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

Percentage Accurate: 99.9% → 99.9%

Time: 8.7s

Alternatives: 8

Speedup: 1.0×

• 29.1% 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 99.9%

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

   1. fma-define 99.9%

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

   2. fma-define 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 65.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -6300000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 12500:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -6300000000.0)
     t_1
     (if (<= y 12500.0) t (if (<= y 7.2e+105) (* y z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -6300000000.0) {
		tmp = t_1;
	} else if (y <= 12500.0) {
		tmp = t;
	} else if (y <= 7.2e+105) {
		tmp = y * z;
	} 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 = y * (x * y)
    if (y <= (-6300000000.0d0)) then
        tmp = t_1
    else if (y <= 12500.0d0) then
        tmp = t
    else if (y <= 7.2d+105) then
        tmp = y * z
    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 = y * (x * y);
	double tmp;
	if (y <= -6300000000.0) {
		tmp = t_1;
	} else if (y <= 12500.0) {
		tmp = t;
	} else if (y <= 7.2e+105) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -6300000000.0:
		tmp = t_1
	elif y <= 12500.0:
		tmp = t
	elif y <= 7.2e+105:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(x * y))
	tmp = 0.0
	if (y <= -6300000000.0)
		tmp = t_1;
	elseif (y <= 12500.0)
		tmp = t;
	elseif (y <= 7.2e+105)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	tmp = 0.0;
	if (y <= -6300000000.0)
		tmp = t_1;
	elseif (y <= 12500.0)
		tmp = t;
	elseif (y <= 7.2e+105)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6300000000.0], t$95$1, If[LessEqual[y, 12500.0], t, If[LessEqual[y, 7.2e+105], N[(y * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.3e9 or 7.1999999999999998e105 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 98.2%

      \[\leadsto \color{blue}{\left(z \cdot \left(1 + \frac{x \cdot y}{z}\right)\right)} \cdot y + t \]
   4. Step-by-step derivation

      1. *-commutative 98.2%

         \[\leadsto \left(z \cdot \left(1 + \frac{\color{blue}{y \cdot x}}{z}\right)\right) \cdot y + t \]

   5. Simplified 98.2%

      \[\leadsto \color{blue}{\left(z \cdot \left(1 + \frac{y \cdot x}{z}\right)\right)} \cdot y + t \]

   6. Taylor expanded in t around 0 93.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(1 + \frac{x \cdot y}{z}\right)\right)} \]

   7. Taylor expanded in z around 0 76.6%

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

   if -6.3e9 < y < 12500

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 67.8%

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

   if 12500 < y < 7.1999999999999998e105

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.6%

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

   4. Taylor expanded in z around inf 73.1%

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

   5. Taylor expanded in y around inf 66.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6300000000:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 12500:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -8200000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 27000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+101}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -8200000000.0)
     t_1
     (if (<= y 27000.0) t (if (<= y 2.1e+101) (* y z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -8200000000.0) {
		tmp = t_1;
	} else if (y <= 27000.0) {
		tmp = t;
	} else if (y <= 2.1e+101) {
		tmp = y * z;
	} 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 <= (-8200000000.0d0)) then
        tmp = t_1
    else if (y <= 27000.0d0) then
        tmp = t
    else if (y <= 2.1d+101) then
        tmp = y * z
    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 <= -8200000000.0) {
		tmp = t_1;
	} else if (y <= 27000.0) {
		tmp = t;
	} else if (y <= 2.1e+101) {
		tmp = y * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * y)
	tmp = 0
	if y <= -8200000000.0:
		tmp = t_1
	elif y <= 27000.0:
		tmp = t
	elif y <= 2.1e+101:
		tmp = y * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x * Float64(y * y))
	tmp = 0.0
	if (y <= -8200000000.0)
		tmp = t_1;
	elseif (y <= 27000.0)
		tmp = t;
	elseif (y <= 2.1e+101)
		tmp = Float64(y * z);
	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 <= -8200000000.0)
		tmp = t_1;
	elseif (y <= 27000.0)
		tmp = t;
	elseif (y <= 2.1e+101)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8200000000.0], t$95$1, If[LessEqual[y, 27000.0], t, If[LessEqual[y, 2.1e+101], N[(y * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.2e9 or 2.1e101 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. +-commutative 75.9%

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

      2. distribute-lft-in 75.0%

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

      3. unpow2 75.0%

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

      4. associate-*l* 79.5%

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

      5. associate-/l* 79.5%

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

      6. associate-*r* 71.8%

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

      7. distribute-lft-out 96.6%

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

      8. *-commutative 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in t around 0 84.5%

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

   7. Taylor expanded in y around inf 71.5%

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

   if -8.2e9 < y < 27000

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 67.8%

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

   if 27000 < y < 2.1e101

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 79.6%

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

   4. Taylor expanded in z around inf 73.1%

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

   5. Taylor expanded in y around inf 66.4%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8200000000:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 27000:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+101}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -92000000000 \lor \neg \left(y \leq 1900\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -92000000000.0) (not (<= y 1900.0)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -92000000000.0) || !(y <= 1900.0)) {
		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 <= (-92000000000.0d0)) .or. (.not. (y <= 1900.0d0))) 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 <= -92000000000.0) || !(y <= 1900.0)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -92000000000.0) or not (y <= 1900.0):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -92000000000.0) || !(y <= 1900.0))
		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 <= -92000000000.0) || ~((y <= 1900.0)))
		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, -92000000000.0], N[Not[LessEqual[y, 1900.0]], $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 < -9.2e10 or 1900 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 74.3%

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

      1. +-commutative 74.3%

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

      2. distribute-lft-in 72.7%

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

      3. unpow2 72.7%

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

      4. associate-*l* 76.7%

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

      5. associate-/l* 76.7%

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

      6. associate-*r* 71.4%

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

      7. distribute-lft-out 94.0%

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

      8. *-commutative 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in t around 0 81.1%

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

   7. Taylor expanded in x around 0 77.1%

      \[\leadsto \color{blue}{x \cdot {y}^{2} + y \cdot z} \]
   8. Step-by-step derivation

      1. *-commutative 77.1%

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

      2. unpow2 77.1%

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

      3. associate-*r* 84.7%

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

      4. distribute-lft-in 94.4%

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

      5. *-commutative 94.4%

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

      6. +-commutative 94.4%

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

   9. Simplified 94.4%

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

   if -9.2e10 < y < 1900

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 90.8%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -92000000000 \lor \neg \left(y \leq 1900\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+83} \lor \neg \left(y \leq 9 \cdot 10^{+101}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e+83) (not (<= y 9e+101))) (* y (* x y)) (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e+83) || !(y <= 9e+101)) {
		tmp = y * (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 <= (-1.4d+83)) .or. (.not. (y <= 9d+101))) then
        tmp = y * (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 <= -1.4e+83) || !(y <= 9e+101)) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e+83) or not (y <= 9e+101):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e+83) || !(y <= 9e+101))
		tmp = Float64(y * 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 <= -1.4e+83) || ~((y <= 9e+101)))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.4e+83], N[Not[LessEqual[y, 9e+101]], $MachinePrecision]], N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e83 or 9.0000000000000004e101 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{\left(z \cdot \left(1 + \frac{x \cdot y}{z}\right)\right)} \cdot y + t \]
   4. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \left(z \cdot \left(1 + \frac{\color{blue}{y \cdot x}}{z}\right)\right) \cdot y + t \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{\left(z \cdot \left(1 + \frac{y \cdot x}{z}\right)\right)} \cdot y + t \]

   6. Taylor expanded in t around 0 98.9%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot \left(1 + \frac{x \cdot y}{z}\right)\right)} \]

   7. Taylor expanded in z around 0 83.1%

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

   if -1.4e83 < y < 9.0000000000000004e101

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 87.0%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+83} \lor \neg \left(y \leq 9 \cdot 10^{+101}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 52.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+89} \lor \neg \left(z \leq 2.6 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -9.6e+89) (not (<= z 2.6e+71))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -9.6e+89) || !(z <= 2.6e+71)) {
		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 <= (-9.6d+89)) .or. (.not. (z <= 2.6d+71))) 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 <= -9.6e+89) || !(z <= 2.6e+71)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -9.6e+89) or not (z <= 2.6e+71):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -9.6e+89) || !(z <= 2.6e+71))
		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 <= -9.6e+89) || ~((z <= 2.6e+71)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -9.6e+89], N[Not[LessEqual[z, 2.6e+71]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -9.60000000000000018e89 or 2.59999999999999991e71 < 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%

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

   4. Taylor expanded in z around inf 88.3%

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

   5. Taylor expanded in y around inf 67.5%

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

   if -9.60000000000000018e89 < z < 2.59999999999999991e71

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 47.3%

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

4. Final simplification 54.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+89} \lor \neg \left(z \leq 2.6 \cdot 10^{+71}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 99.9%

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

3. Final simplification 99.9%

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

Alternative 8: 39.1% 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 38.5%

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

Reproduce

herbie shell --seed 2024132 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))