Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23

Percentage Accurate: 99.9% → 99.9%

Time: 1.0s

Alternatives: 6

Speedup: 1.0×

• 29.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

\[\mathsf{TRUE}\left(\right)\]

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 78.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+42}:\\ \;\;\;\;x \cdot y + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)))
   (if (<= t_1 -5e-127) t_1 (if (<= t_1 2e+42) (+ (* x y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double tmp;
	if (t_1 <= -5e-127) {
		tmp = t_1;
	} else if (t_1 <= 2e+42) {
		tmp = (x * y) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) + z) * y
    if (t_1 <= (-5d-127)) then
        tmp = t_1
    else if (t_1 <= 2d+42) then
        tmp = (x * y) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double tmp;
	if (t_1 <= -5e-127) {
		tmp = t_1;
	} else if (t_1 <= 2e+42) {
		tmp = (x * y) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x * y) + z) * y
	tmp = 0
	if t_1 <= -5e-127:
		tmp = t_1
	elif t_1 <= 2e+42:
		tmp = (x * y) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	tmp = 0.0
	if (t_1 <= -5e-127)
		tmp = t_1;
	elseif (t_1 <= 2e+42)
		tmp = Float64(Float64(x * y) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x * y) + z) * y;
	tmp = 0.0;
	if (t_1 <= -5e-127)
		tmp = t_1;
	elseif (t_1 <= 2e+42)
		tmp = (x * y) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(x * y), $MachinePrecision] + z), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-127], t$95$1, If[LessEqual[t$95$1, 2e+42], N[(N[(x * y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -4.9999999999999997e-127 or 2.00000000000000009e42 < (*.f64 (+.f64 (*.f64 x y) z) y)

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t + \left(x \cdot {y}^{2} + y \cdot z\right)} \]

   5. Applied rewrites 86.9%

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

   if -4.9999999999999997e-127 < (*.f64 (+.f64 (*.f64 x y) z) y) < 2.00000000000000009e42

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(x \cdot {y}^{2} + y \cdot z\right)} + t \]

   5. Applied rewrites 73.6%

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

Alternative 3: 62.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y\right) \cdot y\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{-43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2:\\ \;\;\;\;x \cdot y + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* x y) y)))
   (if (<= y -3.9e-43) t_1 (if (<= y 1.2) (+ (* x y) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x * y) * y;
	double tmp;
	if (y <= -3.9e-43) {
		tmp = t_1;
	} else if (y <= 1.2) {
		tmp = (x * y) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x * y) * y
    if (y <= (-3.9d-43)) then
        tmp = t_1
    else if (y <= 1.2d0) then
        tmp = (x * y) + t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x * y) * y;
	double tmp;
	if (y <= -3.9e-43) {
		tmp = t_1;
	} else if (y <= 1.2) {
		tmp = (x * y) + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x * y) * y
	tmp = 0
	if y <= -3.9e-43:
		tmp = t_1
	elif y <= 1.2:
		tmp = (x * y) + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x * y) * y)
	tmp = 0.0
	if (y <= -3.9e-43)
		tmp = t_1;
	elseif (y <= 1.2)
		tmp = Float64(Float64(x * y) + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x * y) * y;
	tmp = 0.0;
	if (y <= -3.9e-43)
		tmp = t_1;
	elseif (y <= 1.2)
		tmp = (x * y) + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[y, -3.9e-43], t$95$1, If[LessEqual[y, 1.2], N[(N[(x * y), $MachinePrecision] + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9e-43 or 1.19999999999999996 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{t + \left(x \cdot {y}^{2} + y \cdot z\right)} \]

   5. Applied rewrites 92.4%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 74.3%

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

   if -3.9e-43 < y < 1.19999999999999996

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\left(x \cdot {y}^{2} + y \cdot z\right)} + t \]

   5. Applied rewrites 58.6%

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

Alternative 4: 41.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ x \cdot y + t \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\left(x \cdot {y}^{2} + y \cdot z\right)} + t \]

5. Applied rewrites 40.4%

   \[\leadsto \color{blue}{x \cdot y} + t \]
6. Add Preprocessing

Alternative 5: 9.4% accurate, 1.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{t + \left(x \cdot {y}^{2} + y \cdot z\right)} \]

5. Applied rewrites 65.7%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 10.8%

   \[\leadsto x \cdot y + \color{blue}{z} \]
9. Add Preprocessing

Alternative 6: 9.1% accurate, 2.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{t + \left(x \cdot {y}^{2} + y \cdot z\right)} \]

5. Applied rewrites 65.7%

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

6. Taylor expanded in x around 0

   \[\leadsto x \cdot {y}^{2} + \color{blue}{y \cdot z} \]

8. Applied rewrites 10.6%

   \[\leadsto x \cdot \color{blue}{y} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024321 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  :pre (TRUE)
  (+ (* (+ (* x y) z) y) t))