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

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

Alternatives: 3

Speedup: 1.0×

• 21.4% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 53.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) \cdot z \leq -5 \cdot 10^{-280}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* (+ x y) z) -5e-280) (* z x) (* z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x + y) * z) <= -5e-280) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	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 (((x + y) * z) <= (-5d-280)) then
        tmp = z * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x + y) * z) <= -5e-280) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x + y) * z) <= -5e-280:
		tmp = z * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x + y) * z) <= -5e-280)
		tmp = Float64(z * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x + y) * z) <= -5e-280)
		tmp = z * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision], -5e-280], N[(z * x), $MachinePrecision], N[(z * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 x y) z) < -5.00000000000000028e-280

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot z} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 55.2

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

   5. Applied rewrites 55.2%

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

   if -5.00000000000000028e-280 < (*.f64 (+.f64 x y) z)

   1. Initial program 100.0%

      \[\left(x + y\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 49.8

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

   5. Applied rewrites 49.8%

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

Alternative 3: 54.6% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x \cdot z} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. lower-*.f64 58.6

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

5. Applied rewrites 58.6%

   \[\leadsto \color{blue}{z \cdot x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024338 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))