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

Percentage Accurate: 100.0% → 99.0%

Time: 2.6s

Alternatives: 4

Speedup: 1.0×

• 20.7% 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: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \mathsf{fma}\left(z, y, z \cdot x\right) \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (fma z y (* z x)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return fma(z, y, (z * x));
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return fma(z, y, Float64(z * x))
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(z * y + N[(z * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) \cdot z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-+.f64 N/A

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

   4. +-commutative N/A

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

   5. distribute-lft-in N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. *-commutative N/A

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

   9. lower-*.f64 99.2

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

4. Applied rewrites 99.2%

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

Alternative 2: 53.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;\left(x + y\right) \cdot z \leq -4 \cdot 10^{-309}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= (* (+ x y) z) -4e-309) (* z x) (* z y)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (((x + y) * z) <= -4e-309) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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) <= (-4d-309)) then
        tmp = z * x
    else
        tmp = z * y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (((x + y) * z) <= -4e-309) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if ((x + y) * z) <= -4e-309:
		tmp = z * x
	else:
		tmp = z * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (Float64(Float64(x + y) * z) <= -4e-309)
		tmp = Float64(z * x);
	else
		tmp = Float64(z * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x + y) * z) <= -4e-309)
		tmp = z * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision], -4e-309], N[(z * x), $MachinePrecision], N[(z * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 x y) z) < -3.9999999999999977e-309

   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 49.4

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

   5. Applied rewrites 49.4%

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

   if -3.9999999999999977e-309 < (*.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 48.6

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

   5. Applied rewrites 48.6%

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

Alternative 3: 100.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* (+ x y) z))

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return (x + y) * z

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(Float64(x + y) * z)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = (x + y) * z;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 4: 54.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ z \cdot x \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* z x))

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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

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

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return z * x

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(z * x)
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = z * x;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 54.9

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

5. Applied rewrites 54.9%

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

Reproduce

herbie shell --seed 2024337 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))