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

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Alternatives: 3

Speedup: 1.0×

• 21.6% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 53.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -2 \cdot 10^{-202}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= (+ y x) -2e-202) (* z x) (* z y)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y + x) <= -2e-202) {
		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 ((y + x) <= (-2d-202)) 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 ((y + x) <= -2e-202) {
		tmp = z * x;
	} else {
		tmp = z * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y + x) <= -2e-202:
		tmp = z * x
	else:
		tmp = z * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(y + x) <= -2e-202)
		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 ((y + x) <= -2e-202)
		tmp = z * x;
	else
		tmp = z * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(y + x), $MachinePrecision], -2e-202], N[(z * x), $MachinePrecision], N[(z * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -2.0000000000000001e-202

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower-*.f64 59.8

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

   5. Applied rewrites 59.8%

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

   if -2.0000000000000001e-202 < (+.f64 x y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. lower-*.f64 52.9

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

   5. Applied rewrites 52.9%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -2 \cdot 10^{-202}:\\ \;\;\;\;z \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 55.2% 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 y around 0

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

   1. lower-*.f64 59.3

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

5. Applied rewrites 59.3%

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

6. Final simplification 59.3%

   \[\leadsto z \cdot x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024240 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))