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

Percentage Accurate: 100.0% → 99.1%

Time: 4.2s

Alternatives: 4

Speedup: 1.0×

• 20.3% 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: 99.1% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. *-commutative 100.0%

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

   2. distribute-lft-in 98.4%

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

   3. fma-define 99.2%

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

4. Applied egg-rr 99.2%

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

5. Final simplification 99.2%

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

Alternative 2: 81.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.62 \cdot 10^{-161} \lor \neg \left(y \leq 3.6 \cdot 10^{-70}\right) \land y \leq 2.16 \cdot 10^{-10}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (or (<= y 1.62e-161) (and (not (<= y 3.6e-70)) (<= y 2.16e-10)))
   (* z x)
   (* z y)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if ((y <= 1.62e-161) || (!(y <= 3.6e-70) && (y <= 2.16e-10))) {
		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 ((y <= 1.62d-161) .or. (.not. (y <= 3.6d-70)) .and. (y <= 2.16d-10)) 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 ((y <= 1.62e-161) || (!(y <= 3.6e-70) && (y <= 2.16e-10))) {
		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 (y <= 1.62e-161) or (not (y <= 3.6e-70) and (y <= 2.16e-10)):
		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 ((y <= 1.62e-161) || (!(y <= 3.6e-70) && (y <= 2.16e-10)))
		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 ((y <= 1.62e-161) || (~((y <= 3.6e-70)) && (y <= 2.16e-10)))
		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[Or[LessEqual[y, 1.62e-161], And[N[Not[LessEqual[y, 3.6e-70]], $MachinePrecision], LessEqual[y, 2.16e-10]]], N[(z * x), $MachinePrecision], N[(z * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.62e-161 or 3.6000000000000002e-70 < y < 2.16000000000000004e-10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 70.0%

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

      1. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   if 1.62e-161 < y < 3.6000000000000002e-70 or 2.16000000000000004e-10 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 71.4%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.62 \cdot 10^{-161} \lor \neg \left(y \leq 3.6 \cdot 10^{-70}\right) \land y \leq 2.16 \cdot 10^{-10}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 4: 54.1% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

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 * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 48.7%

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

4. Final simplification 48.7%

   \[\leadsto z \cdot y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))