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

Percentage Accurate: 99.9% → 99.9%

Time: 3.1s

Alternatives: 3

Speedup: N/A×

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

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: 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. Final simplification 99.6%

   \[\leadsto x - y \cdot \left(4 \cdot z\right) \]

Alternative 2: 71.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+117} \lor \neg \left(y \leq 4 \cdot 10^{-160}\right):\\ \;\;\;\;y \cdot \left(z \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.2e+117) (not (<= y 4e-160))) (* y (* z -4.0)) x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e+117) || !(y <= 4e-160)) {
		tmp = y * (z * -4.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

NOTE: 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 ((y <= (-6.2d+117)) .or. (.not. (y <= 4d-160))) then
        tmp = y * (z * (-4.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

assert y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.2e+117) || !(y <= 4e-160)) {
		tmp = y * (z * -4.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -6.2e+117) or not (y <= 4e-160):
		tmp = y * (z * -4.0)
	else:
		tmp = x
	return tmp

Julia

y, z = sort([y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.2e+117) || !(y <= 4e-160))
		tmp = Float64(y * Float64(z * -4.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

y, z = num2cell(sort([y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.2e+117) || ~((y <= 4e-160)))
		tmp = y * (z * -4.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: y and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[Or[LessEqual[y, -6.2e+117], N[Not[LessEqual[y, 4e-160]], $MachinePrecision]], N[(y * N[(z * -4.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.1999999999999995e117 or 4e-160 < y

   1. Initial program 100.0%

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

      1. associate-*l* 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 64.8%

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

      1. associate-*r* 64.8%

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

      2. *-commutative 64.8%

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

      3. associate-*r* 64.0%

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

   6. Simplified 64.0%

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

   if -6.1999999999999995e117 < y < 4e-160

   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. Taylor expanded in x around inf 71.3%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+117} \lor \neg \left(y \leq 4 \cdot 10^{-160}\right):\\ \;\;\;\;y \cdot \left(z \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 50.8% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: 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. Taylor expanded in x around inf 54.2%

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

5. Final simplification 54.2%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))