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

Percentage Accurate: 99.9% → 99.9%

Time: 4.7s

Alternatives: 7

Speedup: 1.0×

• 28.6% 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

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

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. Final simplification 99.9%

   \[\leadsto t + y \cdot \left(z + x \cdot y\right) \]

Alternative 2: 63.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot y\right)\\ \mathbf{if}\;y \leq -2 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+39}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-108}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-89}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-13}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* x (* y y))))
   (if (<= y -2e+71)
     t_1
     (if (<= y -8.2e+39)
       (* y z)
       (if (<= y -3.5e-19)
         t_1
         (if (<= y 4.9e-108)
           t
           (if (<= y 1.1e-89) (* y z) (if (<= y 2.25e-13) t t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x * (y * y);
	double tmp;
	if (y <= -2e+71) {
		tmp = t_1;
	} else if (y <= -8.2e+39) {
		tmp = y * z;
	} else if (y <= -3.5e-19) {
		tmp = t_1;
	} else if (y <= 4.9e-108) {
		tmp = t;
	} else if (y <= 1.1e-89) {
		tmp = y * z;
	} else if (y <= 2.25e-13) {
		tmp = t;
	} 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 <= (-2d+71)) then
        tmp = t_1
    else if (y <= (-8.2d+39)) then
        tmp = y * z
    else if (y <= (-3.5d-19)) then
        tmp = t_1
    else if (y <= 4.9d-108) then
        tmp = t
    else if (y <= 1.1d-89) then
        tmp = y * z
    else if (y <= 2.25d-13) then
        tmp = t
    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 <= -2e+71) {
		tmp = t_1;
	} else if (y <= -8.2e+39) {
		tmp = y * z;
	} else if (y <= -3.5e-19) {
		tmp = t_1;
	} else if (y <= 4.9e-108) {
		tmp = t;
	} else if (y <= 1.1e-89) {
		tmp = y * z;
	} else if (y <= 2.25e-13) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x * (y * y)
	tmp = 0
	if y <= -2e+71:
		tmp = t_1
	elif y <= -8.2e+39:
		tmp = y * z
	elif y <= -3.5e-19:
		tmp = t_1
	elif y <= 4.9e-108:
		tmp = t
	elif y <= 1.1e-89:
		tmp = y * z
	elif y <= 2.25e-13:
		tmp = t
	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 <= -2e+71)
		tmp = t_1;
	elseif (y <= -8.2e+39)
		tmp = Float64(y * z);
	elseif (y <= -3.5e-19)
		tmp = t_1;
	elseif (y <= 4.9e-108)
		tmp = t;
	elseif (y <= 1.1e-89)
		tmp = Float64(y * z);
	elseif (y <= 2.25e-13)
		tmp = t;
	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 <= -2e+71)
		tmp = t_1;
	elseif (y <= -8.2e+39)
		tmp = y * z;
	elseif (y <= -3.5e-19)
		tmp = t_1;
	elseif (y <= 4.9e-108)
		tmp = t;
	elseif (y <= 1.1e-89)
		tmp = y * z;
	elseif (y <= 2.25e-13)
		tmp = t;
	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, -2e+71], t$95$1, If[LessEqual[y, -8.2e+39], N[(y * z), $MachinePrecision], If[LessEqual[y, -3.5e-19], t$95$1, If[LessEqual[y, 4.9e-108], t, If[LessEqual[y, 1.1e-89], N[(y * z), $MachinePrecision], If[LessEqual[y, 2.25e-13], t, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0000000000000001e71 or -8.20000000000000008e39 < y < -3.50000000000000015e-19 or 2.25e-13 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 90.9%

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

   3. Taylor expanded in y around inf 71.0%

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

   4. Taylor expanded in y around 0 69.4%

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

      1. unpow2 69.4%

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

      2. *-commutative 69.4%

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

   6. Simplified 69.4%

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

   if -2.0000000000000001e71 < y < -8.20000000000000008e39 or 4.8999999999999998e-108 < y < 1.10000000000000006e-89

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   if -3.50000000000000015e-19 < y < 4.8999999999999998e-108 or 1.10000000000000006e-89 < y < 2.25e-13

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in y around 0 71.6%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+71}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{+39}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-19}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-108}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-89}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-13}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot y\right)\\ \end{array} \]

Alternative 3: 65.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot y\right)\\ \mathbf{if}\;y \leq -5.1 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{+38}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-108}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-91}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-13}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (* x y))))
   (if (<= y -5.1e+73)
     t_1
     (if (<= y -5.9e+38)
       (* y z)
       (if (<= y -4.5e-19)
         t_1
         (if (<= y 4.9e-108)
           t
           (if (<= y 4.2e-91) (* y z) (if (<= y 3.1e-13) t t_1))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (x * y);
	double tmp;
	if (y <= -5.1e+73) {
		tmp = t_1;
	} else if (y <= -5.9e+38) {
		tmp = y * z;
	} else if (y <= -4.5e-19) {
		tmp = t_1;
	} else if (y <= 4.9e-108) {
		tmp = t;
	} else if (y <= 4.2e-91) {
		tmp = y * z;
	} else if (y <= 3.1e-13) {
		tmp = t;
	} 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 <= (-5.1d+73)) then
        tmp = t_1
    else if (y <= (-5.9d+38)) then
        tmp = y * z
    else if (y <= (-4.5d-19)) then
        tmp = t_1
    else if (y <= 4.9d-108) then
        tmp = t
    else if (y <= 4.2d-91) then
        tmp = y * z
    else if (y <= 3.1d-13) then
        tmp = t
    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 <= -5.1e+73) {
		tmp = t_1;
	} else if (y <= -5.9e+38) {
		tmp = y * z;
	} else if (y <= -4.5e-19) {
		tmp = t_1;
	} else if (y <= 4.9e-108) {
		tmp = t;
	} else if (y <= 4.2e-91) {
		tmp = y * z;
	} else if (y <= 3.1e-13) {
		tmp = t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (x * y)
	tmp = 0
	if y <= -5.1e+73:
		tmp = t_1
	elif y <= -5.9e+38:
		tmp = y * z
	elif y <= -4.5e-19:
		tmp = t_1
	elif y <= 4.9e-108:
		tmp = t
	elif y <= 4.2e-91:
		tmp = y * z
	elif y <= 3.1e-13:
		tmp = t
	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 <= -5.1e+73)
		tmp = t_1;
	elseif (y <= -5.9e+38)
		tmp = Float64(y * z);
	elseif (y <= -4.5e-19)
		tmp = t_1;
	elseif (y <= 4.9e-108)
		tmp = t;
	elseif (y <= 4.2e-91)
		tmp = Float64(y * z);
	elseif (y <= 3.1e-13)
		tmp = t;
	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 <= -5.1e+73)
		tmp = t_1;
	elseif (y <= -5.9e+38)
		tmp = y * z;
	elseif (y <= -4.5e-19)
		tmp = t_1;
	elseif (y <= 4.9e-108)
		tmp = t;
	elseif (y <= 4.2e-91)
		tmp = y * z;
	elseif (y <= 3.1e-13)
		tmp = t;
	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, -5.1e+73], t$95$1, If[LessEqual[y, -5.9e+38], N[(y * z), $MachinePrecision], If[LessEqual[y, -4.5e-19], t$95$1, If[LessEqual[y, 4.9e-108], t, If[LessEqual[y, 4.2e-91], N[(y * z), $MachinePrecision], If[LessEqual[y, 3.1e-13], t, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.10000000000000024e73 or -5.89999999999999981e38 < y < -4.50000000000000013e-19 or 3.0999999999999999e-13 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 90.9%

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

   3. Taylor expanded in y around inf 71.0%

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

   if -5.10000000000000024e73 < y < -5.89999999999999981e38 or 4.8999999999999998e-108 < y < 4.1999999999999998e-91

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

   if -4.50000000000000013e-19 < y < 4.8999999999999998e-108 or 4.1999999999999998e-91 < y < 3.0999999999999999e-13

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in y around 0 71.6%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{+38}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-19}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-108}:\\ \;\;\;\;t\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-91}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-13}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \end{array} \]

Alternative 4: 78.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+71} \lor \neg \left(y \leq 6.4 \cdot 10^{+43}\right) \land \left(y \leq 1.65 \cdot 10^{+90} \lor \neg \left(y \leq 1.16 \cdot 10^{+175}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.1e+71)
         (and (not (<= y 6.4e+43))
              (or (<= y 1.65e+90) (not (<= y 1.16e+175)))))
   (* y (* x y))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.1e+71) || (!(y <= 6.4e+43) && ((y <= 1.65e+90) || !(y <= 1.16e+175)))) {
		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 <= (-2.1d+71)) .or. (.not. (y <= 6.4d+43)) .and. (y <= 1.65d+90) .or. (.not. (y <= 1.16d+175))) 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 <= -2.1e+71) || (!(y <= 6.4e+43) && ((y <= 1.65e+90) || !(y <= 1.16e+175)))) {
		tmp = y * (x * y);
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.1e+71) or (not (y <= 6.4e+43) and ((y <= 1.65e+90) or not (y <= 1.16e+175))):
		tmp = y * (x * y)
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.1e+71) || (!(y <= 6.4e+43) && ((y <= 1.65e+90) || !(y <= 1.16e+175))))
		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 <= -2.1e+71) || (~((y <= 6.4e+43)) && ((y <= 1.65e+90) || ~((y <= 1.16e+175)))))
		tmp = y * (x * y);
	else
		tmp = t + (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.1e+71], And[N[Not[LessEqual[y, 6.4e+43]], $MachinePrecision], Or[LessEqual[y, 1.65e+90], N[Not[LessEqual[y, 1.16e+175]], $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 < -2.09999999999999989e71 or 6.40000000000000029e43 < y < 1.65000000000000004e90 or 1.16e175 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 98.6%

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

   3. Taylor expanded in y around inf 88.7%

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

   if -2.09999999999999989e71 < y < 6.40000000000000029e43 or 1.65000000000000004e90 < y < 1.16e175

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 81.9%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+71} \lor \neg \left(y \leq 6.4 \cdot 10^{+43}\right) \land \left(y \leq 1.65 \cdot 10^{+90} \lor \neg \left(y \leq 1.16 \cdot 10^{+175}\right)\right):\\ \;\;\;\;y \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 5: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-25} \lor \neg \left(y \leq 7.5 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3e-25) (not (<= y 7.5e-13)))
   (* y (+ z (* x y)))
   (+ t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e-25) || !(y <= 7.5e-13)) {
		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 <= (-3d-25)) .or. (.not. (y <= 7.5d-13))) 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 <= -3e-25) || !(y <= 7.5e-13)) {
		tmp = y * (z + (x * y));
	} else {
		tmp = t + (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3e-25) or not (y <= 7.5e-13):
		tmp = y * (z + (x * y))
	else:
		tmp = t + (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3e-25) || !(y <= 7.5e-13))
		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 <= -3e-25) || ~((y <= 7.5e-13)))
		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, -3e-25], N[Not[LessEqual[y, 7.5e-13]], $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 < -2.9999999999999998e-25 or 7.5000000000000004e-13 < y

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in t around 0 90.8%

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

   if -2.9999999999999998e-25 < y < 7.5000000000000004e-13

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 92.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-25} \lor \neg \left(y \leq 7.5 \cdot 10^{-13}\right):\\ \;\;\;\;y \cdot \left(z + x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t + y \cdot z\\ \end{array} \]

Alternative 6: 51.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+43}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+90}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.35e+43) (* y z) (if (<= z 3.5e+90) t (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.35e+43) {
		tmp = y * z;
	} else if (z <= 3.5e+90) {
		tmp = t;
	} else {
		tmp = 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 (z <= (-2.35d+43)) then
        tmp = y * z
    else if (z <= 3.5d+90) then
        tmp = t
    else
        tmp = y * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.35e+43) {
		tmp = y * z;
	} else if (z <= 3.5e+90) {
		tmp = t;
	} else {
		tmp = y * z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.35e+43:
		tmp = y * z
	elif z <= 3.5e+90:
		tmp = t
	else:
		tmp = y * z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.35e+43)
		tmp = Float64(y * z);
	elseif (z <= 3.5e+90)
		tmp = t;
	else
		tmp = Float64(y * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.35e+43)
		tmp = y * z;
	elseif (z <= 3.5e+90)
		tmp = t;
	else
		tmp = y * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.35e+43], N[(y * z), $MachinePrecision], If[LessEqual[z, 3.5e+90], t, N[(y * z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.34999999999999999e43 or 3.4999999999999998e90 < z

   1. Initial program 100.0%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in x around 0 80.9%

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

   3. Taylor expanded in z around inf 57.2%

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

   if -2.34999999999999999e43 < z < 3.4999999999999998e90

   1. Initial program 99.9%

      \[\left(x \cdot y + z\right) \cdot y + t \]

   2. Taylor expanded in y around 0 49.7%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+43}:\\ \;\;\;\;y \cdot z\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+90}:\\ \;\;\;\;t\\ \mathbf{else}:\\ \;\;\;\;y \cdot z\\ \end{array} \]

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. Taylor expanded in y around 0 39.2%

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

3. Final simplification 39.2%

   \[\leadsto t \]

Reproduce

herbie shell --seed 2023181 
(FPCore (x y z t)
  :name "Language.Haskell.HsColour.ColourHighlight:unbase from hscolour-1.23"
  :precision binary64
  (+ (* (+ (* x y) z) y) t))