Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{10} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) 10.0))

C

double code(double x, double y) {
	return (x + y) / 10.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / 10.0d0
end function

Java

public static double code(double x, double y) {
	return (x + y) / 10.0;
}

Python

def code(x, y):
	return (x + y) / 10.0

Julia

function code(x, y)
	return Float64(Float64(x + y) / 10.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / 10.0;
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / 10.0), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{10} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) 10.0))

C

double code(double x, double y) {
	return (x + y) / 10.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / 10.0d0
end function

Java

public static double code(double x, double y) {
	return (x + y) / 10.0;
}

Python

def code(x, y):
	return (x + y) / 10.0

Julia

function code(x, y)
	return Float64(Float64(x + y) / 10.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / 10.0;
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / 10.0), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{y}{10} + \frac{x}{10} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (/ y 10.0) (/ x 10.0)))

C

double code(double x, double y) {
	return (y / 10.0) + (x / 10.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y / 10.0d0) + (x / 10.0d0)
end function

Java

public static double code(double x, double y) {
	return (y / 10.0) + (x / 10.0);
}

Python

def code(x, y):
	return (y / 10.0) + (x / 10.0)

Julia

function code(x, y)
	return Float64(Float64(y / 10.0) + Float64(x / 10.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (y / 10.0) + (x / 10.0);
end

Wolfram

code[x_, y_] := N[(N[(y / 10.0), $MachinePrecision] + N[(x / 10.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{10} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{x + y}{10}} \]

   2. lift-+.f64 N/A

      \[\leadsto \frac{\color{blue}{x + y}}{10} \]

   3. +-commutative N/A

      \[\leadsto \frac{\color{blue}{y + x}}{10} \]

   4. div-add N/A

      \[\leadsto \color{blue}{\frac{y}{10} + \frac{x}{10}} \]

   5. lower-+.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{10} + \frac{x}{10}} \]

   6. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{10}} + \frac{x}{10} \]

   7. lower-/.f64 100.0

      \[\leadsto \frac{y}{10} + \color{blue}{\frac{x}{10}} \]

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\frac{y}{10} + \frac{x}{10}} \]
5. Add Preprocessing

Alternative 2: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x + y}{10} \leq -5 \cdot 10^{-201}:\\ \;\;\;\;0.1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ (+ x y) 10.0) -5e-201) (* 0.1 x) (* 0.1 y)))

C

double code(double x, double y) {
	double tmp;
	if (((x + y) / 10.0) <= -5e-201) {
		tmp = 0.1 * x;
	} else {
		tmp = 0.1 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((x + y) / 10.0d0) <= (-5d-201)) then
        tmp = 0.1d0 * x
    else
        tmp = 0.1d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((x + y) / 10.0) <= -5e-201) {
		tmp = 0.1 * x;
	} else {
		tmp = 0.1 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((x + y) / 10.0) <= -5e-201:
		tmp = 0.1 * x
	else:
		tmp = 0.1 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(x + y) / 10.0) <= -5e-201)
		tmp = Float64(0.1 * x);
	else
		tmp = Float64(0.1 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((x + y) / 10.0) <= -5e-201)
		tmp = 0.1 * x;
	else
		tmp = 0.1 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] / 10.0), $MachinePrecision], -5e-201], N[(0.1 * x), $MachinePrecision], N[(0.1 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x y) #s(literal 10 binary64)) < -4.9999999999999999e-201

   1. Initial program 100.0%

      \[\frac{x + y}{10} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{10} \cdot x} \]
   4. Step-by-step derivation

      1. lower-*.f64 56.1

         \[\leadsto \color{blue}{0.1 \cdot x} \]

   5. Applied rewrites 56.1%

      \[\leadsto \color{blue}{0.1 \cdot x} \]

   if -4.9999999999999999e-201 < (/.f64 (+.f64 x y) #s(literal 10 binary64))

   1. Initial program 100.0%

      \[\frac{x + y}{10} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{10} \cdot y} \]
   4. Step-by-step derivation

      1. lower-*.f64 49.6

         \[\leadsto \color{blue}{0.1 \cdot y} \]

   5. Applied rewrites 49.6%

      \[\leadsto \color{blue}{0.1 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{10} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) 10.0))

C

double code(double x, double y) {
	return (x + y) / 10.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / 10.0d0
end function

Java

public static double code(double x, double y) {
	return (x + y) / 10.0;
}

Python

def code(x, y):
	return (x + y) / 10.0

Julia

function code(x, y)
	return Float64(Float64(x + y) / 10.0)
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / 10.0;
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / 10.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{10} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 4: 99.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 0.1, 0.1 \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x 0.1 (* 0.1 y)))

C

double code(double x, double y) {
	return fma(x, 0.1, (0.1 * y));
}

Julia

function code(x, y)
	return fma(x, 0.1, Float64(0.1 * y))
end

Wolfram

code[x_, y_] := N[(x * 0.1 + N[(0.1 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{10} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{x + y}{10}} \]

   2. lift-+.f64 N/A

      \[\leadsto \frac{\color{blue}{x + y}}{10} \]

   3. +-commutative N/A

      \[\leadsto \frac{\color{blue}{y + x}}{10} \]

   4. div-add N/A

      \[\leadsto \color{blue}{\frac{y}{10} + \frac{x}{10}} \]

   5. lower-+.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{10} + \frac{x}{10}} \]

   6. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{10}} + \frac{x}{10} \]

   7. lower-/.f64 100.0

      \[\leadsto \frac{y}{10} + \color{blue}{\frac{x}{10}} \]

4. Applied rewrites 100.0%

   \[\leadsto \color{blue}{\frac{y}{10} + \frac{x}{10}} \]
5. Step-by-step derivation

   1. lift-+.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{10} + \frac{x}{10}} \]

   2. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{y}{10}} + \frac{x}{10} \]

   3. lift-/.f64 N/A

      \[\leadsto \frac{y}{10} + \color{blue}{\frac{x}{10}} \]

   4. frac-add N/A

      \[\leadsto \color{blue}{\frac{y \cdot 10 + 10 \cdot x}{10 \cdot 10}} \]

   5. *-commutative N/A

      \[\leadsto \frac{\color{blue}{10 \cdot y} + 10 \cdot x}{10 \cdot 10} \]

   6. lift-*.f64 N/A

      \[\leadsto \frac{10 \cdot y + \color{blue}{10 \cdot x}}{10 \cdot 10} \]

   7. metadata-eval N/A

      \[\leadsto \frac{10 \cdot y + 10 \cdot x}{\color{blue}{100}} \]

   8. div-add N/A

      \[\leadsto \color{blue}{\frac{10 \cdot y}{100} + \frac{10 \cdot x}{100}} \]

   9. +-commutative N/A

      \[\leadsto \color{blue}{\frac{10 \cdot x}{100} + \frac{10 \cdot y}{100}} \]

   10. lift-*.f64 N/A

       \[\leadsto \frac{\color{blue}{10 \cdot x}}{100} + \frac{10 \cdot y}{100} \]

   11. *-commutative N/A

       \[\leadsto \frac{\color{blue}{x \cdot 10}}{100} + \frac{10 \cdot y}{100} \]

   12. associate-/l* N/A

       \[\leadsto \color{blue}{x \cdot \frac{10}{100}} + \frac{10 \cdot y}{100} \]

   13. metadata-eval N/A

       \[\leadsto x \cdot \color{blue}{\frac{1}{10}} + \frac{10 \cdot y}{100} \]

   14. lower-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{1}{10}, \frac{10 \cdot y}{100}\right)} \]

   15. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{1}{10}, \frac{\color{blue}{y \cdot 10}}{100}\right) \]

   16. associate-/l* N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{1}{10}, \color{blue}{y \cdot \frac{10}{100}}\right) \]

   17. metadata-eval N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{1}{10}, y \cdot \color{blue}{\frac{1}{10}}\right) \]

   18. *-commutative N/A

       \[\leadsto \mathsf{fma}\left(x, \frac{1}{10}, \color{blue}{\frac{1}{10} \cdot y}\right) \]

   19. lift-*.f64 99.5

       \[\leadsto \mathsf{fma}\left(x, 0.1, \color{blue}{0.1 \cdot y}\right) \]

6. Applied rewrites 99.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.1, 0.1 \cdot y\right)} \]
7. Add Preprocessing

Alternative 5: 99.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \left(y + x\right) \cdot 0.1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (+ y x) 0.1))

C

double code(double x, double y) {
	return (y + x) * 0.1;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + x) * 0.1d0
end function

Java

public static double code(double x, double y) {
	return (y + x) * 0.1;
}

Python

def code(x, y):
	return (y + x) * 0.1

Julia

function code(x, y)
	return Float64(Float64(y + x) * 0.1)
end

MATLAB

function tmp = code(x, y)
	tmp = (y + x) * 0.1;
end

Wolfram

code[x_, y_] := N[(N[(y + x), $MachinePrecision] * 0.1), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{10} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{1}{10} \cdot x + \frac{1}{10} \cdot y} \]
4. Step-by-step derivation

   1. distribute-lft-out N/A

      \[\leadsto \color{blue}{\frac{1}{10} \cdot \left(x + y\right)} \]

   2. *-commutative N/A

      \[\leadsto \color{blue}{\left(x + y\right) \cdot \frac{1}{10}} \]

   3. lower-*.f64 N/A

      \[\leadsto \color{blue}{\left(x + y\right) \cdot \frac{1}{10}} \]

   4. +-commutative N/A

      \[\leadsto \color{blue}{\left(y + x\right)} \cdot \frac{1}{10} \]

   5. lower-+.f64 99.5

      \[\leadsto \color{blue}{\left(y + x\right)} \cdot 0.1 \]

5. Applied rewrites 99.5%

   \[\leadsto \color{blue}{\left(y + x\right) \cdot 0.1} \]
6. Add Preprocessing

Alternative 6: 50.4% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ 0.1 \cdot x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 0.1 x))

C

double code(double x, double y) {
	return 0.1 * x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.1d0 * x
end function

Java

public static double code(double x, double y) {
	return 0.1 * x;
}

Python

def code(x, y):
	return 0.1 * x

Julia

function code(x, y)
	return Float64(0.1 * x)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.1 * x;
end

Wolfram

code[x_, y_] := N[(0.1 * x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{10} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\frac{1}{10} \cdot x} \]
4. Step-by-step derivation

   1. lower-*.f64 52.9

      \[\leadsto \color{blue}{0.1 \cdot x} \]

5. Applied rewrites 52.9%

   \[\leadsto \color{blue}{0.1 \cdot x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024342 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10.0))