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

Percentage Accurate: 100.0% → 100.0%

Time: 5.5s

Alternatives: 5

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 49.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -4 \cdot 10^{-288}:\\ \;\;\;\;0.1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (+ y x) -4e-288) (* 0.1 x) (* 0.1 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y + x) <= -4e-288) {
		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 ((y + x) <= (-4d-288)) 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 ((y + x) <= -4e-288) {
		tmp = 0.1 * x;
	} else {
		tmp = 0.1 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y + x) <= -4e-288:
		tmp = 0.1 * x
	else:
		tmp = 0.1 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y + x) <= -4e-288)
		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 ((y + x) <= -4e-288)
		tmp = 0.1 * x;
	else
		tmp = 0.1 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y + x), $MachinePrecision], -4e-288], N[(0.1 * x), $MachinePrecision], N[(0.1 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.00000000000000023e-288

   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 53.1

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

   5. Applied rewrites 53.1%

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

   if -4.00000000000000023e-288 < (+.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 48.8

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

   5. Applied rewrites 48.8%

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

4. Final simplification 51.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -4 \cdot 10^{-288}:\\ \;\;\;\;0.1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.1 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(0.01 * N[(y + x), $MachinePrecision]), $MachinePrecision] * 10.0), $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. frac-2neg N/A

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

   3. lift-+.f64 N/A

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

   4. +-commutative N/A

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

   5. distribute-neg-in N/A

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

   6. unsub-neg N/A

      \[\leadsto \frac{\color{blue}{\left(\mathsf{neg}\left(y\right)\right) - x}}{\mathsf{neg}\left(10\right)} \]

   7. div-sub N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(y\right)}{\mathsf{neg}\left(10\right)} - \frac{x}{\mathsf{neg}\left(10\right)}} \]

   8. lower--.f64 N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(y\right)}{\mathsf{neg}\left(10\right)} - \frac{x}{\mathsf{neg}\left(10\right)}} \]

   9. lower-/.f64 N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(y\right)}{\mathsf{neg}\left(10\right)}} - \frac{x}{\mathsf{neg}\left(10\right)} \]

   10. lower-neg.f64 N/A

       \[\leadsto \frac{\color{blue}{-y}}{\mathsf{neg}\left(10\right)} - \frac{x}{\mathsf{neg}\left(10\right)} \]

   11. metadata-eval N/A

       \[\leadsto \frac{-y}{\color{blue}{-10}} - \frac{x}{\mathsf{neg}\left(10\right)} \]

   12. lower-/.f64 N/A

       \[\leadsto \frac{-y}{-10} - \color{blue}{\frac{x}{\mathsf{neg}\left(10\right)}} \]

   13. metadata-eval 100.0

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

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-sub N/A

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

   5. div-inv N/A

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

   6. lower-*.f64 N/A

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

   7. cancel-sign-sub-inv N/A

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

   8. lift-neg.f64 N/A

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

   9. distribute-lft-neg-out N/A

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

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

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

   11. metadata-eval N/A

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

   12. metadata-eval N/A

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

   13. lower-fma.f64 N/A

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

   14. lower-*.f64 N/A

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

   15. metadata-eval N/A

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

   16. metadata-eval 99.2

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

6. Applied rewrites 99.2%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 10, 10 \cdot x\right) \cdot 0.01} \]
7. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. +-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. distribute-lft-out N/A

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

   7. associate-*l* N/A

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

   8. lower-*.f64 N/A

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

   9. lower-*.f64 N/A

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

   10. +-commutative N/A

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

   11. lower-+.f64 99.6

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

8. Applied rewrites 99.6%

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

9. Final simplification 99.6%

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

Alternative 4: 99.4% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(0.1 * N[(y + 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. div-inv 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. lift-+.f64 N/A

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

   5. +-commutative N/A

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

   6. lower-+.f64 N/A

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

   7. metadata-eval 99.5

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

4. Applied rewrites 99.5%

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

5. Final simplification 99.5%

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

Alternative 5: 50.6% 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 51.9

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

5. Applied rewrites 51.9%

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

Reproduce

herbie shell --seed 2024331 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10.0))