Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Percentage Accurate: 99.8% → 99.8%

Time: 7.2s

Alternatives: 6

Speedup: N/A×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot y - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

double code(double x, double y, double z) {
	return ((x * 3.0) * 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 * 3.0d0) * y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Python

def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot 3\right) \cdot y - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

C

double code(double x, double y, double z) {
	return ((x * 3.0) * 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 * 3.0d0) * y) - z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * 3.0) * y) - z;
}

Python

def code(x, y, z):
	return ((x * 3.0) * y) - z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * 3.0) * y) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * 3.0) * y) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision] - z), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ x \cdot \left(3 \cdot y\right) - z \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (* x (* 3.0 y)) z))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return (x * (3.0 * y)) - 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 = (x * (3.0d0 * y)) - z
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (x * (3.0 * y)) - z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(x * Float64(3.0 * y)) - z)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (x * (3.0 * y)) - z;
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[(3.0 * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 75.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := y \cdot \left(x \cdot 3\right)\\ t_1 := x \cdot \left(3 \cdot y\right)\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 10^{-71}:\\ \;\;\;\;-z\\ \mathbf{elif}\;t_0 \leq 2000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+110}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

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 (* y (* x 3.0))) (t_1 (* x (* 3.0 y))))
   (if (<= t_0 -5e+56)
     t_1
     (if (<= t_0 1e-71)
       (- z)
       (if (<= t_0 2000000.0)
         t_1
         (if (<= t_0 5e+110) (- z) (* 3.0 (* x y))))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = y * (x * 3.0);
	double t_1 = x * (3.0 * y);
	double tmp;
	if (t_0 <= -5e+56) {
		tmp = t_1;
	} else if (t_0 <= 1e-71) {
		tmp = -z;
	} else if (t_0 <= 2000000.0) {
		tmp = t_1;
	} else if (t_0 <= 5e+110) {
		tmp = -z;
	} else {
		tmp = 3.0 * (x * y);
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = y * (x * 3.0d0)
    t_1 = x * (3.0d0 * y)
    if (t_0 <= (-5d+56)) then
        tmp = t_1
    else if (t_0 <= 1d-71) then
        tmp = -z
    else if (t_0 <= 2000000.0d0) then
        tmp = t_1
    else if (t_0 <= 5d+110) then
        tmp = -z
    else
        tmp = 3.0d0 * (x * y)
    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 = y * (x * 3.0);
	double t_1 = x * (3.0 * y);
	double tmp;
	if (t_0 <= -5e+56) {
		tmp = t_1;
	} else if (t_0 <= 1e-71) {
		tmp = -z;
	} else if (t_0 <= 2000000.0) {
		tmp = t_1;
	} else if (t_0 <= 5e+110) {
		tmp = -z;
	} else {
		tmp = 3.0 * (x * y);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = y * (x * 3.0)
	t_1 = x * (3.0 * y)
	tmp = 0
	if t_0 <= -5e+56:
		tmp = t_1
	elif t_0 <= 1e-71:
		tmp = -z
	elif t_0 <= 2000000.0:
		tmp = t_1
	elif t_0 <= 5e+110:
		tmp = -z
	else:
		tmp = 3.0 * (x * y)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(y * Float64(x * 3.0))
	t_1 = Float64(x * Float64(3.0 * y))
	tmp = 0.0
	if (t_0 <= -5e+56)
		tmp = t_1;
	elseif (t_0 <= 1e-71)
		tmp = Float64(-z);
	elseif (t_0 <= 2000000.0)
		tmp = t_1;
	elseif (t_0 <= 5e+110)
		tmp = Float64(-z);
	else
		tmp = Float64(3.0 * Float64(x * y));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = y * (x * 3.0);
	t_1 = x * (3.0 * y);
	tmp = 0.0;
	if (t_0 <= -5e+56)
		tmp = t_1;
	elseif (t_0 <= 1e-71)
		tmp = -z;
	elseif (t_0 <= 2000000.0)
		tmp = t_1;
	elseif (t_0 <= 5e+110)
		tmp = -z;
	else
		tmp = 3.0 * (x * y);
	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[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+56], t$95$1, If[LessEqual[t$95$0, 1e-71], (-z), If[LessEqual[t$95$0, 2000000.0], t$95$1, If[LessEqual[t$95$0, 5e+110], (-z), N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 71.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-80} \lor \neg \left(y \leq 5.4 \cdot 10^{+117}\right):\\ \;\;\;\;3 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.7e-80) (not (<= y 5.4e+117))) (* 3.0 (* x y)) (- z)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.7e-80) || !(y <= 5.4e+117)) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -z;
	}
	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 <= (-4.7d-80)) .or. (.not. (y <= 5.4d+117))) then
        tmp = 3.0d0 * (x * y)
    else
        tmp = -z
    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 <= -4.7e-80) || !(y <= 5.4e+117)) {
		tmp = 3.0 * (x * y);
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if (y <= -4.7e-80) or not (y <= 5.4e+117):
		tmp = 3.0 * (x * y)
	else:
		tmp = -z
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.7e-80) || !(y <= 5.4e+117))
		tmp = Float64(3.0 * Float64(x * y));
	else
		tmp = Float64(-z);
	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 <= -4.7e-80) || ~((y <= 5.4e+117)))
		tmp = 3.0 * (x * y);
	else
		tmp = -z;
	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[Or[LessEqual[y, -4.7e-80], N[Not[LessEqual[y, 5.4e+117]], $MachinePrecision]], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ 3 \cdot \left(x \cdot y\right) - z \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (- (* 3.0 (* x y)) z))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return (3.0 * (x * y)) - 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 = (3.0d0 * (x * y)) - z
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return (3.0 * (x * y)) - z;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (3.0 * (x * y)) - z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(3.0 * Float64(x * y)) - z)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (3.0 * (x * y)) - z;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 49.8% accurate, 3.5× speedup

Math

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

FPCore

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

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return -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 = -z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 2.3% accurate, 7.0× speedup

Math

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

FPCore

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

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return 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 = z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := z

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(3 \cdot y\right) - z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* x (* 3.0 y)) z))

C

double code(double x, double y, double z) {
	return (x * (3.0 * 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 * (3.0d0 * y)) - z
end function

Java

public static double code(double x, double y, double z) {
	return (x * (3.0 * y)) - z;
}

Python

def code(x, y, z):
	return (x * (3.0 * y)) - z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(3.0 * y)) - z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (3.0 * y)) - z;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(3.0 * y), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Reproduce

herbie shell --seed 2024010 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))