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

Percentage Accurate: 99.9% → 99.9%

Time: 5.2s

Alternatives: 5

Speedup: 1.0×

• 29.4% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+214} \lor \neg \left(z \leq 2.25 \cdot 10^{+56}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1e+214) (not (<= z 2.25e+56)))
   (+ t (* y z))
   (+ t (* y (* x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+214) || !(z <= 2.25e+56)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	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) :: tmp
    if ((z <= (-1d+214)) .or. (.not. (z <= 2.25d+56))) then
        tmp = t + (y * z)
    else
        tmp = t + (y * (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1e+214) || !(z <= 2.25e+56)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (y * (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1e+214) or not (z <= 2.25e+56):
		tmp = t + (y * z)
	else:
		tmp = t + (y * (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1e+214) || !(z <= 2.25e+56))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(y * Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1e+214) || ~((z <= 2.25e+56)))
		tmp = t + (y * z);
	else
		tmp = t + (y * (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1e+214], N[Not[LessEqual[z, 2.25e+56]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999995e213 or 2.2500000000000002e56 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.4%

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

   if -9.9999999999999995e213 < z < 2.2500000000000002e56

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 91.4%

      \[\leadsto \color{blue}{\left(x \cdot y\right)} \cdot y + t \]
   4. Step-by-step derivation

      1. *-commutative 91.4%

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

   5. Simplified 91.4%

      \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot y + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+214} \lor \neg \left(z \leq 2.25 \cdot 10^{+56}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{+227} \lor \neg \left(z \leq 1.18 \cdot 10^{+55}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.3e+227) (not (<= z 1.18e+55)))
   (+ t (* y z))
   (+ t (* x (* y y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.3e+227) || !(z <= 1.18e+55)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (x * (y * y));
	}
	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) :: tmp
    if ((z <= (-7.3d+227)) .or. (.not. (z <= 1.18d+55))) then
        tmp = t + (y * z)
    else
        tmp = t + (x * (y * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.3e+227) || !(z <= 1.18e+55)) {
		tmp = t + (y * z);
	} else {
		tmp = t + (x * (y * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.3e+227) or not (z <= 1.18e+55):
		tmp = t + (y * z)
	else:
		tmp = t + (x * (y * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.3e+227) || !(z <= 1.18e+55))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(t + Float64(x * Float64(y * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.3e+227) || ~((z <= 1.18e+55)))
		tmp = t + (y * z);
	else
		tmp = t + (x * (y * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.3e+227], N[Not[LessEqual[z, 1.18e+55]], $MachinePrecision]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t + N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.30000000000000026e227 or 1.1799999999999999e55 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.3%

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

   if -7.30000000000000026e227 < z < 1.1799999999999999e55

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 93.2%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y \cdot z}{x} + {y}^{2}\right)} + t \]
   4. Step-by-step derivation

      1. +-commutative 93.2%

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

      2. unpow2 93.2%

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

      3. associate-/l* 93.7%

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

      4. distribute-lft-out 95.5%

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

   5. Simplified 95.5%

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

   6. Taylor expanded in y around inf 89.9%

      \[\leadsto x \cdot \left(y \cdot \color{blue}{y}\right) + t \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.3 \cdot 10^{+227} \lor \neg \left(z \leq 1.18 \cdot 10^{+55}\right):\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t + x \cdot \left(y \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 66.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(t + N[(y * z), $MachinePrecision]), $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 67.4%

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

4. Final simplification 67.4%

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

Alternative 5: 38.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ t \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := t

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around 0 37.1%

   \[\leadsto \color{blue}{t} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024144 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))