Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, E

Percentage Accurate: 100.0% → 100.0%

Time: 1.9s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \frac{y}{4} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (/ y 4.0)))

C

double code(double x, double y) {
	return x - (y / 4.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (y / 4.0d0)
end function

Java

public static double code(double x, double y) {
	return x - (y / 4.0);
}

Python

def code(x, y):
	return x - (y / 4.0)

Julia

function code(x, y)
	return Float64(x - Float64(y / 4.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (y / 4.0);
end

Wolfram

code[x_, y_] := N[(x - N[(y / 4.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{4} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (/ y 4.0)))

C

double code(double x, double y) {
	return x - (y / 4.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (y / 4.0d0)
end function

Java

public static double code(double x, double y) {
	return x - (y / 4.0);
}

Python

def code(x, y):
	return x - (y / 4.0)

Julia

function code(x, y)
	return Float64(x - Float64(y / 4.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (y / 4.0);
end

Wolfram

code[x_, y_] := N[(x - N[(y / 4.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{y}{4} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (/ y 4.0)))

C

double code(double x, double y) {
	return x - (y / 4.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - (y / 4.0d0)
end function

Java

public static double code(double x, double y) {
	return x - (y / 4.0);
}

Python

def code(x, y):
	return x - (y / 4.0)

Julia

function code(x, y)
	return Float64(x - Float64(y / 4.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x - (y / 4.0);
end

Wolfram

code[x_, y_] := N[(x - N[(y / 4.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{4} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 71.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3300000 \lor \neg \left(y \leq 3 \cdot 10^{-143}\right):\\ \;\;\;\;y \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3300000.0) (not (<= y 3e-143))) (* y -0.25) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3300000.0) || !(y <= 3e-143)) {
		tmp = y * -0.25;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-3300000.0d0)) .or. (.not. (y <= 3d-143))) then
        tmp = y * (-0.25d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3300000.0) || !(y <= 3e-143)) {
		tmp = y * -0.25;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3300000.0) or not (y <= 3e-143):
		tmp = y * -0.25
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3300000.0) || !(y <= 3e-143))
		tmp = Float64(y * -0.25);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3300000.0) || ~((y <= 3e-143)))
		tmp = y * -0.25;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3300000.0], N[Not[LessEqual[y, 3e-143]], $MachinePrecision]], N[(y * -0.25), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e6 or 2.99999999999999985e-143 < y

   1. Initial program 100.0%

      \[x - \frac{y}{4} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 74.4%

      \[\leadsto \color{blue}{-0.25 \cdot y} \]

   if -3.3e6 < y < 2.99999999999999985e-143

   1. Initial program 100.0%

      \[x - \frac{y}{4} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3300000 \lor \neg \left(y \leq 3 \cdot 10^{-143}\right):\\ \;\;\;\;y \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.9% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{4} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 50.9%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024116 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- x (/ y 4.0)))