Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.5% → 99.7%

Time: 2.8s

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: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-14} \lor \neg \left(x \leq 4 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3e-14) (not (<= x 4e+48)))
   (* y (/ (* x 2.0) (- x y)))
   (/ (* x 2.0) (/ (- x y) y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3e-14) || !(x <= 4e+48)) {
		tmp = y * ((x * 2.0) / (x - y));
	} else {
		tmp = (x * 2.0) / ((x - y) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-3d-14)) .or. (.not. (x <= 4d+48))) then
        tmp = y * ((x * 2.0d0) / (x - y))
    else
        tmp = (x * 2.0d0) / ((x - y) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -3e-14) || !(x <= 4e+48)) {
		tmp = y * ((x * 2.0) / (x - y));
	} else {
		tmp = (x * 2.0) / ((x - y) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3e-14) or not (x <= 4e+48):
		tmp = y * ((x * 2.0) / (x - y))
	else:
		tmp = (x * 2.0) / ((x - y) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3e-14) || !(x <= 4e+48))
		tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y)));
	else
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3e-14) || ~((x <= 4e+48)))
		tmp = y * ((x * 2.0) / (x - y));
	else
		tmp = (x * 2.0) / ((x - y) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3e-14], N[Not[LessEqual[x, 4e+48]], $MachinePrecision]], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.9999999999999998e-14 or 4.00000000000000018e48 < x

   1. Initial program 72.3%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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%

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

   if -2.9999999999999998e-14 < x < 4.00000000000000018e48

   1. Initial program 78.9%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-14} \lor \neg \left(x \leq 4 \cdot 10^{+48}\right):\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \end{array} \]

Alternative 2: 94.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-136} \lor \neg \left(x \leq 1.2 \cdot 10^{-198}\right):\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.45e-136) (not (<= x 1.2e-198)))
   (* y (/ (* x 2.0) (- x y)))
   (* x -2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.45e-136) || !(x <= 1.2e-198)) {
		tmp = y * ((x * 2.0) / (x - y));
	} else {
		tmp = x * -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 <= (-2.45d-136)) .or. (.not. (x <= 1.2d-198))) then
        tmp = y * ((x * 2.0d0) / (x - y))
    else
        tmp = x * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.45e-136) || !(x <= 1.2e-198)) {
		tmp = y * ((x * 2.0) / (x - y));
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.45e-136) or not (x <= 1.2e-198):
		tmp = y * ((x * 2.0) / (x - y))
	else:
		tmp = x * -2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.45e-136) || !(x <= 1.2e-198))
		tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y)));
	else
		tmp = Float64(x * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.45e-136) || ~((x <= 1.2e-198)))
		tmp = y * ((x * 2.0) / (x - y));
	else
		tmp = x * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.45e-136], N[Not[LessEqual[x, 1.2e-198]], $MachinePrecision]], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.45e-136 or 1.19999999999999993e-198 < x

   1. Initial program 77.1%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   if -2.45e-136 < x < 1.19999999999999993e-198

   1. Initial program 70.5%

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

      1. associate-*l/ 64.0%

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

   3. Simplified 64.0%

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

   4. Taylor expanded in x around 0 90.9%

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

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.45 \cdot 10^{-136} \lor \neg \left(x \leq 1.2 \cdot 10^{-198}\right):\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]

Alternative 3: 74.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+50}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.8e-34) (* 2.0 y) (if (<= x 4e+50) (* x -2.0) (* 2.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.8e-34) {
		tmp = 2.0 * y;
	} else if (x <= 4e+50) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.8d-34)) then
        tmp = 2.0d0 * y
    else if (x <= 4d+50) then
        tmp = x * (-2.0d0)
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.8e-34) {
		tmp = 2.0 * y;
	} else if (x <= 4e+50) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.8e-34:
		tmp = 2.0 * y
	elif x <= 4e+50:
		tmp = x * -2.0
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.8e-34)
		tmp = Float64(2.0 * y);
	elseif (x <= 4e+50)
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.8e-34)
		tmp = 2.0 * y;
	elseif (x <= 4e+50)
		tmp = x * -2.0;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.8e-34], N[(2.0 * y), $MachinePrecision], If[LessEqual[x, 4e+50], N[(x * -2.0), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.79999999999999997e-34 or 4.0000000000000003e50 < x

   1. Initial program 72.7%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   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%

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

   4. Taylor expanded in x around inf 80.9%

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

   if -2.79999999999999997e-34 < x < 4.0000000000000003e50

   1. Initial program 78.5%

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

      1. associate-*l/ 79.7%

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

   3. Simplified 79.7%

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

   4. Taylor expanded in x around 0 77.4%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-34}:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+50}:\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]

Alternative 4: 50.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x \cdot -2 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.7%

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

   1. associate-*l/ 89.7%

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

3. Simplified 89.7%

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

4. Taylor expanded in x around 0 49.3%

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

5. Final simplification 49.3%

   \[\leadsto x \cdot -2 \]

Developer target: 99.4% 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 2023199 
(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)))