03e+183) {
		tmp = x * (2.0 / ((x - y) / y));
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.85d+132)) then
        tmp = y * 2.0d0
    else if (x <= 1.03d+183) then
        tmp = x * (2.0d0 / ((x - y) / y))
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.85e+132) {
		tmp = y * 2.0;
	} else if (x <= 1.03e+183) {
		tmp = x * (2.0 / ((x - y) / y));
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.85e+132:
		tmp = y * 2.0
	elif x <= 1.03e+183:
		tmp = x * (2.0 / ((x - y) / y))
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.85e+132)
		tmp = Float64(y * 2.0);
	elseif (x <= 1.03e+183)
		tmp = Float64(x * Float64(2.0 / Float64(Float64(x - y) / y)));
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.85e+132)
		tmp = y * 2.0;
	elseif (x <= 1.03e+183)
		tmp = x * (2.0 / ((x - y) / y));
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.85e+132], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 1.03e+183], N[(x * N[(2.0 / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8499999999999999e132 or 1.03000000000000005e183 < x

   1. Initial program 70.4%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 52.2%

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

      2. associate-*r/ 52.1%

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

   3. Simplified 52.1%

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

   4. Taylor expanded in x around inf 92.4%

      \[\leadsto \color{blue}{2 \cdot y} \]

   if -2.8499999999999999e132 < x < 1.03000000000000005e183

   1. Initial program 80.6%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 96.5%

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

      2. associate-*r/ 96.4%

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

   3. Simplified 96.4%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.85 \cdot 10^{+132}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 1.03 \cdot 10^{+183}:\\ \;\;\;\;x \cdot \frac{2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]

Alternative 3: 72.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-119}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+92}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.16e-119) (* y 2.0) (if (<= x 9.2e+92) (* x -2.0) (* y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.16e-119) {
		tmp = y * 2.0;
	} else if (x <= 9.2e+92) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.16d-119)) then
        tmp = y * 2.0d0
    else if (x <= 9.2d+92) then
        tmp = x * (-2.0d0)
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.16e-119) {
		tmp = y * 2.0;
	} else if (x <= 9.2e+92) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.16e-119:
		tmp = y * 2.0
	elif x <= 9.2e+92:
		tmp = x * -2.0
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.16e-119)
		tmp = Float64(y * 2.0);
	elseif (x <= 9.2e+92)
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.16e-119)
		tmp = y * 2.0;
	elseif (x <= 9.2e+92)
		tmp = x * -2.0;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.16e-119], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 9.2e+92], N[(x * -2.0), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.16e-119 or 9.19999999999999994e92 < x

   1. Initial program 77.2%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 72.6%

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

      2. associate-*r/ 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in x around inf 80.8%

      \[\leadsto \color{blue}{2 \cdot y} \]

   if -1.16e-119 < x < 9.19999999999999994e92

   1. Initial program 78.5%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.4%

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

      2. associate-*r/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in x around 0 78.3%

      \[\leadsto x \cdot \color{blue}{-2} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.16 \cdot 10^{-119}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+92}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]

Alternative 4: 50.2% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ y \cdot 2 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* y 2.0))

C

double code(double x, double y) {
	return y * 2.0;
}

Fortran

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

Java

public static double code(double x, double y) {
	return y * 2.0;
}

Python

def code(x, y):
	return y * 2.0

Julia

function code(x, y)
	return Float64(y * 2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = y * 2.0;
end

Wolfram

code[x_, y_] := N[(y * 2.0), $MachinePrecision]

Derivation

1. Initial program 77.8%

   \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
2. Step-by-step derivation

   1. associate-/l* 84.2%

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

   2. associate-*r/ 84.1%

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

3. Simplified 84.1%

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

4. Taylor expanded in x around inf 55.0%

   \[\leadsto \color{blue}{2 \cdot y} \]

5. Final simplification 55.0%

   \[\leadsto y \cdot 2 \]

Developer target: 99.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ (* 2.0 x) (- x y)) y)))
   (if (< x -1.7210442634149447e+81)
     t_0
     (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / 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 = ((2.0d0 * x) / (x - y)) * y
    if (x < (-1.7210442634149447d+81)) then
        tmp = t_0
    else if (x < 83645045635564430.0d0) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    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) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((2.0 * x) / (x - y)) * y
	tmp = 0
	if x < -1.7210442634149447e+81:
		tmp = t_0
	elif x < 83645045635564430.0:
		tmp = (x * 2.0) / ((x - y) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(2.0 * x) / Float64(x - y)) * y)
	tmp = 0.0
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((2.0 * x) / (x - y)) * y;
	tmp = 0.0;
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = (x * 2.0) / ((x - y) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[Less[x, -1.7210442634149447e+81], t$95$0, If[Less[x, 83645045635564430.0], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023208 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))