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

Percentage Accurate: 100.0% → 100.0%

Time: 6.1s

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, 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 2: 49.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-266}:\\ \;\;\;\;x \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (+ x y) -1e-266) (* x 0.1) (* y 0.1)))

C

double code(double x, double y) {
	double tmp;
	if ((x + y) <= -1e-266) {
		tmp = x * 0.1;
	} else {
		tmp = y * 0.1;
	}
	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) <= (-1d-266)) then
        tmp = x * 0.1d0
    else
        tmp = y * 0.1d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x + y) <= -1e-266) {
		tmp = x * 0.1;
	} else {
		tmp = y * 0.1;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x + y) <= -1e-266:
		tmp = x * 0.1
	else:
		tmp = y * 0.1
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x + y) <= -1e-266)
		tmp = Float64(x * 0.1);
	else
		tmp = Float64(y * 0.1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x + y) <= -1e-266)
		tmp = x * 0.1;
	else
		tmp = y * 0.1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-266], N[(x * 0.1), $MachinePrecision], N[(y * 0.1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.9999999999999998e-267

   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 51.5

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

   5. Applied rewrites 51.5%

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

   if -9.9999999999999998e-267 < (+.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 49.4

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

   5. Applied rewrites 49.4%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-266}:\\ \;\;\;\;x \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.6% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(10.0 * N[(N[(x + y), $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. clear-num N/A

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

   3. associate-/r/ N/A

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

   4. lift-+.f64 N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. lower-*.f64 N/A

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

   9. metadata-eval 99.4

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

4. Applied rewrites 99.4%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.1, y \cdot 0.1\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. metadata-eval N/A

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

   3. div-inv N/A

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

   4. lower-/.f64 99.7

      \[\leadsto \mathsf{fma}\left(x, 0.1, \color{blue}{\frac{y}{10}}\right) \]

6. Applied rewrites 99.7%

   \[\leadsto \mathsf{fma}\left(x, 0.1, \color{blue}{\frac{y}{10}}\right) \]
7. Step-by-step derivation

   1. lift-fma.f64 N/A

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

   2. metadata-eval N/A

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

   3. div-inv N/A

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

   4. lift-/.f64 N/A

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

   5. frac-add N/A

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

   6. div-inv N/A

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

   7. metadata-eval N/A

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

   8. metadata-eval N/A

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

   9. metadata-eval N/A

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

   10. lower-*.f64 N/A

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

   11. metadata-eval N/A

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

   12. metadata-eval N/A

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

   13. associate-*r* N/A

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

   14. neg-mul-1 N/A

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

   15. lower-fma.f64 N/A

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

   16. neg-mul-1 N/A

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

   17. associate-*r* N/A

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

   18. metadata-eval N/A

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

   19. metadata-eval N/A

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

   20. *-commutative N/A

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

   21. lower-*.f64 N/A

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

   22. metadata-eval 99.2

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

8. Applied rewrites 99.2%

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

   1. lift-*.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. distribute-rgt-out N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 N/A

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

   10. lower-+.f64 99.6

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

10. Applied rewrites 99.6%

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

11. Final simplification 99.6%

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

Alternative 4: 99.4% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_] := N[(x * 0.1 + N[(y * 0.1), $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. clear-num N/A

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

   3. associate-/r/ N/A

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

   4. lift-+.f64 N/A

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

   5. distribute-rgt-in N/A

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

   6. lower-fma.f64 N/A

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

   7. metadata-eval N/A

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

   8. lower-*.f64 N/A

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

   9. metadata-eval 99.4

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

4. Applied rewrites 99.4%

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

Alternative 5: 99.5% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] * 0.1), $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. metadata-eval 99.4

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

4. Applied rewrites 99.4%

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

Alternative 6: 50.3% accurate, 2.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(x * 0.1), $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 50.7

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

5. Applied rewrites 50.7%

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

6. Final simplification 50.7%

   \[\leadsto x \cdot 0.1 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024230 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10.0))