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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

Alternatives: 3

Speedup: 2.2×

Specification

Math

\[\begin{array}{l} \\ \frac{1}{2} \cdot \left(x + y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ 1.0 2.0) (+ x y)))

C

double code(double x, double y) {
	return (1.0 / 2.0) * (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 / 2.0d0) * (x + y)
end function

Java

public static double code(double x, double y) {
	return (1.0 / 2.0) * (x + y);
}

Python

def code(x, y):
	return (1.0 / 2.0) * (x + y)

Julia

function code(x, y)
	return Float64(Float64(1.0 / 2.0) * Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 / 2.0) * (x + y);
end

Wolfram

code[x_, y_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{2} \cdot \left(x + y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ 1.0 2.0) (+ x y)))

C

double code(double x, double y) {
	return (1.0 / 2.0) * (x + y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 / 2.0d0) * (x + y)
end function

Java

public static double code(double x, double y) {
	return (1.0 / 2.0) * (x + y);
}

Python

def code(x, y):
	return (1.0 / 2.0) * (x + y)

Julia

function code(x, y)
	return Float64(Float64(1.0 / 2.0) * Float64(x + y))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 / 2.0) * (x + y);
end

Wolfram

code[x_, y_] := N[(N[(1.0 / 2.0), $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \left(y + x\right) \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (+ y x) 0.5))

C

double code(double x, double y) {
	return (y + x) * 0.5;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + x) * 0.5d0
end function

Java

public static double code(double x, double y) {
	return (y + x) * 0.5;
}

Python

def code(x, y):
	return (y + x) * 0.5

Julia

function code(x, y)
	return Float64(Float64(y + x) * 0.5)
end

MATLAB

function tmp = code(x, y)
	tmp = (y + x) * 0.5;
end

Wolfram

code[x_, y_] := N[(N[(y + x), $MachinePrecision] * 0.5), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{1}{2} \cdot \left(x + y\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(x + y\right)} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\left(x + y\right) \cdot \frac{1}{2}} \]

   3. lower-*.f64 100.0

      \[\leadsto \color{blue}{\left(x + y\right) \cdot \frac{1}{2}} \]

   4. lift-+.f64 N/A

      \[\leadsto \color{blue}{\left(x + y\right)} \cdot \frac{1}{2} \]

   5. +-commutative N/A

      \[\leadsto \color{blue}{\left(y + x\right)} \cdot \frac{1}{2} \]

   6. lower-+.f64 100.0

      \[\leadsto \color{blue}{\left(y + x\right)} \cdot \frac{1}{2} \]

   7. lift-/.f64 N/A

      \[\leadsto \left(y + x\right) \cdot \color{blue}{\frac{1}{2}} \]

   8. metadata-eval 100.0

      \[\leadsto \left(y + x\right) \cdot \color{blue}{0.5} \]

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\left(y + x\right) \cdot 0.5} \]
5. Add Preprocessing

Alternative 2: 50.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;{2}^{-1} \cdot \left(x + y\right) \leq -2 \cdot 10^{-259}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* (pow 2.0 -1.0) (+ x y)) -2e-259) (* 0.5 x) (* 0.5 y)))

C

double code(double x, double y) {
	double tmp;
	if ((pow(2.0, -1.0) * (x + y)) <= -2e-259) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((2.0d0 ** (-1.0d0)) * (x + y)) <= (-2d-259)) then
        tmp = 0.5d0 * x
    else
        tmp = 0.5d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((Math.pow(2.0, -1.0) * (x + y)) <= -2e-259) {
		tmp = 0.5 * x;
	} else {
		tmp = 0.5 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (math.pow(2.0, -1.0) * (x + y)) <= -2e-259:
		tmp = 0.5 * x
	else:
		tmp = 0.5 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64((2.0 ^ -1.0) * Float64(x + y)) <= -2e-259)
		tmp = Float64(0.5 * x);
	else
		tmp = Float64(0.5 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((2.0 ^ -1.0) * (x + y)) <= -2e-259)
		tmp = 0.5 * x;
	else
		tmp = 0.5 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[Power[2.0, -1.0], $MachinePrecision] * N[(x + y), $MachinePrecision]), $MachinePrecision], -2e-259], N[(0.5 * x), $MachinePrecision], N[(0.5 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y)) < -2.0000000000000001e-259

   1. Initial program 100.0%

      \[\frac{1}{2} \cdot \left(x + y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]
   4. Step-by-step derivation

      1. lower-*.f64 52.4

         \[\leadsto \color{blue}{0.5 \cdot x} \]

   5. Applied rewrites 52.4%

      \[\leadsto \color{blue}{0.5 \cdot x} \]

   if -2.0000000000000001e-259 < (*.f64 (/.f64 #s(literal 1 binary64) #s(literal 2 binary64)) (+.f64 x y))

   1. Initial program 100.0%

      \[\frac{1}{2} \cdot \left(x + y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{2} \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 53.0

         \[\leadsto \color{blue}{0.5 \cdot y} \]

   5. Applied rewrites 53.0%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;{2}^{-1} \cdot \left(x + y\right) \leq -2 \cdot 10^{-259}:\\ \;\;\;\;0.5 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.2% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.5 x))

C

double code(double x, double y) {
	return 0.5 * x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 * x
end function

Java

public static double code(double x, double y) {
	return 0.5 * x;
}

Python

def code(x, y):
	return 0.5 * x

Julia

function code(x, y)
	return Float64(0.5 * x)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.5 * x;
end

Wolfram

code[x_, y_] := N[(0.5 * x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{1}{2} \cdot \left(x + y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot x} \]
4. Step-by-step derivation

   1. lower-*.f64 49.4

      \[\leadsto \color{blue}{0.5 \cdot x} \]

5. Applied rewrites 49.4%

   \[\leadsto \color{blue}{0.5 \cdot x} \]
6. Add Preprocessing

Developer Target 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{2} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) 2.0))

C

double code(double x, double y) {
	return (x + y) / 2.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / 2.0d0
end function

Java

public static double code(double x, double y) {
	return (x + y) / 2.0;
}

Python

def code(x, y):
	return (x + y) / 2.0

Julia

function code(x, y)
	return Float64(Float64(x + y) / 2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / 2.0;
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / 2.0), $MachinePrecision]

Reproduce

herbie shell --seed 2024337 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, G"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (+ x y) 2))

  (* (/ 1.0 2.0) (+ x y)))