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

Percentage Accurate: 99.9% → 99.9%

Time: 2.6s

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: 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]

Derivation

1. Initial program 100.0%

   \[x - \left(y \cdot 4\right) \cdot z \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 66.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+116} \lor \neg \left(y \leq 5.6 \cdot 10^{-121}\right):\\ \;\;\;\;z \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.5e+116) (not (<= y 5.6e-121))) (* z (* y -4.0)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+116) || !(y <= 5.6e-121)) {
		tmp = z * (y * -4.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

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 ((y <= (-6.5d+116)) .or. (.not. (y <= 5.6d-121))) then
        tmp = z * (y * (-4.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.5e+116) || !(y <= 5.6e-121)) {
		tmp = z * (y * -4.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.5e+116) or not (y <= 5.6e-121):
		tmp = z * (y * -4.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.5e+116) || !(y <= 5.6e-121))
		tmp = Float64(z * Float64(y * -4.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.5e+116) || ~((y <= 5.6e-121)))
		tmp = z * (y * -4.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.5e+116], N[Not[LessEqual[y, 5.6e-121]], $MachinePrecision]], N[(z * N[(y * -4.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.4999999999999998e116 or 5.6000000000000002e-121 < y

   1. Initial program 100.0%

      \[x - \left(y \cdot 4\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 68.5%

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

      1. associate-*r* 68.5%

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

      2. *-commutative 68.5%

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

      3. *-commutative 68.5%

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

   5. Simplified 68.5%

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

   if -6.4999999999999998e116 < y < 5.6000000000000002e-121

   1. Initial program 100.0%

      \[x - \left(y \cdot 4\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.9%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+116} \lor \neg \left(y \leq 5.6 \cdot 10^{-121}\right):\\ \;\;\;\;z \cdot \left(y \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.0% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 x)

C

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

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
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

   \[x - \left(y \cdot 4\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around inf 53.2%

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

Reproduce

herbie shell --seed 2024118 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))