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

Percentage Accurate: 100.0% → 100.0%

Time: 2.2s

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: 75.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-16}:\\ \;\;\;\;y \cdot -0.25\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.25\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.75e-16) (* y -0.25) (if (<= y 3.8e+16) x (* y -0.25))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.75e-16) {
		tmp = y * -0.25;
	} else if (y <= 3.8e+16) {
		tmp = x;
	} else {
		tmp = y * -0.25;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.75d-16)) then
        tmp = y * (-0.25d0)
    else if (y <= 3.8d+16) then
        tmp = x
    else
        tmp = y * (-0.25d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.75e-16) {
		tmp = y * -0.25;
	} else if (y <= 3.8e+16) {
		tmp = x;
	} else {
		tmp = y * -0.25;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.75e-16:
		tmp = y * -0.25
	elif y <= 3.8e+16:
		tmp = x
	else:
		tmp = y * -0.25
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.75e-16)
		tmp = Float64(y * -0.25);
	elseif (y <= 3.8e+16)
		tmp = x;
	else
		tmp = Float64(y * -0.25);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.75e-16)
		tmp = y * -0.25;
	elseif (y <= 3.8e+16)
		tmp = x;
	else
		tmp = y * -0.25;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.75e-16], N[(y * -0.25), $MachinePrecision], If[LessEqual[y, 3.8e+16], x, N[(y * -0.25), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.75000000000000009e-16 or 3.8e16 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 81.9%

         \[\leadsto \mathsf{*.f64}\left(\frac{-1}{4}, \color{blue}{y}\right) \]

   5. Simplified 81.9%

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

   if -1.75000000000000009e-16 < y < 3.8e16

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

   5. Simplified 81.6%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-16}:\\ \;\;\;\;y \cdot -0.25\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.25\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.5% 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

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

5. Simplified 49.8%

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

Reproduce

herbie shell --seed 2024192 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- x (/ y 4.0)))