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 99.8%

   \[x - \frac{3}{8} \cdot y \]
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: 74.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+27}:\\ \;\;\;\;y \cdot -0.375\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8.8e+15) x (if (<= x 3e+27) (* y -0.375) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8.8e+15) {
		tmp = x;
	} else if (x <= 3e+27) {
		tmp = y * -0.375;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-8.8d+15)) then
        tmp = x
    else if (x <= 3d+27) then
        tmp = y * (-0.375d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -8.8e+15) {
		tmp = x;
	} else if (x <= 3e+27) {
		tmp = y * -0.375;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8.8e+15:
		tmp = x
	elif x <= 3e+27:
		tmp = y * -0.375
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8.8e+15)
		tmp = x;
	elseif (x <= 3e+27)
		tmp = Float64(y * -0.375);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8.8e+15)
		tmp = x;
	elseif (x <= 3e+27)
		tmp = y * -0.375;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8.8e+15], x, If[LessEqual[x, 3e+27], N[(y * -0.375), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.8e15 or 2.99999999999999976e27 < x

   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 73.5%

      \[\leadsto \color{blue}{x} \]

   if -8.8e15 < x < 2.99999999999999976e27

   1. Initial program 99.7%

      \[x - \frac{3}{8} \cdot y \]
   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 77.3

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

   5. Simplified 77.3%

      \[\leadsto \color{blue}{-0.375 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.8 \cdot 10^{+15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+27}:\\ \;\;\;\;y \cdot -0.375\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.1% 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 99.8%

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

3. Taylor expanded in x around inf

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

5. Simplified 45.5%

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

Reproduce

herbie shell --seed 2024201 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (/ 3.0 8.0) y)))