Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.5% → 99.7%

Time: 3.3s

Alternatives: 4

Speedup: 1.0×

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, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{2}{\frac{1}{y} + \frac{-1}{x}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 2.0 (+ (/ 1.0 y) (/ -1.0 x))))

C

double code(double x, double y) {
	return 2.0 / ((1.0 / y) + (-1.0 / x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 2.0d0 / ((1.0d0 / y) + ((-1.0d0) / x))
end function

Java

public static double code(double x, double y) {
	return 2.0 / ((1.0 / y) + (-1.0 / x));
}

Python

def code(x, y):
	return 2.0 / ((1.0 / y) + (-1.0 / x))

Julia

function code(x, y)
	return Float64(2.0 / Float64(Float64(1.0 / y) + Float64(-1.0 / x)))
end

MATLAB

function tmp = code(x, y)
	tmp = 2.0 / ((1.0 / y) + (-1.0 / x));
end

Wolfram

code[x_, y_] := N[(2.0 / N[(N[(1.0 / y), $MachinePrecision] + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 78.9%

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

   1. associate-/l* 84.5%

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

   2. *-commutative 84.5%

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

   3. associate-/l* 84.3%

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

   4. div-sub 84.3%

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

   5. *-inverses 84.3%

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

   6. metadata-eval 84.3%

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

   7. div-sub 84.3%

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

   8. metadata-eval 84.3%

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

   9. metadata-eval 84.3%

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

   10. associate-/r* 84.3%

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

   11. neg-mul-1 84.3%

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

   12. sub-neg 84.3%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \frac{2}{\frac{1}{y} + \frac{-1}{x}} \]

Alternative 2: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+95} \lor \neg \left(y \leq 8.8 \cdot 10^{+130}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{2 \cdot x}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.35e+95) (not (<= y 8.8e+130)))
   (* x -2.0)
   (* y (/ (* 2.0 x) (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.35e+95) || !(y <= 8.8e+130)) {
		tmp = x * -2.0;
	} else {
		tmp = y * ((2.0 * x) / (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 <= (-1.35d+95)) .or. (.not. (y <= 8.8d+130))) then
        tmp = x * (-2.0d0)
    else
        tmp = y * ((2.0d0 * x) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.35e+95) || !(y <= 8.8e+130)) {
		tmp = x * -2.0;
	} else {
		tmp = y * ((2.0 * x) / (x - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.35e+95) or not (y <= 8.8e+130):
		tmp = x * -2.0
	else:
		tmp = y * ((2.0 * x) / (x - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.35e+95) || !(y <= 8.8e+130))
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(y * Float64(Float64(2.0 * x) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.35e+95) || ~((y <= 8.8e+130)))
		tmp = x * -2.0;
	else
		tmp = y * ((2.0 * x) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.35e+95], N[Not[LessEqual[y, 8.8e+130]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(y * N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35e95 or 8.79999999999999974e130 < y

   1. Initial program 69.3%

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

      1. associate-*l/ 69.8%

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

   3. Simplified 69.8%

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

   4. Taylor expanded in x around 0 90.9%

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

   if -1.35e95 < y < 8.79999999999999974e130

   1. Initial program 83.8%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+95} \lor \neg \left(y \leq 8.8 \cdot 10^{+130}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{2 \cdot x}{x - y}\\ \end{array} \]

Alternative 3: 73.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+76} \lor \neg \left(y \leq 2 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.8e+76) (not (<= y 2e-39))) (* x -2.0) (* 2.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.8e+76) || !(y <= 2e-39)) {
		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 ((y <= (-7.8d+76)) .or. (.not. (y <= 2d-39))) 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 ((y <= -7.8e+76) || !(y <= 2e-39)) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.8e+76) or not (y <= 2e-39):
		tmp = x * -2.0
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.8e+76) || !(y <= 2e-39))
		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 ((y <= -7.8e+76) || ~((y <= 2e-39)))
		tmp = x * -2.0;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.8e+76], N[Not[LessEqual[y, 2e-39]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.79999999999999979e76 or 1.99999999999999986e-39 < y

   1. Initial program 73.1%

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

      1. associate-*l/ 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in x around 0 82.0%

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

   if -7.79999999999999979e76 < y < 1.99999999999999986e-39

   1. Initial program 83.9%

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

      1. associate-*l/ 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 81.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+76} \lor \neg \left(y \leq 2 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]

Alternative 4: 50.9% 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 78.9%

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

   1. associate-*l/ 88.6%

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

3. Simplified 88.6%

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

4. Taylor expanded in x around 0 48.1%

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

5. Final simplification 48.1%

   \[\leadsto x \cdot -2 \]

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 2023301 
(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)))