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

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 4

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. Final simplification 100.0%

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

Alternative 2: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.25 \cdot 10^{-120}:\\ \;\;\;\;x \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 2.25e-120) (* x 0.1) (* y 0.1)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.25e-120) {
		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 <= 2.25d-120) 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 <= 2.25e-120) {
		tmp = x * 0.1;
	} else {
		tmp = y * 0.1;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.25e-120:
		tmp = x * 0.1
	else:
		tmp = y * 0.1
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.25e-120)
		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 <= 2.25e-120)
		tmp = x * 0.1;
	else
		tmp = y * 0.1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.25e-120], N[(x * 0.1), $MachinePrecision], N[(y * 0.1), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.25e-120

   1. Initial program 100.0%

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

      1. *-lft-identity 100.0%

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

      2. metadata-eval 100.0%

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

      3. associate-*r/ 100.0%

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

      4. associate-/l* 99.6%

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

      5. associate-/r/ 99.5%

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

      6. metadata-eval 99.5%

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

      7. metadata-eval 99.5%

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

      8. metadata-eval 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 57.9%

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

   if 2.25e-120 < y

   1. Initial program 99.9%

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

      1. *-lft-identity 99.9%

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

      2. metadata-eval 99.9%

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

      3. associate-*r/ 99.9%

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

      4. associate-/l* 99.6%

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

      5. associate-/r/ 99.3%

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

      6. metadata-eval 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

      9. metadata-eval 99.3%

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

      10. *-commutative 99.3%

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

      11. metadata-eval 99.3%

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

      12. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 62.5%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.25 \cdot 10^{-120}:\\ \;\;\;\;x \cdot 0.1\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.1\\ \end{array} \]

Alternative 3: 99.4% accurate, 1.0× 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. Step-by-step derivation

   1. *-lft-identity 100.0%

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

   2. metadata-eval 100.0%

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

   3. associate-*r/ 100.0%

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

   4. associate-/l* 99.6%

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

   5. associate-/r/ 99.4%

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

   6. metadata-eval 99.4%

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

   7. metadata-eval 99.4%

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

   8. metadata-eval 99.4%

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

   9. metadata-eval 99.4%

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

   10. *-commutative 99.4%

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

   11. metadata-eval 99.4%

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

   12. metadata-eval 99.4%

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

3. Simplified 99.4%

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

4. Final simplification 99.4%

   \[\leadsto \left(x + y\right) \cdot 0.1 \]

Alternative 4: 50.1% 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. Step-by-step derivation

   1. *-lft-identity 100.0%

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

   2. metadata-eval 100.0%

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

   3. associate-*r/ 100.0%

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

   4. associate-/l* 99.6%

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

   5. associate-/r/ 99.4%

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

   6. metadata-eval 99.4%

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

   7. metadata-eval 99.4%

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

   8. metadata-eval 99.4%

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

   9. metadata-eval 99.4%

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

   10. *-commutative 99.4%

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

   11. metadata-eval 99.4%

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

   12. metadata-eval 99.4%

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

3. Simplified 99.4%

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

4. Taylor expanded in x around inf 50.7%

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

5. Final simplification 50.7%

   \[\leadsto x \cdot 0.1 \]

Reproduce

herbie shell --seed 2023320 
(FPCore (x y)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, A"
  :precision binary64
  (/ (+ x y) 10.0))