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

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

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: 100.0% 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

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

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 99.6%

   \[x - \left(y \cdot 4\right) \cdot z \]
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: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [y, z] = \mathsf{sort}([y, z])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-60} \lor \neg \left(z \leq 4.2 \cdot 10^{+43}\right) \land \left(z \leq 6.4 \cdot 10^{+84} \lor \neg \left(z \leq 2.2 \cdot 10^{+123}\right)\right):\\ \;\;\;\;y \cdot \left(z \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

NOTE: y and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.4e-60)
         (and (not (<= z 4.2e+43)) (or (<= z 6.4e+84) (not (<= z 2.2e+123)))))
   (* y (* z -4.0))
   x))

C

assert(y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.4e-60) || (!(z <= 4.2e+43) && ((z <= 6.4e+84) || !(z <= 2.2e+123)))) {
		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 ((z <= (-4.4d-60)) .or. (.not. (z <= 4.2d+43)) .and. (z <= 6.4d+84) .or. (.not. (z <= 2.2d+123))) 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 ((z <= -4.4e-60) || (!(z <= 4.2e+43) && ((z <= 6.4e+84) || !(z <= 2.2e+123)))) {
		tmp = y * (z * -4.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

[y, z] = sort([y, z])
def code(x, y, z):
	tmp = 0
	if (z <= -4.4e-60) or (not (z <= 4.2e+43) and ((z <= 6.4e+84) or not (z <= 2.2e+123))):
		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 ((z <= -4.4e-60) || (!(z <= 4.2e+43) && ((z <= 6.4e+84) || !(z <= 2.2e+123))))
		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 ((z <= -4.4e-60) || (~((z <= 4.2e+43)) && ((z <= 6.4e+84) || ~((z <= 2.2e+123)))))
		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[z, -4.4e-60], And[N[Not[LessEqual[z, 4.2e+43]], $MachinePrecision], Or[LessEqual[z, 6.4e+84], N[Not[LessEqual[z, 2.2e+123]], $MachinePrecision]]]], N[(y * N[(z * -4.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.3999999999999998e-60 or 4.20000000000000003e43 < z < 6.4000000000000002e84 or 2.19999999999999992e123 < z

   1. Initial program 100.0%

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

      1. associate-*l* 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 72.4%

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

      1. associate-*r* 72.4%

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

      2. *-commutative 72.4%

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

      3. associate-*r* 71.5%

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

   6. Simplified 71.5%

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

   if -4.3999999999999998e-60 < z < 4.20000000000000003e43 or 6.4000000000000002e84 < z < 2.19999999999999992e123

   1. Initial program 99.3%

      \[x - \left(y \cdot 4\right) \cdot z \]
   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 73.9%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-60} \lor \neg \left(z \leq 4.2 \cdot 10^{+43}\right) \land \left(z \leq 6.4 \cdot 10^{+84} \lor \neg \left(z \leq 2.2 \cdot 10^{+123}\right)\right):\\ \;\;\;\;y \cdot \left(z \cdot -4\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 99.6%

   \[x - \left(y \cdot 4\right) \cdot z \]
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 53.4%

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

5. Final simplification 53.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))