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

Percentage Accurate: 99.8% → 99.8%

Time: 830.0ms

Alternatives: 4

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

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

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]

Derivation

1. Initial program 99.4%

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

Alternative 2: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x \cdot 3\right) \cdot y\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-135}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 10^{-88}:\\ \;\;\;\;x \cdot 3 - z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (* x 3.0) y)))
   (if (<= t_0 -2e-135) t_0 (if (<= t_0 1e-88) (- (* x 3.0) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = (x * 3.0) * y;
	double tmp;
	if (t_0 <= -2e-135) {
		tmp = t_0;
	} else if (t_0 <= 1e-88) {
		tmp = (x * 3.0) - z;
	} 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 * 3.0d0) * y
    if (t_0 <= (-2d-135)) then
        tmp = t_0
    else if (t_0 <= 1d-88) then
        tmp = (x * 3.0d0) - z
    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 * 3.0) * y;
	double tmp;
	if (t_0 <= -2e-135) {
		tmp = t_0;
	} else if (t_0 <= 1e-88) {
		tmp = (x * 3.0) - z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (x * 3.0) * y
	tmp = 0
	if t_0 <= -2e-135:
		tmp = t_0
	elif t_0 <= 1e-88:
		tmp = (x * 3.0) - z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(x * 3.0) * y)
	tmp = 0.0
	if (t_0 <= -2e-135)
		tmp = t_0;
	elseif (t_0 <= 1e-88)
		tmp = Float64(Float64(x * 3.0) - z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (x * 3.0) * y;
	tmp = 0.0;
	if (t_0 <= -2e-135)
		tmp = t_0;
	elseif (t_0 <= 1e-88)
		tmp = (x * 3.0) - z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(x * 3.0), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$0, -2e-135], t$95$0, If[LessEqual[t$95$0, 1e-88], N[(N[(x * 3.0), $MachinePrecision] - z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x #s(literal 3 binary64)) y) < -2.0000000000000001e-135 or 9.99999999999999934e-89 < (*.f64 (*.f64 x #s(literal 3 binary64)) y)

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 74.3%

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

   if -2.0000000000000001e-135 < (*.f64 (*.f64 x #s(literal 3 binary64)) y) < 9.99999999999999934e-89

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 76.2%

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

Alternative 3: 40.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ x \cdot 3 - z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 38.4%

   \[\leadsto \color{blue}{x \cdot 3} - z \]
6. Add Preprocessing

Alternative 4: 3.5% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ x \cdot 3 \end{array} \]

FPCore

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

C

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

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 * 3.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 55.3%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 3.4%

   \[\leadsto x \cdot \color{blue}{3} \]
9. 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 2024313 
(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))