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

Percentage Accurate: 100.0% → 100.0%

Time: 10.4s

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(y / Float64(-(-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 99.9%

   \[\frac{x + y}{10} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. frac-2neg N/A

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

   2. +-commutative N/A

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

   3. distribute-neg-in N/A

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

   4. unsub-neg N/A

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

   5. div-sub N/A

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

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

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

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

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

   8. neg-lowering-neg.f64 N/A

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

   9. metadata-eval N/A

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

   10. /-lowering-/.f64 N/A

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

   11. metadata-eval 100.0

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \frac{y}{--10} - \frac{x}{-10} \]
6. Add Preprocessing

Alternative 2: 50.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -1 \cdot 10^{-259}:\\ \;\;\;\;x \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (+ y x) -1e-259) (* x 0.1) (* y 0.1)))

C

double code(double x, double y) {
	double tmp;
	if ((y + x) <= -1e-259) {
		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 ((y + x) <= (-1d-259)) 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 ((y + x) <= -1e-259) {
		tmp = x * 0.1;
	} else {
		tmp = y * 0.1;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y + x) <= -1e-259:
		tmp = x * 0.1
	else:
		tmp = y * 0.1
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y + x) <= -1e-259)
		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 ((y + x) <= -1e-259)
		tmp = x * 0.1;
	else
		tmp = y * 0.1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y + x), $MachinePrecision], -1e-259], N[(x * 0.1), $MachinePrecision], N[(y * 0.1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -1.0000000000000001e-259

   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. *-lowering-*.f64 50.2

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

   5. Simplified 50.2%

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

   if -1.0000000000000001e-259 < (+.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. *-lowering-*.f64 48.8

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

   5. Simplified 48.8%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -1 \cdot 10^{-259}:\\ \;\;\;\;x \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 99.9%

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

3. Final simplification 99.9%

   \[\leadsto \frac{y + x}{10} \]
4. 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 99.9%

   \[\frac{x + y}{10} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. clear-num N/A

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

   2. associate-/r/ N/A

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

   3. distribute-rgt-in N/A

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

   4. accelerator-lowering-fma.f64 N/A

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

   5. metadata-eval N/A

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

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

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

   7. metadata-eval 99.4

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

4. Applied egg-rr 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

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

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 99.9%

   \[\frac{x + y}{10} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. div-inv N/A

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

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

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

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

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

   4. metadata-eval 99.3

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

4. Applied egg-rr 99.3%

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

5. Final simplification 99.3%

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

Alternative 6: 49.4% 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 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. *-lowering-*.f64 50.6

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

5. Simplified 50.6%

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

6. Final simplification 50.6%

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

Reproduce

herbie shell --seed 2024204 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10.0))