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

Percentage Accurate: 99.9% → 100.0%

Time: 3.4s

Alternatives: 3

Speedup: 2.9×

Specification

Math

\[\begin{array}{l} \\ x - \frac{3}{8} \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (* (/ 3.0 8.0) y)))

C

double code(double x, double y) {
	return x - ((3.0 / 8.0) * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - ((3.0d0 / 8.0d0) * y)
end function

Java

public static double code(double x, double y) {
	return x - ((3.0 / 8.0) * y);
}

Python

def code(x, y):
	return x - ((3.0 / 8.0) * y)

Julia

function code(x, y)
	return Float64(x - Float64(Float64(3.0 / 8.0) * y))
end

MATLAB

function tmp = code(x, y)
	tmp = x - ((3.0 / 8.0) * y);
end

Wolfram

code[x_, y_] := N[(x - N[(N[(3.0 / 8.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \frac{3}{8} \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x (* (/ 3.0 8.0) y)))

C

double code(double x, double y) {
	return x - ((3.0 / 8.0) * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x - ((3.0d0 / 8.0d0) * y)
end function

Java

public static double code(double x, double y) {
	return x - ((3.0 / 8.0) * y);
}

Python

def code(x, y):
	return x - ((3.0 / 8.0) * y)

Julia

function code(x, y)
	return Float64(x - Float64(Float64(3.0 / 8.0) * y))
end

MATLAB

function tmp = code(x, y)
	tmp = x - ((3.0 / 8.0) * y);
end

Wolfram

code[x_, y_] := N[(x - N[(N[(3.0 / 8.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, -0.375, x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y -0.375 x))

C

double code(double x, double y) {
	return fma(y, -0.375, x);
}

Julia

function code(x, y)
	return fma(y, -0.375, x)
end

Wolfram

code[x_, y_] := N[(y * -0.375 + x), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x - \frac{3}{8} \cdot y \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto \color{blue}{x + \left(\mathsf{neg}\left(\frac{3}{8} \cdot y\right)\right)} \]

   2. +-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{3}{8} \cdot y\right)\right) + x} \]

   3. *-commutative N/A

      \[\leadsto \left(\mathsf{neg}\left(\color{blue}{y \cdot \frac{3}{8}}\right)\right) + x \]

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

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{neg}\left(\frac{3}{8}\right)\right)} + x \]

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

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{neg}\left(\frac{3}{8}\right), x\right)} \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(y, \mathsf{neg}\left(\color{blue}{\frac{3}{8}}\right), x\right) \]

   7. metadata-eval 100.0

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{-0.375}, x\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, -0.375, x\right)} \]
5. Add Preprocessing

Alternative 2: 73.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{3}{8}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{+76}:\\ \;\;\;\;y \cdot -0.375\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.375\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (/ 3.0 8.0))))
   (if (<= t_0 -2e+76) (* y -0.375) (if (<= t_0 5e-20) x (* y -0.375)))))

C

double code(double x, double y) {
	double t_0 = y * (3.0 / 8.0);
	double tmp;
	if (t_0 <= -2e+76) {
		tmp = y * -0.375;
	} else if (t_0 <= 5e-20) {
		tmp = x;
	} else {
		tmp = y * -0.375;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (3.0d0 / 8.0d0)
    if (t_0 <= (-2d+76)) then
        tmp = y * (-0.375d0)
    else if (t_0 <= 5d-20) then
        tmp = x
    else
        tmp = y * (-0.375d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * (3.0 / 8.0);
	double tmp;
	if (t_0 <= -2e+76) {
		tmp = y * -0.375;
	} else if (t_0 <= 5e-20) {
		tmp = x;
	} else {
		tmp = y * -0.375;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (3.0 / 8.0)
	tmp = 0
	if t_0 <= -2e+76:
		tmp = y * -0.375
	elif t_0 <= 5e-20:
		tmp = x
	else:
		tmp = y * -0.375
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(3.0 / 8.0))
	tmp = 0.0
	if (t_0 <= -2e+76)
		tmp = Float64(y * -0.375);
	elseif (t_0 <= 5e-20)
		tmp = x;
	else
		tmp = Float64(y * -0.375);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (3.0 / 8.0);
	tmp = 0.0;
	if (t_0 <= -2e+76)
		tmp = y * -0.375;
	elseif (t_0 <= 5e-20)
		tmp = x;
	else
		tmp = y * -0.375;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(3.0 / 8.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -2e+76], N[(y * -0.375), $MachinePrecision], If[LessEqual[t$95$0, 5e-20], x, N[(y * -0.375), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y) < -2.0000000000000001e76 or 4.9999999999999999e-20 < (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y)

   1. Initial program 99.8%

      \[x - \frac{3}{8} \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-3}{8} \cdot y} \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 79.9

         \[\leadsto \color{blue}{-0.375 \cdot y} \]

   5. Simplified 79.9%

      \[\leadsto \color{blue}{-0.375 \cdot y} \]

   if -2.0000000000000001e76 < (*.f64 (/.f64 #s(literal 3 binary64) #s(literal 8 binary64)) y) < 4.9999999999999999e-20

   1. Initial program 100.0%

      \[x - \frac{3}{8} \cdot y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 80.6%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \frac{3}{8} \leq -2 \cdot 10^{+76}:\\ \;\;\;\;y \cdot -0.375\\ \mathbf{elif}\;y \cdot \frac{3}{8} \leq 5 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.375\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.7% accurate, 20.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 99.9%

   \[x - \frac{3}{8} \cdot y \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Simplified 51.3%

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

Reproduce

herbie shell --seed 2024204 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (/ 3.0 8.0) y)))