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

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 7

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: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -5 \cdot 10^{-240}:\\ \;\;\;\;0.1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (+ x y) -5e-240) (* 0.1 x) (* 0.1 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x + y) <= -5e-240) {
		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) <= (-5d-240)) 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) <= -5e-240) {
		tmp = 0.1 * x;
	} else {
		tmp = 0.1 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x + y) <= -5e-240:
		tmp = 0.1 * x
	else:
		tmp = 0.1 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x + y) <= -5e-240)
		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) <= -5e-240)
		tmp = 0.1 * x;
	else
		tmp = 0.1 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x + y), $MachinePrecision], -5e-240], N[(0.1 * x), $MachinePrecision], N[(0.1 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -5.0000000000000004e-240

   1. Initial program 99.9%

      \[\frac{x + y}{10} \]
   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 52.6

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

   5. Applied rewrites 52.6%

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

   if -5.0000000000000004e-240 < (+.f64 x y)

   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 56.8

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

   5. Applied rewrites 56.8%

      \[\leadsto \color{blue}{0.1 \cdot y} \]
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: 99.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ 10 \cdot \left(\left(y + x\right) \cdot 0.01\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 10.0 (* (+ y x) 0.01)))

C

double code(double x, double y) {
	return 10.0 * ((y + x) * 0.01);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 10.0d0 * ((y + x) * 0.01d0)
end function

Java

public static double code(double x, double y) {
	return 10.0 * ((y + x) * 0.01);
}

Python

def code(x, y):
	return 10.0 * ((y + x) * 0.01)

Julia

function code(x, y)
	return Float64(10.0 * Float64(Float64(y + x) * 0.01))
end

MATLAB

function tmp = code(x, y)
	tmp = 10.0 * ((y + x) * 0.01);
end

Wolfram

code[x_, y_] := N[(10.0 * N[(N[(y + x), $MachinePrecision] * 0.01), $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

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

   6. distribute-rgt-in N/A

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

   7. lift-+.f64 N/A

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

   8. metadata-eval N/A

      \[\leadsto \frac{10 \cdot \left(y + x\right)}{\color{blue}{100}} \]

   9. associate-/l* N/A

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

   10. lower-*.f64 N/A

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

   11. lower-/.f64 99.5

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

   12. lift-+.f64 N/A

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

   13. +-commutative N/A

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

   14. lower-+.f64 99.5

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

6. Applied rewrites 99.5%

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

7. Taylor expanded in x around 0

   \[\leadsto 10 \cdot \color{blue}{\left(\frac{1}{100} \cdot x + \frac{1}{100} \cdot y\right)} \]
8. Step-by-step derivation

   1. distribute-lft-out N/A

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. +-commutative N/A

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

   5. lower-+.f64 99.6

      \[\leadsto 10 \cdot \left(\color{blue}{\left(y + x\right)} \cdot 0.01\right) \]

9. Applied rewrites 99.6%

   \[\leadsto 10 \cdot \color{blue}{\left(\left(y + x\right) \cdot 0.01\right)} \]
10. Add Preprocessing

Alternative 5: 99.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

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

   10. associate-/l* N/A

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

   11. metadata-eval N/A

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

   12. lower-fma.f64 N/A

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

   13. lift-*.f64 N/A

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

   14. *-commutative N/A

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

   15. associate-/l* N/A

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

   16. metadata-eval N/A

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

   17. *-commutative N/A

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

   18. lift-*.f64 99.5

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

6. Applied rewrites 99.5%

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

Alternative 6: 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 7: 49.0% 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 49.3

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

5. Applied rewrites 49.3%

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

Reproduce

herbie shell --seed 2024326 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10.0))