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

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

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: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-300}:\\ \;\;\;\;x \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (+ x y) -2e-300) (* x 0.1) (* y 0.1)))

C

double code(double x, double y) {
	double tmp;
	if ((x + y) <= -2e-300) {
		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) <= (-2d-300)) 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) <= -2e-300) {
		tmp = x * 0.1;
	} else {
		tmp = y * 0.1;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x + y) <= -2e-300:
		tmp = x * 0.1
	else:
		tmp = y * 0.1
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x + y) <= -2e-300)
		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) <= -2e-300)
		tmp = x * 0.1;
	else
		tmp = y * 0.1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x + y), $MachinePrecision], -2e-300], N[(x * 0.1), $MachinePrecision], N[(y * 0.1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -2.00000000000000005e-300

   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 51.3

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

   5. Simplified 51.3%

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

   if -2.00000000000000005e-300 < (+.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 52.2

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

   5. Simplified 52.2%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + y \leq -2 \cdot 10^{-300}:\\ \;\;\;\;x \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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

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

   2. div-inv N/A

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

   3. *-commutative 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 egg-rr 99.5%

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

Alternative 4: 99.4% 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

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

   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 99.5

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

4. Applied egg-rr 99.5%

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

Alternative 5: 51.0% 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 50.4

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

5. Simplified 50.4%

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

6. Final simplification 50.4%

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

Reproduce

herbie shell --seed 2024207 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10.0))