Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A

Percentage Accurate: 99.9% → 100.0%

Time: 5.5s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x - \left(y \cdot 4\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))

C

double code(double x, double y, double z) {
	return x - ((y * 4.0) * 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 - ((y * 4.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}

Python

def code(x, y, z):
	return x - ((y * 4.0) * z)

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(y * 4.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((y * 4.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(y * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(y \cdot 4\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* y 4.0) z)))

C

double code(double x, double y, double z) {
	return x - ((y * 4.0) * 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 - ((y * 4.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x - ((y * 4.0) * z);
}

Python

def code(x, y, z):
	return x - ((y * 4.0) * z)

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(y * 4.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((y * 4.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(y * 4.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y \cdot -4, z, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (* y -4.0) z x))

C

double code(double x, double y, double z) {
	return fma((y * -4.0), z, x);
}

Julia

function code(x, y, z)
	return fma(Float64(y * -4.0), z, x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y * -4.0), $MachinePrecision] * z + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \left(y \cdot 4\right) \cdot z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto x + \color{blue}{\left(\mathsf{neg}\left(\left(y \cdot 4\right) \cdot z\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left(\left(y \cdot 4\right) \cdot z\right)\right) + \color{blue}{x} \]

   3. distribute-lft-neg-in N/A

      \[\leadsto \left(\mathsf{neg}\left(y \cdot 4\right)\right) \cdot z + x \]

   4. fma-define N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y \cdot 4\right), \color{blue}{z}, x\right) \]

   5. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(\mathsf{neg}\left(y \cdot 4\right)\right), \color{blue}{z}, x\right) \]

   6. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(y \cdot \left(\mathsf{neg}\left(4\right)\right)\right), z, x\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, \left(\mathsf{neg}\left(4\right)\right)\right), z, x\right) \]

   8. metadata-eval 100.0%

      \[\leadsto \mathsf{fma.f64}\left(\mathsf{*.f64}\left(y, -4\right), z, x\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y \cdot -4, z, x\right)} \]
5. Add Preprocessing

Alternative 2: 70.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -4 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{+14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -4.0 (* y z))))
   (if (<= y -2.3e+14) t_0 (if (<= y 7.6e-103) x t_0))))

C

double code(double x, double y, double z) {
	double t_0 = -4.0 * (y * z);
	double tmp;
	if (y <= -2.3e+14) {
		tmp = t_0;
	} else if (y <= 7.6e-103) {
		tmp = x;
	} 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 = (-4.0d0) * (y * z)
    if (y <= (-2.3d+14)) then
        tmp = t_0
    else if (y <= 7.6d-103) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -4.0 * (y * z);
	double tmp;
	if (y <= -2.3e+14) {
		tmp = t_0;
	} else if (y <= 7.6e-103) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -4.0 * (y * z)
	tmp = 0
	if y <= -2.3e+14:
		tmp = t_0
	elif y <= 7.6e-103:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-4.0 * Float64(y * z))
	tmp = 0.0
	if (y <= -2.3e+14)
		tmp = t_0;
	elseif (y <= 7.6e-103)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -4.0 * (y * z);
	tmp = 0.0;
	if (y <= -2.3e+14)
		tmp = t_0;
	elseif (y <= 7.6e-103)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-4.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.3e+14], t$95$0, If[LessEqual[y, 7.6e-103], x, t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3e14 or 7.6000000000000001e-103 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(-4, \color{blue}{\left(y \cdot z\right)}\right) \]

      2. *-lowering-*.f64 74.3%

         \[\leadsto \mathsf{*.f64}\left(-4, \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   5. Simplified 74.3%

      \[\leadsto \color{blue}{-4 \cdot \left(y \cdot z\right)} \]

   if -2.3e14 < y < 7.6000000000000001e-103

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Simplified 79.3%

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

Alternative 3: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - z \cdot \left(y \cdot 4\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* z (* y 4.0))))

C

double code(double x, double y, double z) {
	return x - (z * (y * 4.0));
}

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 - (z * (y * 4.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x - (z * (y * 4.0));
}

Python

def code(x, y, z):
	return x - (z * (y * 4.0))

Julia

function code(x, y, z)
	return Float64(x - Float64(z * Float64(y * 4.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - (z * (y * 4.0));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(z * N[(y * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 4: 51.2% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Simplified 50.3%

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

Reproduce

herbie shell --seed 2024158 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4.0) z)))