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

Percentage Accurate: 100.0% → 100.0%

Time: 1.8s

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: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-55}:\\ \;\;\;\;y \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.65e-73) x (if (<= x 2.85e-55) (* y -0.25) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.65e-73) {
		tmp = x;
	} else if (x <= 2.85e-55) {
		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 (x <= (-2.65d-73)) then
        tmp = x
    else if (x <= 2.85d-55) 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 (x <= -2.65e-73) {
		tmp = x;
	} else if (x <= 2.85e-55) {
		tmp = y * -0.25;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.65e-73:
		tmp = x
	elif x <= 2.85e-55:
		tmp = y * -0.25
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.65e-73)
		tmp = x;
	elseif (x <= 2.85e-55)
		tmp = Float64(y * -0.25);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.65e-73)
		tmp = x;
	elseif (x <= 2.85e-55)
		tmp = y * -0.25;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.65e-73], x, If[LessEqual[x, 2.85e-55], N[(y * -0.25), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.64999999999999986e-73 or 2.8500000000000001e-55 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 77.6%

      \[\leadsto \color{blue}{x} \]

   if -2.64999999999999986e-73 < x < 2.8500000000000001e-55

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 86.6%

      \[\leadsto \color{blue}{-0.25 \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative 86.6%

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

   5. Simplified 86.6%

      \[\leadsto \color{blue}{y \cdot -0.25} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 50.3% 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 49.8%

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

Reproduce

herbie shell --seed 2024180 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- x (/ y 4.0)))