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

Percentage Accurate: 100.0% → 100.0%

Time: 9.3s

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, 0.7× 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. frac-2neg N/A

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

   2. +-commutative N/A

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

   3. distribute-neg-in N/A

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

   4. unsub-neg N/A

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

   5. div-sub N/A

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

   6. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\mathsf{neg}\left(y\right)}{\mathsf{neg}\left(10\right)}\right), \color{blue}{\left(\frac{x}{\mathsf{neg}\left(10\right)}\right)}\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(\mathsf{neg}\left(y\right)\right), \left(\mathsf{neg}\left(10\right)\right)\right), \left(\frac{\color{blue}{x}}{\mathsf{neg}\left(10\right)}\right)\right) \]

   8. neg-sub0 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left(0 - y\right), \left(\mathsf{neg}\left(10\right)\right)\right), \left(\frac{x}{\mathsf{neg}\left(10\right)}\right)\right) \]

   9. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, y\right), \left(\mathsf{neg}\left(10\right)\right)\right), \left(\frac{x}{\mathsf{neg}\left(10\right)}\right)\right) \]

   10. metadata-eval N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, y\right), -10\right), \left(\frac{x}{\mathsf{neg}\left(10\right)}\right)\right) \]

   11. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, y\right), -10\right), \mathsf{/.f64}\left(x, \color{blue}{\left(\mathsf{neg}\left(10\right)\right)}\right)\right) \]

   12. metadata-eval 100.0%

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(0, y\right), -10\right), \mathsf{/.f64}\left(x, -10\right)\right) \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{0 - y}{-10} - \frac{x}{-10}} \]
5. Step-by-step derivation

   1. --lowering--.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{0 - y}{-10}\right), \color{blue}{\left(\frac{x}{-10}\right)}\right) \]

   2. sub0-neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\mathsf{neg}\left(y\right)}{-10}\right), \left(\frac{x}{-10}\right)\right) \]

   3. metadata-eval N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{\mathsf{neg}\left(y\right)}{\mathsf{neg}\left(10\right)}\right), \left(\frac{x}{-10}\right)\right) \]

   4. frac-2neg N/A

      \[\leadsto \mathsf{\_.f64}\left(\left(\frac{y}{10}\right), \left(\frac{\color{blue}{x}}{-10}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, 10\right), \left(\frac{\color{blue}{x}}{-10}\right)\right) \]

   6. /-lowering-/.f64 100.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{/.f64}\left(y, 10\right), \mathsf{/.f64}\left(x, \color{blue}{-10}\right)\right) \]

6. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\frac{y}{10} - \frac{x}{-10}} \]
7. Add Preprocessing

Alternative 2: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{10}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{10}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -2.25e-76) (/ x 10.0) (/ y 10.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.25e-76) {
		tmp = x / 10.0;
	} else {
		tmp = y / 10.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.25d-76)) then
        tmp = x / 10.0d0
    else
        tmp = y / 10.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.25e-76) {
		tmp = x / 10.0;
	} else {
		tmp = y / 10.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.25e-76:
		tmp = x / 10.0
	else:
		tmp = y / 10.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.25e-76)
		tmp = Float64(x / 10.0);
	else
		tmp = Float64(y / 10.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.25e-76)
		tmp = x / 10.0;
	else
		tmp = y / 10.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.25e-76], N[(x / 10.0), $MachinePrecision], N[(y / 10.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, 10\right) \]
   4. Step-by-step derivation

   5. Simplified 68.9%

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

   if -2.25e-76 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{y}, 10\right) \]
   4. Step-by-step derivation

   5. Simplified 57.6%

      \[\leadsto \frac{\color{blue}{y}}{10} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{10}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -2.25e-76) (/ x 10.0) (* y 0.1)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.25e-76) {
		tmp = x / 10.0;
	} 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 <= (-2.25d-76)) then
        tmp = x / 10.0d0
    else
        tmp = y * 0.1d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.25e-76) {
		tmp = x / 10.0;
	} else {
		tmp = y * 0.1;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.25e-76:
		tmp = x / 10.0
	else:
		tmp = y * 0.1
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.25e-76)
		tmp = Float64(x / 10.0);
	else
		tmp = Float64(y * 0.1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.25e-76)
		tmp = x / 10.0;
	else
		tmp = y * 0.1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.25e-76], N[(x / 10.0), $MachinePrecision], N[(y * 0.1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25e-76

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{x}, 10\right) \]
   4. Step-by-step derivation

   5. Simplified 68.9%

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

   if -2.25e-76 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{10}, \color{blue}{y}\right) \]

   5. Simplified 57.2%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{10}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-76}:\\ \;\;\;\;x \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -1.25e-76) (* x 0.1) (* y 0.1)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.25e-76) {
		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 <= (-1.25d-76)) 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 <= -1.25e-76) {
		tmp = x * 0.1;
	} else {
		tmp = y * 0.1;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.25e-76:
		tmp = x * 0.1
	else:
		tmp = y * 0.1
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.25e-76)
		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 <= -1.25e-76)
		tmp = x * 0.1;
	else
		tmp = y * 0.1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.25e-76], N[(x * 0.1), $MachinePrecision], N[(y * 0.1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.2499999999999999e-76

   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. *-lowering-*.f64 68.6%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{10}, \color{blue}{x}\right) \]

   5. Simplified 68.6%

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

   if -1.2499999999999999e-76 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 57.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{10}, \color{blue}{y}\right) \]

   5. Simplified 57.2%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{-76}:\\ \;\;\;\;x \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 6: 99.5% accurate, 1.0× 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. Step-by-step derivation

   1. div-inv N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(x + y\right), \color{blue}{\left(\frac{1}{10}\right)}\right) \]

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), \left(\frac{\color{blue}{1}}{10}\right)\right) \]

   4. metadata-eval 99.4%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{+.f64}\left(x, y\right), \frac{1}{10}\right) \]

4. Applied egg-rr 99.4%

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

5. Final simplification 99.4%

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

Alternative 7: 50.4% accurate, 1.7× 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. *-lowering-*.f64 51.0%

      \[\leadsto \mathsf{*.f64}\left(\frac{1}{10}, \color{blue}{x}\right) \]

5. Simplified 51.0%

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

6. Final simplification 51.0%

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

Reproduce

herbie shell --seed 2024138 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10.0))