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

Percentage Accurate: 100.0% → 99.8%

Time: 4.4s

Alternatives: 4

Speedup: N/A×

Specification

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: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \frac{x}{\frac{2}{y}} - \frac{z}{8} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (/ x (/ 2.0 y)) (/ z 8.0)))

C

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

Fortran

NOTE: x, 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 / (2.0d0 / y)) - (z / 8.0d0)
end function

Java

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (x / (2.0 / y)) - (z / 8.0)

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(x / Float64(2.0 / y)) - Float64(z / 8.0))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (x / (2.0 / y)) - (z / 8.0);
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(x / N[(2.0 / y), $MachinePrecision]), $MachinePrecision] - N[(z / 8.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.7%

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

4. Applied egg-rr 0

   \[\leadsto expr\]
5. Add Preprocessing

Alternative 2: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-87}:\\ \;\;\;\;0.5 \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+42}:\\ \;\;\;\;-0.125 \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{2} \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -2.9e-87)
   (* 0.5 (* x y))
   (if (<= y 4.8e+42) (* -0.125 z) (* (/ y 2.0) x))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e-87) {
		tmp = 0.5 * (x * y);
	} else if (y <= 4.8e+42) {
		tmp = -0.125 * z;
	} else {
		tmp = (y / 2.0) * x;
	}
	return tmp;
}

Fortran

NOTE: x, 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 <= (-2.9d-87)) then
        tmp = 0.5d0 * (x * y)
    else if (y <= 4.8d+42) then
        tmp = (-0.125d0) * z
    else
        tmp = (y / 2.0d0) * x
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.9e-87) {
		tmp = 0.5 * (x * y);
	} else if (y <= 4.8e+42) {
		tmp = -0.125 * z;
	} else {
		tmp = (y / 2.0) * x;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -2.9e-87:
		tmp = 0.5 * (x * y)
	elif y <= 4.8e+42:
		tmp = -0.125 * z
	else:
		tmp = (y / 2.0) * x
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -2.9e-87)
		tmp = Float64(0.5 * Float64(x * y));
	elseif (y <= 4.8e+42)
		tmp = Float64(-0.125 * z);
	else
		tmp = Float64(Float64(y / 2.0) * x);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -2.9e-87)
		tmp = 0.5 * (x * y);
	elseif (y <= 4.8e+42)
		tmp = -0.125 * z;
	else
		tmp = (y / 2.0) * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -2.9e-87], N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+42], N[(-0.125 * z), $MachinePrecision], N[(N[(y / 2.0), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8999999999999999e-87

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -2.8999999999999999e-87 < y < 4.7999999999999997e42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if 4.7999999999999997e42 < y

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   7. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 72.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 0.5 \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{-88}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+43}:\\ \;\;\;\;-0.125 \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 0.5 (* x y))))
   (if (<= y -5.4e-88) t_0 (if (<= y 2e+43) (* -0.125 z) t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 0.5 * (x * y);
	double tmp;
	if (y <= -5.4e-88) {
		tmp = t_0;
	} else if (y <= 2e+43) {
		tmp = -0.125 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

NOTE: x, 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) :: t_0
    real(8) :: tmp
    t_0 = 0.5d0 * (x * y)
    if (y <= (-5.4d-88)) then
        tmp = t_0
    else if (y <= 2d+43) then
        tmp = (-0.125d0) * z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = 0.5 * (x * y);
	double tmp;
	if (y <= -5.4e-88) {
		tmp = t_0;
	} else if (y <= 2e+43) {
		tmp = -0.125 * z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 0.5 * (x * y)
	tmp = 0
	if y <= -5.4e-88:
		tmp = t_0
	elif y <= 2e+43:
		tmp = -0.125 * z
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(0.5 * Float64(x * y))
	tmp = 0.0
	if (y <= -5.4e-88)
		tmp = t_0;
	elseif (y <= 2e+43)
		tmp = Float64(-0.125 * z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = 0.5 * (x * y);
	tmp = 0.0;
	if (y <= -5.4e-88)
		tmp = t_0;
	elseif (y <= 2e+43)
		tmp = -0.125 * z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(0.5 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e-88], t$95$0, If[LessEqual[y, 2e+43], N[(-0.125 * z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.39999999999999989e-88 or 2.00000000000000003e43 < y

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]

   if -5.39999999999999989e-88 < y < 2.00000000000000003e43

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 0

      \[\leadsto expr\]

   5. Simplified 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ -0.125 \cdot z \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* -0.125 z))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return -0.125 * z;
}

Fortran

NOTE: x, 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 = (-0.125d0) * z
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return -0.125 * z;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return -0.125 * z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(-0.125 * z)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = -0.125 * z;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(-0.125 * z), $MachinePrecision]

Derivation

1. Initial program 99.7%

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

3. Taylor expanded in x around 0 0

   \[\leadsto expr\]

5. Simplified 0

   \[\leadsto expr\]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2.0) (/ z 8.0)))