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

Percentage Accurate: 99.9% → 99.9%

Time: 7.9s

Alternatives: 7

Speedup: 1.0×

• 29.2% 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: 78.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+76} \lor \neg \left(y \leq -4.9 \cdot 10^{+32} \lor \neg \left(y \leq -3.2 \cdot 10^{-21}\right) \land y \leq 8.6 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5e+76)
         (not
          (or (<= y -4.9e+32) (and (not (<= y -3.2e-21)) (<= y 8.6e+102)))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e+76) || !((y <= -4.9e+32) || (!(y <= -3.2e-21) && (y <= 8.6e+102)))) {
		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 <= (-3.5d+76)) .or. (.not. (y <= (-4.9d+32)) .or. (.not. (y <= (-3.2d-21))) .and. (y <= 8.6d+102))) 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 <= -3.5e+76) || !((y <= -4.9e+32) || (!(y <= -3.2e-21) && (y <= 8.6e+102)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.5e+76) or not ((y <= -4.9e+32) or (not (y <= -3.2e-21) and (y <= 8.6e+102))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.5e+76) || !((y <= -4.9e+32) || (!(y <= -3.2e-21) && (y <= 8.6e+102))))
		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 <= -3.5e+76) || ~(((y <= -4.9e+32) || (~((y <= -3.2e-21)) && (y <= 8.6e+102)))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.5e+76], N[Not[Or[LessEqual[y, -4.9e+32], And[N[Not[LessEqual[y, -3.2e-21]], $MachinePrecision], LessEqual[y, 8.6e+102]]]], $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 < -3.5e76 or -4.9000000000000001e32 < y < -3.2000000000000002e-21 or 8.6000000000000002e102 < 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 94.4%

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

      1. associate-/l* 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in t around 0 92.6%

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

      1. associate-/l* 89.9%

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

   8. Applied egg-rr 89.9%

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

      1. associate-*r/ 92.6%

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

      2. *-commutative 92.6%

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

      3. associate-*r/ 92.6%

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

   10. Simplified 92.6%

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

   11. Taylor expanded in z around 0 81.8%

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

   if -3.5e76 < y < -4.9000000000000001e32 or -3.2000000000000002e-21 < y < 8.6000000000000002e102

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 89.9%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+76} \lor \neg \left(y \leq -4.9 \cdot 10^{+32} \lor \neg \left(y \leq -3.2 \cdot 10^{-21}\right) \land y \leq 8.6 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-114}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+101}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -3.8e-30)
     t_1
     (if (<= y 9.5e-114) t (if (<= y 5.1e+101) (* 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 <= -3.8e-30) {
		tmp = t_1;
	} else if (y <= 9.5e-114) {
		tmp = t;
	} else if (y <= 5.1e+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 = y * (x * y)
    if (y <= (-3.8d-30)) then
        tmp = t_1
    else if (y <= 9.5d-114) then
        tmp = t
    else if (y <= 5.1d+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 = y * (x * y);
	double tmp;
	if (y <= -3.8e-30) {
		tmp = t_1;
	} else if (y <= 9.5e-114) {
		tmp = t;
	} else if (y <= 5.1e+101) {
		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 <= -3.8e-30:
		tmp = t_1
	elif y <= 9.5e-114:
		tmp = t
	elif y <= 5.1e+101:
		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 <= -3.8e-30)
		tmp = t_1;
	elseif (y <= 9.5e-114)
		tmp = t;
	elseif (y <= 5.1e+101)
		tmp = Float64(y * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (x * y);
	tmp = 0.0;
	if (y <= -3.8e-30)
		tmp = t_1;
	elseif (y <= 9.5e-114)
		tmp = t;
	elseif (y <= 5.1e+101)
		tmp = y * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e-30], t$95$1, If[LessEqual[y, 9.5e-114], t, If[LessEqual[y, 5.1e+101], N[(y * z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000003e-30 or 5.09999999999999995e101 < 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 94.9%

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

      1. associate-/l* 91.7%

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

   5. Simplified 91.7%

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

   6. Taylor expanded in t around 0 89.1%

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

      1. associate-/l* 86.7%

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

   8. Applied egg-rr 86.7%

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

      1. associate-*r/ 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-*r/ 89.1%

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

   10. Simplified 89.1%

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

   11. Taylor expanded in z around 0 76.0%

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

   if -3.8000000000000003e-30 < y < 9.49999999999999958e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.8%

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

   if 9.49999999999999958e-114 < y < 5.09999999999999995e101

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 76.0%

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

   4. Taylor expanded in z around inf 65.2%

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

   5. Taylor expanded in y around inf 47.6%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-114}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 5.1 \cdot 10^{+101}:\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-30} \lor \neg \left(y \leq 9.2 \cdot 10^{-60}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.8e-30) (not (<= y 9.2e-60)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.8e-30) || !(y <= 9.2e-60)) {
		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 <= (-7.8d-30)) .or. (.not. (y <= 9.2d-60))) 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 <= -7.8e-30) || !(y <= 9.2e-60)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.8e-30) or not (y <= 9.2e-60):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.8e-30) || !(y <= 9.2e-60))
		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 <= -7.8e-30) || ~((y <= 9.2e-60)))
		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, -7.8e-30], N[Not[LessEqual[y, 9.2e-60]], $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 < -7.8000000000000007e-30 or 9.2000000000000005e-60 < y

   1. Initial program 99.8%

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

   3. Taylor expanded in z around inf 93.5%

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

      1. associate-/l* 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in t around 0 86.4%

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

      1. associate-/l* 84.3%

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

   8. Applied egg-rr 84.3%

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

      1. associate-*r/ 86.4%

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

      2. *-commutative 86.4%

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

      3. associate-*r/ 86.4%

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

   10. Simplified 86.4%

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

   11. Taylor expanded in z around 0 90.7%

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

   if -7.8000000000000007e-30 < y < 9.2000000000000005e-60

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 95.1%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-30} \lor \neg \left(y \leq 9.2 \cdot 10^{-60}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+16} \lor \neg \left(z \leq 1.32 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.4e+16) (not (<= z 1.32e+114))) (* y z) t))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.4e+16) || !(z <= 1.32e+114)) {
		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 <= (-3.4d+16)) .or. (.not. (z <= 1.32d+114))) 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 <= -3.4e+16) || !(z <= 1.32e+114)) {
		tmp = y * z;
	} else {
		tmp = t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.4e+16) or not (z <= 1.32e+114):
		tmp = y * z
	else:
		tmp = t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.4e+16) || !(z <= 1.32e+114))
		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 <= -3.4e+16) || ~((z <= 1.32e+114)))
		tmp = y * z;
	else
		tmp = t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.4e+16], N[Not[LessEqual[z, 1.32e+114]], $MachinePrecision]], N[(y * z), $MachinePrecision], t]

Derivation

1. Split input into 2 regimes

2. if z < -3.4e16 or 1.3200000000000001e114 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 80.3%

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

   4. Taylor expanded in z around inf 80.3%

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

   5. Taylor expanded in y around inf 60.5%

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

   if -3.4e16 < z < 1.3200000000000001e114

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 47.7%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+16} \lor \neg \left(z \leq 1.32 \cdot 10^{+114}\right):\\ \;\;\;\;y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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 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 99.9%

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

3. Taylor expanded in y around 0 38.2%

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

Reproduce

herbie shell --seed 2024087 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))