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

Percentage Accurate: 100.0% → 100.0%

Time: 2.0s

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: 74.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+71} \lor \neg \left(y \leq 1.02 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8.2e+71) (not (<= y 1.02e-13))) (* y -0.25) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8.2e+71) || !(y <= 1.02e-13)) {
		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 <= (-8.2d+71)) .or. (.not. (y <= 1.02d-13))) 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 <= -8.2e+71) || !(y <= 1.02e-13)) {
		tmp = y * -0.25;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8.2e+71) or not (y <= 1.02e-13):
		tmp = y * -0.25
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8.2e+71) || !(y <= 1.02e-13))
		tmp = Float64(y * -0.25);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8.2e+71) || ~((y <= 1.02e-13)))
		tmp = y * -0.25;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8.2e+71], N[Not[LessEqual[y, 1.02e-13]], $MachinePrecision]], N[(y * -0.25), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000004e71 or 1.0199999999999999e-13 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.4%

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

      1. *-commutative 82.4%

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

   5. Simplified 82.4%

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

   if -8.2000000000000004e71 < y < 1.0199999999999999e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.7%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+71} \lor \neg \left(y \leq 1.02 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot -0.25\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.6% 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 52.4%

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

Reproduce

herbie shell --seed 2024130 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, E"
  :precision binary64
  (- x (/ y 4.0)))