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

Percentage Accurate: 100.0% → 100.0%

Time: 1.7s

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: 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

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

FPCore

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

C

double code(double x, double y, double z) {
	return x - (4.0 * (y * 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 - (4.0d0 * (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. *-commutative 99.6%

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

   2. associate-*l* 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 69.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+116}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.4e+54) x (if (<= x 2.9e+116) (* (* y z) -4.0) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.4e+54) {
		tmp = x;
	} else if (x <= 2.9e+116) {
		tmp = (y * z) * -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 (x <= (-5.4d+54)) then
        tmp = x
    else if (x <= 2.9d+116) then
        tmp = (y * z) * (-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 (x <= -5.4e+54) {
		tmp = x;
	} else if (x <= 2.9e+116) {
		tmp = (y * z) * -4.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.4e+54:
		tmp = x
	elif x <= 2.9e+116:
		tmp = (y * z) * -4.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.4e+54)
		tmp = x;
	elseif (x <= 2.9e+116)
		tmp = Float64(Float64(y * z) * -4.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.4e+54)
		tmp = x;
	elseif (x <= 2.9e+116)
		tmp = (y * z) * -4.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.4e+54], x, If[LessEqual[x, 2.9e+116], N[(N[(y * z), $MachinePrecision] * -4.0), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.40000000000000022e54 or 2.9000000000000001e116 < x

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 80.0%

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

   if -5.40000000000000022e54 < x < 2.9000000000000001e116

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 77.0%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+116}:\\ \;\;\;\;\left(y \cdot z\right) \cdot -4\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 50.3% 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 99.6%

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

   1. *-commutative 99.6%

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

   2. associate-*l* 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around inf 46.4%

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

5. Final simplification 46.4%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023182 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))