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

Percentage Accurate: 99.9% → 99.9%

Time: 11.0s

Alternatives: 8

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, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. *-commutative 99.9%

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

   2. fma-define 99.9%

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

   3. fma-define 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 78.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq -0.0011 \lor \neg \left(y \leq -4 \cdot 10^{-25}\right) \land y \leq 1.52 \cdot 10^{+85}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.2e+105)
   (* y (* y x))
   (if (or (<= y -0.0011) (and (not (<= y -4e-25)) (<= y 1.52e+85)))
     (+ t (* y z))
     (* x (* y y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.2e+105) {
		tmp = y * (y * x);
	} else if ((y <= -0.0011) || (!(y <= -4e-25) && (y <= 1.52e+85))) {
		tmp = t + (y * z);
	} else {
		tmp = 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 (y <= (-9.2d+105)) then
        tmp = y * (y * x)
    else if ((y <= (-0.0011d0)) .or. (.not. (y <= (-4d-25))) .and. (y <= 1.52d+85)) then
        tmp = t + (y * z)
    else
        tmp = 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 (y <= -9.2e+105) {
		tmp = y * (y * x);
	} else if ((y <= -0.0011) || (!(y <= -4e-25) && (y <= 1.52e+85))) {
		tmp = t + (y * z);
	} else {
		tmp = x * (y * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.2e+105:
		tmp = y * (y * x)
	elif (y <= -0.0011) or (not (y <= -4e-25) and (y <= 1.52e+85)):
		tmp = t + (y * z)
	else:
		tmp = x * (y * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.2e+105)
		tmp = Float64(y * Float64(y * x));
	elseif ((y <= -0.0011) || (!(y <= -4e-25) && (y <= 1.52e+85)))
		tmp = Float64(t + Float64(y * z));
	else
		tmp = Float64(x * Float64(y * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.2e+105)
		tmp = y * (y * x);
	elseif ((y <= -0.0011) || (~((y <= -4e-25)) && (y <= 1.52e+85)))
		tmp = t + (y * z);
	else
		tmp = x * (y * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.2e+105], N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -0.0011], And[N[Not[LessEqual[y, -4e-25]], $MachinePrecision], LessEqual[y, 1.52e+85]]], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.1999999999999991e105

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 89.3%

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

   4. Taylor expanded in y around inf 70.7%

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

      1. unpow2 70.7%

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

      2. *-commutative 70.7%

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

      3. associate-*r* 86.0%

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

   6. Simplified 86.0%

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

   if -9.1999999999999991e105 < y < -0.00110000000000000007 or -4.00000000000000015e-25 < y < 1.52e85

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.2%

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

   if -0.00110000000000000007 < y < -4.00000000000000015e-25 or 1.52e85 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in t around inf 89.9%

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

   4. Taylor expanded in y around inf 77.3%

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

      1. unpow2 77.3%

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

      2. *-commutative 77.3%

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

      3. associate-*r* 76.9%

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

   6. Simplified 76.9%

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

      1. associate-*r* 77.3%

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

   8. Applied egg-rr 77.3%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+105}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq -0.0011 \lor \neg \left(y \leq -4 \cdot 10^{-25}\right) \land y \leq 1.52 \cdot 10^{+85}:\\ \;\;\;\;t + y \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq -60:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-26} \lor \neg \left(y \leq 1.05 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.3e+56)
   (* y (* y x))
   (if (<= y -60.0)
     (* y z)
     (if (or (<= y -9.5e-26) (not (<= y 1.05e+20))) (* x (* y y)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.3e+56) {
		tmp = y * (y * x);
	} else if (y <= -60.0) {
		tmp = y * z;
	} else if ((y <= -9.5e-26) || !(y <= 1.05e+20)) {
		tmp = x * (y * y);
	} 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 (y <= (-3.3d+56)) then
        tmp = y * (y * x)
    else if (y <= (-60.0d0)) then
        tmp = y * z
    else if ((y <= (-9.5d-26)) .or. (.not. (y <= 1.05d+20))) then
        tmp = x * (y * y)
    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 (y <= -3.3e+56) {
		tmp = y * (y * x);
	} else if (y <= -60.0) {
		tmp = y * z;
	} else if ((y <= -9.5e-26) || !(y <= 1.05e+20)) {
		tmp = x * (y * y);
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.3e+56:
		tmp = y * (y * x)
	elif y <= -60.0:
		tmp = y * z
	elif (y <= -9.5e-26) or not (y <= 1.05e+20):
		tmp = x * (y * y)
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.3e+56)
		tmp = Float64(y * Float64(y * x));
	elseif (y <= -60.0)
		tmp = Float64(y * z);
	elseif ((y <= -9.5e-26) || !(y <= 1.05e+20))
		tmp = Float64(x * Float64(y * y));
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.3e+56)
		tmp = y * (y * x);
	elseif (y <= -60.0)
		tmp = y * z;
	elseif ((y <= -9.5e-26) || ~((y <= 1.05e+20)))
		tmp = x * (y * y);
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.3e+56], N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -60.0], N[(y * z), $MachinePrecision], If[Or[LessEqual[y, -9.5e-26], N[Not[LessEqual[y, 1.05e+20]], $MachinePrecision]], N[(x * N[(y * y), $MachinePrecision]), $MachinePrecision], t]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.30000000000000002e56

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 89.8%

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

   4. Taylor expanded in y around inf 62.7%

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

      1. unpow2 62.7%

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

      2. *-commutative 62.7%

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

      3. associate-*r* 74.4%

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

   6. Simplified 74.4%

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

   if -3.30000000000000002e56 < y < -60

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 53.8%

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

   if -60 < y < -9.4999999999999995e-26 or 1.05e20 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 88.9%

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

   4. Taylor expanded in y around inf 67.0%

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

      1. unpow2 67.0%

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

      2. *-commutative 67.0%

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

      3. associate-*r* 66.8%

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

   6. Simplified 66.8%

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

      1. associate-*r* 67.0%

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

   8. Applied egg-rr 67.0%

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

   if -9.4999999999999995e-26 < y < 1.05e20

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.0%

      \[\leadsto \color{blue}{t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq -60:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-26} \lor \neg \left(y \leq 1.05 \cdot 10^{+20}\right):\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(y \cdot x\right)\\ \mathbf{if}\;y \leq -2.75 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -38:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-26} \lor \neg \left(y \leq 4.3 \cdot 10^{+21}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* y x))))
   (if (<= y -2.75e+56)
     t_1
     (if (<= y -38.0)
       (* y z)
       (if (or (<= y -2e-26) (not (<= y 4.3e+21))) t_1 t)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (y * x);
	double tmp;
	if (y <= -2.75e+56) {
		tmp = t_1;
	} else if (y <= -38.0) {
		tmp = y * z;
	} else if ((y <= -2e-26) || !(y <= 4.3e+21)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (y * x)
    if (y <= (-2.75d+56)) then
        tmp = t_1
    else if (y <= (-38.0d0)) then
        tmp = y * z
    else if ((y <= (-2d-26)) .or. (.not. (y <= 4.3d+21))) then
        tmp = t_1
    else
        tmp = t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (y * x);
	double tmp;
	if (y <= -2.75e+56) {
		tmp = t_1;
	} else if (y <= -38.0) {
		tmp = y * z;
	} else if ((y <= -2e-26) || !(y <= 4.3e+21)) {
		tmp = t_1;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (y * x)
	tmp = 0
	if y <= -2.75e+56:
		tmp = t_1
	elif y <= -38.0:
		tmp = y * z
	elif (y <= -2e-26) or not (y <= 4.3e+21):
		tmp = t_1
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(y * x))
	tmp = 0.0
	if (y <= -2.75e+56)
		tmp = t_1;
	elseif (y <= -38.0)
		tmp = Float64(y * z);
	elseif ((y <= -2e-26) || !(y <= 4.3e+21))
		tmp = t_1;
	else
		tmp = t;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (y * x);
	tmp = 0.0;
	if (y <= -2.75e+56)
		tmp = t_1;
	elseif (y <= -38.0)
		tmp = y * z;
	elseif ((y <= -2e-26) || ~((y <= 4.3e+21)))
		tmp = t_1;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.75e+56], t$95$1, If[LessEqual[y, -38.0], N[(y * z), $MachinePrecision], If[Or[LessEqual[y, -2e-26], N[Not[LessEqual[y, 4.3e+21]], $MachinePrecision]], t$95$1, t]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7500000000000001e56 or -38 < y < -2.0000000000000001e-26 or 4.3e21 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in t around inf 89.3%

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

   4. Taylor expanded in y around inf 65.3%

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

      1. unpow2 65.3%

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

      2. *-commutative 65.3%

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

      3. associate-*r* 69.9%

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

   6. Simplified 69.9%

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

   if -2.7500000000000001e56 < y < -38

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 53.8%

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

   if -2.0000000000000001e-26 < y < 4.3e21

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 67.0%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{+56}:\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;y \leq -38:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-26} \lor \neg \left(y \leq 4.3 \cdot 10^{+21}\right):\\ \;\;\;\;y \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-25} \lor \neg \left(y \leq 5.5 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \left(z + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.8e-25) (not (<= y 5.5e+18)))
   (* y (+ z (* y x)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.8e-25) || !(y <= 5.5e+18)) {
		tmp = y * (z + (y * x));
	} 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 <= (-1.8d-25)) .or. (.not. (y <= 5.5d+18))) then
        tmp = y * (z + (y * x))
    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 <= -1.8e-25) || !(y <= 5.5e+18)) {
		tmp = y * (z + (y * x));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.8e-25) or not (y <= 5.5e+18):
		tmp = y * (z + (y * x))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.8e-25) || !(y <= 5.5e+18))
		tmp = Float64(y * Float64(z + Float64(y * x)));
	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 <= -1.8e-25) || ~((y <= 5.5e+18)))
		tmp = y * (z + (y * x));
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.8e-25], N[Not[LessEqual[y, 5.5e+18]], $MachinePrecision]], N[(y * N[(z + N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t + N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e-25 or 5.5e18 < 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 85.9%

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

   if -1.8e-25 < y < 5.5e18

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 92.3%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-25} \lor \neg \left(y \leq 5.5 \cdot 10^{+18}\right):\\ \;\;\;\;y \cdot \left(z + y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+137} \lor \neg \left(z \leq 6.6 \cdot 10^{+109}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.5e+137) (not (<= z 6.6e+109))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.5e+137) || !(z <= 6.6e+109)) {
		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 <= (-2.5d+137)) .or. (.not. (z <= 6.6d+109))) 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 <= -2.5e+137) || !(z <= 6.6e+109)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.5e+137) or not (z <= 6.6e+109):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.5e+137) || !(z <= 6.6e+109))
		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 <= -2.5e+137) || ~((z <= 6.6e+109)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.5e+137], N[Not[LessEqual[z, 6.6e+109]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -2.5000000000000001e137 or 6.5999999999999998e109 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 73.4%

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

   if -2.5000000000000001e137 < z < 6.5999999999999998e109

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 48.2%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+137} \lor \neg \left(z \leq 6.6 \cdot 10^{+109}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + (y * x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 8: 38.2% 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 40.8%

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

Reproduce

herbie shell --seed 2024097 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))