Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A

Percentage Accurate: 99.9% → 100.0%

Time: 3.7s

Alternatives: 3

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \left(y \cdot 4\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x - ((y * 4.0) * z)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(y \cdot 4\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x - ((y * 4.0) * z)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x - y \cdot \left(4 \cdot z\right) \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- x (* y (* 4.0 z))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return x - (y * (4.0 * z));
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - (y * (4.0d0 * z))
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return x - (y * (4.0 * z));
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x - (y * (4.0 * z))

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(x - Float64(y * Float64(4.0 * z)))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x - (y * (4.0 * z));
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(x - N[(y * N[(4.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \left(y \cdot 4\right) \cdot z \]
2. Step-by-step derivation

   1. associate-*l* 99.6%

      \[\leadsto x - \color{blue}{y \cdot \left(4 \cdot z\right)} \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x - y \cdot \left(4 \cdot z\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 70.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-21} \lor \neg \left(z \leq 4.6 \cdot 10^{-44}\right):\\ \;\;\;\;y \cdot \left(z \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.56e-21) (not (<= z 4.6e-44))) (* y (* z -4.0)) x))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.56e-21) || !(z <= 4.6e-44)) {
		tmp = y * (z * -4.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.56d-21)) .or. (.not. (z <= 4.6d-44))) then
        tmp = y * (z * (-4.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.56e-21) || !(z <= 4.6e-44)) {
		tmp = y * (z * -4.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -1.56e-21) or not (z <= 4.6e-44):
		tmp = y * (z * -4.0)
	else:
		tmp = x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.56e-21) || !(z <= 4.6e-44))
		tmp = Float64(y * Float64(z * -4.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.56e-21) || ~((z <= 4.6e-44)))
		tmp = y * (z * -4.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[z, -1.56e-21], N[Not[LessEqual[z, 4.6e-44]], $MachinePrecision]], N[(y * N[(z * -4.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.55999999999999999e-21 or 4.59999999999999996e-44 < z

   1. Initial program 100.0%

      \[x - \left(y \cdot 4\right) \cdot z \]
   2. Step-by-step derivation

      1. associate-*l* 99.4%

         \[\leadsto x - \color{blue}{y \cdot \left(4 \cdot z\right)} \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x - y \cdot \left(4 \cdot z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 68.7%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot -4} \]

      2. associate-*r* 68.1%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot -4\right)} \]

   7. Simplified 68.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot -4\right)} \]

   if -1.55999999999999999e-21 < z < 4.59999999999999996e-44

   1. Initial program 100.0%

      \[x - \left(y \cdot 4\right) \cdot z \]
   2. Step-by-step derivation

      1. associate-*l* 100.0%

         \[\leadsto x - \color{blue}{y \cdot \left(4 \cdot z\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x - y \cdot \left(4 \cdot z\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 76.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.56 \cdot 10^{-21} \lor \neg \left(z \leq 4.6 \cdot 10^{-44}\right):\\ \;\;\;\;y \cdot \left(z \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.7% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 x)

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return x;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return x;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return x
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[x - \left(y \cdot 4\right) \cdot z \]
2. Step-by-step derivation

   1. associate-*l* 99.6%

      \[\leadsto x - \color{blue}{y \cdot \left(4 \cdot z\right)} \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x - y \cdot \left(4 \cdot z\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 49.8%

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

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))