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

Percentage Accurate: 100.0% → 100.0%

Time: 1.7s

Alternatives: 3

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot z \]

2. Final simplification 100.0%

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

Alternative 2: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 5.7 \cdot 10^{-70}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= y 5.7e-70) (* x z) (* y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.7e-70) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 5.7d-70) then
        tmp = x * z
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 5.7e-70) {
		tmp = x * z;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 5.7e-70:
		tmp = x * z
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 5.7e-70)
		tmp = Float64(x * z);
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 5.7e-70)
		tmp = x * z;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 5.7e-70], N[(x * z), $MachinePrecision], N[(y * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.70000000000000028e-70

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot z \]

   2. Taylor expanded in x around inf 60.1%

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

   if 5.70000000000000028e-70 < y

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot z \]

   2. Taylor expanded in x around 0 77.5%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.7 \cdot 10^{-70}:\\ \;\;\;\;x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

Alternative 3: 53.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ y \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y z))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y * z
end function

Java

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

Python

def code(x, y, z):
	return y * z

Julia

function code(x, y, z)
	return Float64(y * z)
end

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y * z), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot z \]

2. Taylor expanded in x around 0 58.1%

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

3. Final simplification 58.1%

   \[\leadsto y \cdot z \]

Reproduce

herbie shell --seed 2023196 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))