Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

Percentage Accurate: 100.0% → 100.0%

Time: 1.0s

Alternatives: 4

Speedup: 1.0×

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

\[\begin{array}{l} \\ \frac{x \cdot y}{2} - \frac{z}{8} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))

C

double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

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) / 2.0d0) - (z / 8.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

Python

def code(x, y, z):
	return ((x * y) / 2.0) - (z / 8.0)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * y) / 2.0) - Float64(z / 8.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * y) / 2.0) - (z / 8.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y}{2} - \frac{z}{8} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))

C

double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

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) / 2.0d0) - (z / 8.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

Python

def code(x, y, z):
	return ((x * y) / 2.0) - (z / 8.0)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * y) / 2.0) - Float64(z / 8.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * y) / 2.0) - (z / 8.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y}{2} - \frac{z}{8} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (/ (* x y) 2.0) (/ z 8.0)))

C

double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

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) / 2.0d0) - (z / 8.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((x * y) / 2.0) - (z / 8.0);
}

Python

def code(x, y, z):
	return ((x * y) / 2.0) - (z / 8.0)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * y) / 2.0) - Float64(z / 8.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * y) / 2.0) - (z / 8.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x \cdot y}{2} - \frac{z}{8} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 79.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot y}{2}\\ \mathbf{if}\;x \cdot y \leq -2.1 \cdot 10^{-54}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \cdot y \leq 1.25 \cdot 10^{+70}:\\ \;\;\;\;x \cdot y - \frac{z}{8}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x y) 2.0)))
   (if (<= (* x y) -2.1e-54)
     t_0
     (if (<= (* x y) 1.25e+70) (- (* x y) (/ z 8.0)) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * y) / 2.0;
	double tmp;
	if ((x * y) <= -2.1e-54) {
		tmp = t_0;
	} else if ((x * y) <= 1.25e+70) {
		tmp = (x * y) - (z / 8.0);
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = (x * y) / 2.0d0
    if ((x * y) <= (-2.1d-54)) then
        tmp = t_0
    else if ((x * y) <= 1.25d+70) then
        tmp = (x * y) - (z / 8.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (x * y) / 2.0;
	double tmp;
	if ((x * y) <= -2.1e-54) {
		tmp = t_0;
	} else if ((x * y) <= 1.25e+70) {
		tmp = (x * y) - (z / 8.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * y) / 2.0
	tmp = 0
	if (x * y) <= -2.1e-54:
		tmp = t_0
	elif (x * y) <= 1.25e+70:
		tmp = (x * y) - (z / 8.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * y) / 2.0)
	tmp = 0.0
	if (Float64(x * y) <= -2.1e-54)
		tmp = t_0;
	elseif (Float64(x * y) <= 1.25e+70)
		tmp = Float64(Float64(x * y) - Float64(z / 8.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * y) / 2.0;
	tmp = 0.0;
	if ((x * y) <= -2.1e-54)
		tmp = t_0;
	elseif ((x * y) <= 1.25e+70)
		tmp = (x * y) - (z / 8.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2.1e-54], t$95$0, If[LessEqual[N[(x * y), $MachinePrecision], 1.25e+70], N[(N[(x * y), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -2.1e-54 or 1.2500000000000001e70 < (*.f64 x y)

   1. Initial program 100.0%

      \[\frac{x \cdot y}{2} - \frac{z}{8} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(x \cdot y\right) - \frac{1}{8} \cdot z} \]

   5. Applied rewrites 83.1%

      \[\leadsto \color{blue}{\frac{x \cdot y}{2}} \]

   if -2.1e-54 < (*.f64 x y) < 1.2500000000000001e70

   1. Initial program 100.0%

      \[\frac{x \cdot y}{2} - \frac{z}{8} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(x \cdot y\right)} - \frac{z}{8} \]

   5. Applied rewrites 83.6%

      \[\leadsto \color{blue}{x \cdot y} - \frac{z}{8} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 51.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y}{2} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x y) 2.0))

C

double code(double x, double y, double z) {
	return (x * y) / 2.0;
}

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) / 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) / 2.0;
}

Python

def code(x, y, z):
	return (x * y) / 2.0

Julia

function code(x, y, z)
	return Float64(Float64(x * y) / 2.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) / 2.0;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] / 2.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x \cdot y}{2} - \frac{z}{8} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(x \cdot y\right) - \frac{1}{8} \cdot z} \]

5. Applied rewrites 53.9%

   \[\leadsto \color{blue}{\frac{x \cdot y}{2}} \]
6. Add Preprocessing

Alternative 4: 21.3% accurate, 5.2× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x \cdot y}{2} - \frac{z}{8} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(x \cdot y\right) - \frac{1}{8} \cdot z} \]

5. Applied rewrites 53.9%

   \[\leadsto \color{blue}{\frac{x \cdot y}{2}} \]

6. Taylor expanded in x around 0

   \[\leadsto \frac{1}{2} \cdot \color{blue}{\left(x \cdot y\right)} \]

8. Applied rewrites 20.5%

   \[\leadsto x \cdot \color{blue}{y} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  :pre (TRUE)
  (- (/ (* x y) 2.0) (/ z 8.0)))