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

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

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, 0.5× 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(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. 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. Add Preprocessing

Alternative 2: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-257}:\\ \;\;\;\;0.1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (+ x y) -1e-257) (* 0.1 x) (* 0.1 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x + y) <= -1e-257) {
		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) <= (-1d-257)) 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) <= -1e-257) {
		tmp = 0.1 * x;
	} else {
		tmp = 0.1 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x + y) <= -1e-257:
		tmp = 0.1 * x
	else:
		tmp = 0.1 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x + y) <= -1e-257)
		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) <= -1e-257)
		tmp = 0.1 * x;
	else
		tmp = 0.1 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x + y), $MachinePrecision], -1e-257], N[(0.1 * x), $MachinePrecision], N[(0.1 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -9.9999999999999998e-258

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 50.5

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

   5. Applied rewrites 50.5%

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

   if -9.9999999999999998e-258 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 46.8

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

   5. Applied rewrites 46.8%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -1 \cdot 10^{-257}:\\ \;\;\;\;0.1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;0.1 \cdot y\\ \end{array} \]
5. 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. 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 99.5

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

4. Applied rewrites 99.5%

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

5. Final simplification 99.5%

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

Alternative 5: 99.5% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(0.1 * N[(x + 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. 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%

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

Alternative 6: 50.1% 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 y around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 51.7

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

5. Applied rewrites 51.7%

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

6. Final simplification 51.7%

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

Reproduce

herbie shell --seed 2024277 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10.0))