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

Percentage Accurate: 99.8% → 99.8%

Time: 6.2s

Alternatives: 5

Speedup: 1.0×

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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
2. Add Preprocessing

3. Final simplification 99.8%

   \[\leadsto y \cdot \left(3 \cdot x\right) - z \]
4. Add Preprocessing

Alternative 2: 76.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := y \cdot \left(3 \cdot x\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 10^{-89}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot 3\\ \end{array} \end{array} \]

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 (* 3.0 x))))
   (if (<= t_0 -4e+73) t_0 (if (<= t_0 1e-89) (- z) (* (* y x) 3.0)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = y * (3.0 * x);
	double tmp;
	if (t_0 <= -4e+73) {
		tmp = t_0;
	} else if (t_0 <= 1e-89) {
		tmp = -z;
	} else {
		tmp = (y * x) * 3.0;
	}
	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 = y * (3.0d0 * x)
    if (t_0 <= (-4d+73)) then
        tmp = t_0
    else if (t_0 <= 1d-89) then
        tmp = -z
    else
        tmp = (y * x) * 3.0d0
    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 * (3.0 * x);
	double tmp;
	if (t_0 <= -4e+73) {
		tmp = t_0;
	} else if (t_0 <= 1e-89) {
		tmp = -z;
	} else {
		tmp = (y * x) * 3.0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = y * (3.0 * x)
	tmp = 0
	if t_0 <= -4e+73:
		tmp = t_0
	elif t_0 <= 1e-89:
		tmp = -z
	else:
		tmp = (y * x) * 3.0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(y * Float64(3.0 * x))
	tmp = 0.0
	if (t_0 <= -4e+73)
		tmp = t_0;
	elseif (t_0 <= 1e-89)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(y * x) * 3.0);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = y * (3.0 * x);
	tmp = 0.0;
	if (t_0 <= -4e+73)
		tmp = t_0;
	elseif (t_0 <= 1e-89)
		tmp = -z;
	else
		tmp = (y * x) * 3.0;
	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[(y * N[(3.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+73], t$95$0, If[LessEqual[t$95$0, 1e-89], (-z), N[(N[(y * x), $MachinePrecision] * 3.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 (*.f64 x #s(literal 3 binary64)) y) < -3.99999999999999993e73

   1. Initial program 99.8%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 3} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 3 \]

      4. lower-*.f64 88.8

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 3 \]

   5. Applied rewrites 88.8%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 88.8%

      \[\leadsto \color{blue}{\left(3 \cdot x\right) \cdot y} \]

   if -3.99999999999999993e73 < (*.f64 (*.f64 x #s(literal 3 binary64)) y) < 1.00000000000000004e-89

   1. Initial program 99.9%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 82.4

         \[\leadsto \color{blue}{-z} \]

   5. Applied rewrites 82.4%

      \[\leadsto \color{blue}{-z} \]

   if 1.00000000000000004e-89 < (*.f64 (*.f64 x #s(literal 3 binary64)) y)

   1. Initial program 99.6%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 3} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 3 \]

      4. lower-*.f64 77.0

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 3 \]

   5. Applied rewrites 77.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(3 \cdot x\right) \leq -4 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \mathbf{elif}\;y \cdot \left(3 \cdot x\right) \leq 10^{-89}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := y \cdot \left(3 \cdot x\right)\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+73}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 10^{-89}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

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 (* y (* 3.0 x))))
   (if (<= t_0 -4e+73) t_0 (if (<= t_0 1e-89) (- z) t_0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = y * (3.0 * x);
	double tmp;
	if (t_0 <= -4e+73) {
		tmp = t_0;
	} else if (t_0 <= 1e-89) {
		tmp = -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 = y * (3.0d0 * x)
    if (t_0 <= (-4d+73)) then
        tmp = t_0
    else if (t_0 <= 1d-89) then
        tmp = -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 = y * (3.0 * x);
	double tmp;
	if (t_0 <= -4e+73) {
		tmp = t_0;
	} else if (t_0 <= 1e-89) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = y * (3.0 * x)
	tmp = 0
	if t_0 <= -4e+73:
		tmp = t_0
	elif t_0 <= 1e-89:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(y * Float64(3.0 * x))
	tmp = 0.0
	if (t_0 <= -4e+73)
		tmp = t_0;
	elseif (t_0 <= 1e-89)
		tmp = Float64(-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 = y * (3.0 * x);
	tmp = 0.0;
	if (t_0 <= -4e+73)
		tmp = t_0;
	elseif (t_0 <= 1e-89)
		tmp = -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[(y * N[(3.0 * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+73], t$95$0, If[LessEqual[t$95$0, 1e-89], (-z), t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 3 binary64)) y) < -3.99999999999999993e73 or 1.00000000000000004e-89 < (*.f64 (*.f64 x #s(literal 3 binary64)) y)

   1. Initial program 99.7%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 3} \]

      2. lower-*.f64 N/A

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot 3} \]

      3. *-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 3 \]

      4. lower-*.f64 81.0

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot 3 \]

   5. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot 3} \]
   6. Step-by-step derivation

   7. Applied rewrites 80.9%

      \[\leadsto \color{blue}{\left(3 \cdot x\right) \cdot y} \]

   if -3.99999999999999993e73 < (*.f64 (*.f64 x #s(literal 3 binary64)) y) < 1.00000000000000004e-89

   1. Initial program 99.9%

      \[\left(x \cdot 3\right) \cdot y - z \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot z} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

      2. lower-neg.f64 82.4

         \[\leadsto \color{blue}{-z} \]

   5. Applied rewrites 82.4%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(3 \cdot x\right) \leq -4 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \mathbf{elif}\;y \cdot \left(3 \cdot x\right) \leq 10^{-89}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.7% accurate, 4.7× 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

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{-1 \cdot z} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. lower-neg.f64 50.0

      \[\leadsto \color{blue}{-z} \]

5. Applied rewrites 50.0%

   \[\leadsto \color{blue}{-z} \]
6. Add Preprocessing

Alternative 5: 2.3% accurate, 14.0× 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

1. Initial program 99.8%

   \[\left(x \cdot 3\right) \cdot y - z \]
2. Add Preprocessing

3. Taylor expanded in z around inf

   \[\leadsto \color{blue}{-1 \cdot z} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(z\right)} \]

   2. lower-neg.f64 50.0

      \[\leadsto \color{blue}{-z} \]

5. Applied rewrites 50.0%

   \[\leadsto \color{blue}{-z} \]
6. Step-by-step derivation

7. Applied rewrites 2.3%

   \[\leadsto z \]
8. Add Preprocessing

Developer Target 1: 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 2024244 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* x (* 3 y)) z))

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