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

Percentage Accurate: 99.9% → 99.9%

Time: 1.1s

Alternatives: 6

Speedup: 1.0×

• 28.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

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 99.9%

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

Alternative 2: 80.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+43}:\\ \;\;\;\;x \cdot y + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)))
   (if (<= t_1 -1e+44) t_1 (if (<= t_1 2e+43) (+ (* 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 <= -1e+44) {
		tmp = t_1;
	} else if (t_1 <= 2e+43) {
		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 <= (-1d+44)) then
        tmp = t_1
    else if (t_1 <= 2d+43) 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 <= -1e+44) {
		tmp = t_1;
	} else if (t_1 <= 2e+43) {
		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 <= -1e+44:
		tmp = t_1
	elif t_1 <= 2e+43:
		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 <= -1e+44)
		tmp = t_1;
	elseif (t_1 <= 2e+43)
		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 <= -1e+44)
		tmp = t_1;
	elseif (t_1 <= 2e+43)
		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, -1e+44], t$95$1, If[LessEqual[t$95$1, 2e+43], 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) < -1.0000000000000001e44 or 2.00000000000000003e43 < (*.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 91.9%

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

   if -1.0000000000000001e44 < (*.f64 (+.f64 (*.f64 x y) z) y) < 2.00000000000000003e43

   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 77.0%

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

Alternative 3: 63.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot y + z\right) \cdot y\\ t_2 := \left(x \cdot y\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+85}:\\ \;\;\;\;x \cdot y + t\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (+ (* x y) z) y)) (t_2 (* (* x y) y)))
   (if (<= t_1 -1e+67) t_2 (if (<= t_1 5e+85) (+ (* x y) t) t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((x * y) + z) * y;
	double t_2 = (x * y) * y;
	double tmp;
	if (t_1 <= -1e+67) {
		tmp = t_2;
	} else if (t_1 <= 5e+85) {
		tmp = (x * y) + t;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = ((x * y) + z) * y
    t_2 = (x * y) * y
    if (t_1 <= (-1d+67)) then
        tmp = t_2
    else if (t_1 <= 5d+85) then
        tmp = (x * y) + t
    else
        tmp = t_2
    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 t_2 = (x * y) * y;
	double tmp;
	if (t_1 <= -1e+67) {
		tmp = t_2;
	} else if (t_1 <= 5e+85) {
		tmp = (x * y) + t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((x * y) + z) * y
	t_2 = (x * y) * y
	tmp = 0
	if t_1 <= -1e+67:
		tmp = t_2
	elif t_1 <= 5e+85:
		tmp = (x * y) + t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(x * y) + z) * y)
	t_2 = Float64(Float64(x * y) * y)
	tmp = 0.0
	if (t_1 <= -1e+67)
		tmp = t_2;
	elseif (t_1 <= 5e+85)
		tmp = Float64(Float64(x * y) + t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((x * y) + z) * y;
	t_2 = (x * y) * y;
	tmp = 0.0;
	if (t_1 <= -1e+67)
		tmp = t_2;
	elseif (t_1 <= 5e+85)
		tmp = (x * y) + t;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+67], t$95$2, If[LessEqual[t$95$1, 5e+85], N[(N[(x * y), $MachinePrecision] + t), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (+.f64 (*.f64 x y) z) y) < -9.99999999999999983e66 or 5.0000000000000001e85 < (*.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 92.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 64.3%

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

   if -9.99999999999999983e66 < (*.f64 (+.f64 (*.f64 x y) z) y) < 5.0000000000000001e85

   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 73.7%

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

Alternative 4: 41.1% 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 99.9%

   \[\left(x \cdot y + z\right) \cdot y + t \]
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 39.8%

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

Alternative 5: 9.3% 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 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 64.4%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 8.1%

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

Alternative 6: 9.0% 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 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 64.4%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 7.5%

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

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))