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

Percentage Accurate: 99.9% → 99.9%

Time: 8.3s

Alternatives: 7

Speedup: 1.0×

• 28.8% 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, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. fma-def 100.0%

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

   2. fma-def 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, t\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 2: 88.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+32} \lor \neg \left(y \leq 230000\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e+32) (not (<= y 230000.0)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e+32) || !(y <= 230000.0)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	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 ((y <= (-1.3d+32)) .or. (.not. (y <= 230000.0d0))) then
        tmp = y * (z + (x * y))
    else
        tmp = t + (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e+32) || !(y <= 230000.0)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.3e+32) or not (y <= 230000.0):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.3e+32) || !(y <= 230000.0))
		tmp = Float64(y * Float64(z + Float64(x * y)));
	else
		tmp = Float64(t + Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.3e+32) || ~((y <= 230000.0)))
		tmp = y * (z + (x * y));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.3e+32], N[Not[LessEqual[y, 230000.0]], $MachinePrecision]], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.3000000000000001e32 or 2.3e5 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around 0 89.6%

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

   if -1.3000000000000001e32 < y < 2.3e5

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.9%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+32} \lor \neg \left(y \leq 230000\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+98}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+34}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4e+98)
   (+ t (* y z))
   (if (<= z 6.2e+34) (+ t (* y (* x y))) (* y (+ z (* x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4e+98) {
		tmp = t + (y * z);
	} else if (z <= 6.2e+34) {
		tmp = t + (y * (x * y));
	} else {
		tmp = y * (z + (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 <= (-4d+98)) then
        tmp = t + (y * z)
    else if (z <= 6.2d+34) then
        tmp = t + (y * (x * y))
    else
        tmp = y * (z + (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 <= -4e+98) {
		tmp = t + (y * z);
	} else if (z <= 6.2e+34) {
		tmp = t + (y * (x * y));
	} else {
		tmp = y * (z + (x * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4e+98:
		tmp = t + (y * z)
	elif z <= 6.2e+34:
		tmp = t + (y * (x * y))
	else:
		tmp = y * (z + (x * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4e+98)
		tmp = Float64(t + Float64(y * z));
	elseif (z <= 6.2e+34)
		tmp = Float64(t + Float64(y * Float64(x * y)));
	else
		tmp = Float64(y * Float64(z + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4e+98)
		tmp = t + (y * z);
	elseif (z <= 6.2e+34)
		tmp = t + (y * (x * y));
	else
		tmp = y * (z + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4e+98], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+34], N[(t + N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.99999999999999999e98

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.0%

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

   if -3.99999999999999999e98 < z < 6.19999999999999955e34

   1. Initial program 99.9%

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

      1. add-sqr-sqrt 63.1%

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

      2. pow2 63.1%

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

      3. *-commutative 63.1%

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

      4. fma-def 63.1%

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

   4. Applied egg-rr 63.1%

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

   5. Taylor expanded in y around inf 49.1%

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

      1. unpow2 49.1%

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

      2. swap-sqr 45.5%

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

      3. add-sqr-sqrt 87.2%

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

      4. associate-*r* 92.5%

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

   7. Applied egg-rr 92.5%

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

   if 6.19999999999999955e34 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in t around 0 84.3%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+98}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+34}:\\ \;\;\;\;t + y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+179} \lor \neg \left(z \leq 1.95 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.2e+179) (not (<= z 1.95e+15))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+179) || !(z <= 1.95e+15)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	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 <= (-6.2d+179)) .or. (.not. (z <= 1.95d+15))) then
        tmp = y * z
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.2e+179) || !(z <= 1.95e+15)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.2e+179) or not (z <= 1.95e+15):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.2e+179) || !(z <= 1.95e+15))
		tmp = Float64(y * z);
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.2e+179) || ~((z <= 1.95e+15)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.2e+179], N[Not[LessEqual[z, 1.95e+15]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -6.2e179 or 1.95e15 < 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 79.7%

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

   4. Taylor expanded in y around inf 62.8%

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

   if -6.2e179 < z < 1.95e15

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 49.6%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+179} \lor \neg \left(z \leq 1.95 \cdot 10^{+15}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 6: 65.9% 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 100.0%

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

3. Taylor expanded in x around 0 67.0%

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

4. Final simplification 67.0%

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

Alternative 7: 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 100.0%

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

3. Taylor expanded in y around 0 38.5%

   \[\leadsto \color{blue}{t} \]

4. Final simplification 38.5%

   \[\leadsto t \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024031 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))