Data.Colour.Matrix:inverse from colour-2.3.3, B

Percentage Accurate: 91.0% → 97.5%

Time: 7.1s

Alternatives: 9

Speedup: 0.7×

• 27.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

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

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

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

Initial Program: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (/ (- (* x y) (* z t)) a))

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) - (z * t)) / a;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = ((x * y) - (z * t)) / a
end function

Java

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

Python

def code(x, y, z, t, a):
	return ((x * y) - (z * t)) / a

Julia

function code(x, y, z, t, a)
	return Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = ((x * y) - (z * t)) / a;
end

Wolfram

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

Alternative 1: 97.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+304)))
     (- (/ x (/ a y)) (/ z (/ a t)))
     (/ t_1 a))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+304)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+304)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+304):
		tmp = (x / (a / y)) - (z / (a / t))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+304))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+304)))
		tmp = (x / (a / y)) - (z / (a / t));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+304]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 4.9999999999999997e304 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 67.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

      1. div-sub 60.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} - \frac{z \cdot t}{a}} \]

      2. associate-/l* 75.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} - \frac{z \cdot t}{a} \]

      3. associate-/l* 90.8%

         \[\leadsto \frac{x}{\frac{a}{y}} - \color{blue}{\frac{z}{\frac{a}{t}}} \]

   3. Applied egg-rr 90.8%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999997e304

   1. Initial program 98.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+304}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 2: 72.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-20}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -1e+15)
   (* y (/ x a))
   (if (<= (* x y) 2e-20) (/ (- z) (/ a t)) (* x (* y (/ 1.0 a))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+15) {
		tmp = y * (x / a);
	} else if ((x * y) <= 2e-20) {
		tmp = -z / (a / t);
	} else {
		tmp = x * (y * (1.0 / a));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((x * y) <= (-1d+15)) then
        tmp = y * (x / a)
    else if ((x * y) <= 2d-20) then
        tmp = -z / (a / t)
    else
        tmp = x * (y * (1.0d0 / a))
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -1e+15) {
		tmp = y * (x / a);
	} else if ((x * y) <= 2e-20) {
		tmp = -z / (a / t);
	} else {
		tmp = x * (y * (1.0 / a));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -1e+15:
		tmp = y * (x / a)
	elif (x * y) <= 2e-20:
		tmp = -z / (a / t)
	else:
		tmp = x * (y * (1.0 / a))
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -1e+15)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 2e-20)
		tmp = Float64(Float64(-z) / Float64(a / t));
	else
		tmp = Float64(x * Float64(y * Float64(1.0 / a)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -1e+15)
		tmp = y * (x / a);
	elseif ((x * y) <= 2e-20)
		tmp = -z / (a / t);
	else
		tmp = x * (y * (1.0 / a));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -1e+15], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-20], N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1e15

   1. Initial program 91.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 70.0%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 71.8%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

   4. Simplified 71.8%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

   if -1e15 < (*.f64 x y) < 1.99999999999999989e-20

   1. Initial program 93.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around 0 74.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 74.1%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. mul-1-neg 74.1%

         \[\leadsto \frac{\color{blue}{-t \cdot z}}{a} \]

      3. distribute-rgt-neg-out 74.1%

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

      4. *-commutative 74.1%

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

      5. associate-/l* 76.8%

         \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]

      6. associate-/r/ 75.5%

         \[\leadsto \color{blue}{\frac{-z}{a} \cdot t} \]

   4. Simplified 75.5%

      \[\leadsto \color{blue}{\frac{-z}{a} \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 75.5%

         \[\leadsto \color{blue}{t \cdot \frac{-z}{a}} \]

      2. frac-2neg 75.5%

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

      3. remove-double-neg 75.5%

         \[\leadsto t \cdot \frac{\color{blue}{z}}{-a} \]

      4. associate-*r/ 74.1%

         \[\leadsto \color{blue}{\frac{t \cdot z}{-a}} \]

   6. Applied egg-rr 74.1%

      \[\leadsto \color{blue}{\frac{t \cdot z}{-a}} \]
   7. Step-by-step derivation

      1. associate-/l* 75.9%

         \[\leadsto \color{blue}{\frac{t}{\frac{-a}{z}}} \]

      2. associate-/r/ 76.8%

         \[\leadsto \color{blue}{\frac{t}{-a} \cdot z} \]

   8. Simplified 76.8%

      \[\leadsto \color{blue}{\frac{t}{-a} \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 76.8%

         \[\leadsto \color{blue}{z \cdot \frac{t}{-a}} \]

      2. frac-2neg 76.8%

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

      3. remove-double-neg 76.8%

         \[\leadsto z \cdot \frac{-t}{\color{blue}{a}} \]

      4. distribute-frac-neg 76.8%

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

      5. distribute-rgt-neg-in 76.8%

         \[\leadsto \color{blue}{-z \cdot \frac{t}{a}} \]

      6. *-commutative 76.8%

         \[\leadsto -\color{blue}{\frac{t}{a} \cdot z} \]

      7. clear-num 76.7%

         \[\leadsto -\color{blue}{\frac{1}{\frac{a}{t}}} \cdot z \]

      8. associate-/r/ 76.5%

         \[\leadsto -\color{blue}{\frac{1}{\frac{\frac{a}{t}}{z}}} \]

      9. clear-num 76.8%

         \[\leadsto -\color{blue}{\frac{z}{\frac{a}{t}}} \]

      10. distribute-neg-frac 76.8%

          \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]

   10. Applied egg-rr 76.8%

       \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]

   if 1.99999999999999989e-20 < (*.f64 x y)

   1. Initial program 89.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 74.7%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 77.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   4. Simplified 77.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
   5. Step-by-step derivation

      1. associate-/l* 74.7%

         \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]

      2. associate-*r/ 77.4%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

      3. *-commutative 77.4%

         \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]

      4. div-inv 77.4%

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

      5. associate-*l* 81.7%

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

   6. Applied egg-rr 81.7%

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{a} \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -1 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-20}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \frac{1}{a}\right)\\ \end{array} \]

Alternative 3: 65.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{-z}{a}\\ \mathbf{if}\;y \leq -4.6 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 29000000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- z) a))))
   (if (<= y -4.6e-119)
     (* x (/ y a))
     (if (<= y 1.1e-43)
       t_1
       (if (<= y 29000000000000.0)
         (/ (* x y) a)
         (if (<= y 5.8e+138) t_1 (/ x (/ a y))))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-z / a);
	double tmp;
	if (y <= -4.6e-119) {
		tmp = x * (y / a);
	} else if (y <= 1.1e-43) {
		tmp = t_1;
	} else if (y <= 29000000000000.0) {
		tmp = (x * y) / a;
	} else if (y <= 5.8e+138) {
		tmp = t_1;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (-z / a)
    if (y <= (-4.6d-119)) then
        tmp = x * (y / a)
    else if (y <= 1.1d-43) then
        tmp = t_1
    else if (y <= 29000000000000.0d0) then
        tmp = (x * y) / a
    else if (y <= 5.8d+138) then
        tmp = t_1
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-z / a);
	double tmp;
	if (y <= -4.6e-119) {
		tmp = x * (y / a);
	} else if (y <= 1.1e-43) {
		tmp = t_1;
	} else if (y <= 29000000000000.0) {
		tmp = (x * y) / a;
	} else if (y <= 5.8e+138) {
		tmp = t_1;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	t_1 = t * (-z / a)
	tmp = 0
	if y <= -4.6e-119:
		tmp = x * (y / a)
	elif y <= 1.1e-43:
		tmp = t_1
	elif y <= 29000000000000.0:
		tmp = (x * y) / a
	elif y <= 5.8e+138:
		tmp = t_1
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-z) / a))
	tmp = 0.0
	if (y <= -4.6e-119)
		tmp = Float64(x * Float64(y / a));
	elseif (y <= 1.1e-43)
		tmp = t_1;
	elseif (y <= 29000000000000.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (y <= 5.8e+138)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-z / a);
	tmp = 0.0;
	if (y <= -4.6e-119)
		tmp = x * (y / a);
	elseif (y <= 1.1e-43)
		tmp = t_1;
	elseif (y <= 29000000000000.0)
		tmp = (x * y) / a;
	elseif (y <= 5.8e+138)
		tmp = t_1;
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.6e-119], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-43], t$95$1, If[LessEqual[y, 29000000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 5.8e+138], t$95$1, N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.59999999999999987e-119

   1. Initial program 91.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 60.3%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 60.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   4. Simplified 60.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 62.2%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   6. Applied egg-rr 62.2%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   if -4.59999999999999987e-119 < y < 1.09999999999999999e-43 or 2.9e13 < y < 5.80000000000000019e138

   1. Initial program 92.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

      1. div-sub 91.1%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} - \frac{z \cdot t}{a}} \]

      2. associate-/l* 85.8%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} - \frac{z \cdot t}{a} \]

      3. associate-/l* 89.7%

         \[\leadsto \frac{x}{\frac{a}{y}} - \color{blue}{\frac{z}{\frac{a}{t}}} \]

   3. Applied egg-rr 89.7%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}} \]

   4. Taylor expanded in x around 0 68.1%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. mul-1-neg 68.1%

         \[\leadsto \color{blue}{-\frac{t \cdot z}{a}} \]

      2. associate-*r/ 71.3%

         \[\leadsto -\color{blue}{t \cdot \frac{z}{a}} \]

      3. distribute-rgt-neg-in 71.3%

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

   6. Simplified 71.3%

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

   if 1.09999999999999999e-43 < y < 2.9e13

   1. Initial program 99.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 60.3%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]

   if 5.80000000000000019e138 < y

   1. Initial program 87.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 62.7%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 68.4%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

   4. Simplified 68.4%

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

      1. associate-*r/ 62.7%

         \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]

      2. *-commutative 62.7%

         \[\leadsto \frac{\color{blue}{x \cdot y}}{a} \]

      3. associate-/l* 74.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   6. Applied egg-rr 74.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-43}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq 29000000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 4: 66.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 0.0255:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;y \leq 31000000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.7e-118)
   (* x (/ y a))
   (if (<= y 0.0255)
     (* z (/ t (- a)))
     (if (<= y 31000000000000.0)
       (/ (* x y) a)
       (if (<= y 1.6e+138) (* t (/ (- z) a)) (/ x (/ a y)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.7e-118) {
		tmp = x * (y / a);
	} else if (y <= 0.0255) {
		tmp = z * (t / -a);
	} else if (y <= 31000000000000.0) {
		tmp = (x * y) / a;
	} else if (y <= 1.6e+138) {
		tmp = t * (-z / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.7d-118)) then
        tmp = x * (y / a)
    else if (y <= 0.0255d0) then
        tmp = z * (t / -a)
    else if (y <= 31000000000000.0d0) then
        tmp = (x * y) / a
    else if (y <= 1.6d+138) then
        tmp = t * (-z / a)
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.7e-118) {
		tmp = x * (y / a);
	} else if (y <= 0.0255) {
		tmp = z * (t / -a);
	} else if (y <= 31000000000000.0) {
		tmp = (x * y) / a;
	} else if (y <= 1.6e+138) {
		tmp = t * (-z / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.7e-118:
		tmp = x * (y / a)
	elif y <= 0.0255:
		tmp = z * (t / -a)
	elif y <= 31000000000000.0:
		tmp = (x * y) / a
	elif y <= 1.6e+138:
		tmp = t * (-z / a)
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.7e-118)
		tmp = Float64(x * Float64(y / a));
	elseif (y <= 0.0255)
		tmp = Float64(z * Float64(t / Float64(-a)));
	elseif (y <= 31000000000000.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (y <= 1.6e+138)
		tmp = Float64(t * Float64(Float64(-z) / a));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.7e-118)
		tmp = x * (y / a);
	elseif (y <= 0.0255)
		tmp = z * (t / -a);
	elseif (y <= 31000000000000.0)
		tmp = (x * y) / a;
	elseif (y <= 1.6e+138)
		tmp = t * (-z / a);
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.7e-118], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0255], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 31000000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.6e+138], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.70000000000000014e-118

   1. Initial program 91.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 60.3%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 60.1%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   4. Simplified 60.1%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 62.2%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   6. Applied egg-rr 62.2%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   if -3.70000000000000014e-118 < y < 0.0254999999999999984

   1. Initial program 92.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around 0 68.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 68.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. mul-1-neg 68.7%

         \[\leadsto \frac{\color{blue}{-t \cdot z}}{a} \]

      3. distribute-rgt-neg-out 68.7%

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

      4. *-commutative 68.7%

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

      5. associate-/l* 72.1%

         \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]

      6. associate-/r/ 70.5%

         \[\leadsto \color{blue}{\frac{-z}{a} \cdot t} \]

   4. Simplified 70.5%

      \[\leadsto \color{blue}{\frac{-z}{a} \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 70.5%

         \[\leadsto \color{blue}{t \cdot \frac{-z}{a}} \]

      2. frac-2neg 70.5%

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

      3. remove-double-neg 70.5%

         \[\leadsto t \cdot \frac{\color{blue}{z}}{-a} \]

      4. associate-*r/ 68.7%

         \[\leadsto \color{blue}{\frac{t \cdot z}{-a}} \]

   6. Applied egg-rr 68.7%

      \[\leadsto \color{blue}{\frac{t \cdot z}{-a}} \]
   7. Step-by-step derivation

      1. associate-/l* 71.0%

         \[\leadsto \color{blue}{\frac{t}{\frac{-a}{z}}} \]

      2. associate-/r/ 72.2%

         \[\leadsto \color{blue}{\frac{t}{-a} \cdot z} \]

   8. Simplified 72.2%

      \[\leadsto \color{blue}{\frac{t}{-a} \cdot z} \]

   if 0.0254999999999999984 < y < 3.1e13

   1. Initial program 100.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 75.1%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]

   if 3.1e13 < y < 1.6000000000000001e138

   1. Initial program 94.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

      1. div-sub 94.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} - \frac{z \cdot t}{a}} \]

      2. associate-/l* 89.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} - \frac{z \cdot t}{a} \]

      3. associate-/l* 94.2%

         \[\leadsto \frac{x}{\frac{a}{y}} - \color{blue}{\frac{z}{\frac{a}{t}}} \]

   3. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}} \]

   4. Taylor expanded in x around 0 57.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. mul-1-neg 57.3%

         \[\leadsto \color{blue}{-\frac{t \cdot z}{a}} \]

      2. associate-*r/ 62.6%

         \[\leadsto -\color{blue}{t \cdot \frac{z}{a}} \]

      3. distribute-rgt-neg-in 62.6%

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

   6. Simplified 62.6%

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

   if 1.6000000000000001e138 < y

   1. Initial program 87.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 62.7%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 68.4%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

   4. Simplified 68.4%

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

      1. associate-*r/ 62.7%

         \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]

      2. *-commutative 62.7%

         \[\leadsto \frac{\color{blue}{x \cdot y}}{a} \]

      3. associate-/l* 74.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   6. Applied egg-rr 74.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{-118}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 0.0255:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;y \leq 31000000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 66.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-43}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq 29000000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.8e-89)
   (* x (/ y a))
   (if (<= y 1.1e-43)
     (/ (- z) (/ a t))
     (if (<= y 29000000000000.0)
       (/ (* x y) a)
       (if (<= y 1.95e+138) (* t (/ (- z) a)) (/ x (/ a y)))))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.8e-89) {
		tmp = x * (y / a);
	} else if (y <= 1.1e-43) {
		tmp = -z / (a / t);
	} else if (y <= 29000000000000.0) {
		tmp = (x * y) / a;
	} else if (y <= 1.95e+138) {
		tmp = t * (-z / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.8d-89)) then
        tmp = x * (y / a)
    else if (y <= 1.1d-43) then
        tmp = -z / (a / t)
    else if (y <= 29000000000000.0d0) then
        tmp = (x * y) / a
    else if (y <= 1.95d+138) then
        tmp = t * (-z / a)
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.8e-89) {
		tmp = x * (y / a);
	} else if (y <= 1.1e-43) {
		tmp = -z / (a / t);
	} else if (y <= 29000000000000.0) {
		tmp = (x * y) / a;
	} else if (y <= 1.95e+138) {
		tmp = t * (-z / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.8e-89:
		tmp = x * (y / a)
	elif y <= 1.1e-43:
		tmp = -z / (a / t)
	elif y <= 29000000000000.0:
		tmp = (x * y) / a
	elif y <= 1.95e+138:
		tmp = t * (-z / a)
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.8e-89)
		tmp = Float64(x * Float64(y / a));
	elseif (y <= 1.1e-43)
		tmp = Float64(Float64(-z) / Float64(a / t));
	elseif (y <= 29000000000000.0)
		tmp = Float64(Float64(x * y) / a);
	elseif (y <= 1.95e+138)
		tmp = Float64(t * Float64(Float64(-z) / a));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.8e-89)
		tmp = x * (y / a);
	elseif (y <= 1.1e-43)
		tmp = -z / (a / t);
	elseif (y <= 29000000000000.0)
		tmp = (x * y) / a;
	elseif (y <= 1.95e+138)
		tmp = t * (-z / a);
	else
		tmp = x / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.8e-89], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e-43], N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 29000000000000.0], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.95e+138], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.80000000000000032e-89

   1. Initial program 91.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 61.4%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 61.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   4. Simplified 61.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 63.4%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   6. Applied egg-rr 63.4%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   if -4.80000000000000032e-89 < y < 1.09999999999999999e-43

   1. Initial program 92.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around 0 69.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 69.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. mul-1-neg 69.6%

         \[\leadsto \frac{\color{blue}{-t \cdot z}}{a} \]

      3. distribute-rgt-neg-out 69.6%

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

      4. *-commutative 69.6%

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

      5. associate-/l* 73.1%

         \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]

      6. associate-/r/ 72.3%

         \[\leadsto \color{blue}{\frac{-z}{a} \cdot t} \]

   4. Simplified 72.3%

      \[\leadsto \color{blue}{\frac{-z}{a} \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 72.3%

         \[\leadsto \color{blue}{t \cdot \frac{-z}{a}} \]

      2. frac-2neg 72.3%

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

      3. remove-double-neg 72.3%

         \[\leadsto t \cdot \frac{\color{blue}{z}}{-a} \]

      4. associate-*r/ 69.6%

         \[\leadsto \color{blue}{\frac{t \cdot z}{-a}} \]

   6. Applied egg-rr 69.6%

      \[\leadsto \color{blue}{\frac{t \cdot z}{-a}} \]
   7. Step-by-step derivation

      1. associate-/l* 72.9%

         \[\leadsto \color{blue}{\frac{t}{\frac{-a}{z}}} \]

      2. associate-/r/ 73.1%

         \[\leadsto \color{blue}{\frac{t}{-a} \cdot z} \]

   8. Simplified 73.1%

      \[\leadsto \color{blue}{\frac{t}{-a} \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 73.1%

         \[\leadsto \color{blue}{z \cdot \frac{t}{-a}} \]

      2. frac-2neg 73.1%

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

      3. remove-double-neg 73.1%

         \[\leadsto z \cdot \frac{-t}{\color{blue}{a}} \]

      4. distribute-frac-neg 73.1%

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

      5. distribute-rgt-neg-in 73.1%

         \[\leadsto \color{blue}{-z \cdot \frac{t}{a}} \]

      6. *-commutative 73.1%

         \[\leadsto -\color{blue}{\frac{t}{a} \cdot z} \]

      7. clear-num 73.0%

         \[\leadsto -\color{blue}{\frac{1}{\frac{a}{t}}} \cdot z \]

      8. associate-/r/ 73.0%

         \[\leadsto -\color{blue}{\frac{1}{\frac{\frac{a}{t}}{z}}} \]

      9. clear-num 73.1%

         \[\leadsto -\color{blue}{\frac{z}{\frac{a}{t}}} \]

      10. distribute-neg-frac 73.1%

          \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]

   10. Applied egg-rr 73.1%

       \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]

   if 1.09999999999999999e-43 < y < 2.9e13

   1. Initial program 99.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 60.3%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]

   if 2.9e13 < y < 1.9499999999999999e138

   1. Initial program 94.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Step-by-step derivation

      1. div-sub 94.4%

         \[\leadsto \color{blue}{\frac{x \cdot y}{a} - \frac{z \cdot t}{a}} \]

      2. associate-/l* 89.0%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} - \frac{z \cdot t}{a} \]

      3. associate-/l* 94.2%

         \[\leadsto \frac{x}{\frac{a}{y}} - \color{blue}{\frac{z}{\frac{a}{t}}} \]

   3. Applied egg-rr 94.2%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}} \]

   4. Taylor expanded in x around 0 57.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   5. Step-by-step derivation

      1. mul-1-neg 57.3%

         \[\leadsto \color{blue}{-\frac{t \cdot z}{a}} \]

      2. associate-*r/ 62.6%

         \[\leadsto -\color{blue}{t \cdot \frac{z}{a}} \]

      3. distribute-rgt-neg-in 62.6%

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

   6. Simplified 62.6%

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

   if 1.9499999999999999e138 < y

   1. Initial program 87.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 62.7%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 68.4%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

   4. Simplified 68.4%

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

      1. associate-*r/ 62.7%

         \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]

      2. *-commutative 62.7%

         \[\leadsto \frac{\color{blue}{x \cdot y}}{a} \]

      3. associate-/l* 74.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]

   6. Applied egg-rr 74.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-89}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-43}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \mathbf{elif}\;y \leq 29000000000000:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{+138}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq 4 \cdot 10^{+252}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) 4e+252) (/ (- (* x y) (* z t)) a) (/ (- z) (/ a t))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= 4e+252) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = -z / (a / t);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z * t) <= 4d+252) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = -z / (a / t)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= 4e+252) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = -z / (a / t);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= 4e+252:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = -z / (a / t)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= 4e+252)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(-z) / Float64(a / t));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= 4e+252)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = -z / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], 4e+252], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[((-z) / N[(a / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < 4.0000000000000004e252

   1. Initial program 95.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   if 4.0000000000000004e252 < (*.f64 z t)

   1. Initial program 54.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around 0 65.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot z}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 65.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(t \cdot z\right)}{a}} \]

      2. mul-1-neg 65.2%

         \[\leadsto \frac{\color{blue}{-t \cdot z}}{a} \]

      3. distribute-rgt-neg-out 65.2%

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

      4. *-commutative 65.2%

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

      5. associate-/l* 100.0%

         \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]

      6. associate-/r/ 99.9%

         \[\leadsto \color{blue}{\frac{-z}{a} \cdot t} \]

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{-z}{a} \cdot t} \]
   5. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \color{blue}{t \cdot \frac{-z}{a}} \]

      2. frac-2neg 99.9%

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

      3. remove-double-neg 99.9%

         \[\leadsto t \cdot \frac{\color{blue}{z}}{-a} \]

      4. associate-*r/ 65.2%

         \[\leadsto \color{blue}{\frac{t \cdot z}{-a}} \]

   6. Applied egg-rr 65.2%

      \[\leadsto \color{blue}{\frac{t \cdot z}{-a}} \]
   7. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\frac{t}{\frac{-a}{z}}} \]

      2. associate-/r/ 99.8%

         \[\leadsto \color{blue}{\frac{t}{-a} \cdot z} \]

   8. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{t}{-a} \cdot z} \]
   9. Step-by-step derivation

      1. *-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \frac{t}{-a}} \]

      2. frac-2neg 99.8%

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

      3. remove-double-neg 99.8%

         \[\leadsto z \cdot \frac{-t}{\color{blue}{a}} \]

      4. distribute-frac-neg 99.8%

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

      5. distribute-rgt-neg-in 99.8%

         \[\leadsto \color{blue}{-z \cdot \frac{t}{a}} \]

      6. *-commutative 99.8%

         \[\leadsto -\color{blue}{\frac{t}{a} \cdot z} \]

      7. clear-num 100.0%

         \[\leadsto -\color{blue}{\frac{1}{\frac{a}{t}}} \cdot z \]

      8. associate-/r/ 99.8%

         \[\leadsto -\color{blue}{\frac{1}{\frac{\frac{a}{t}}{z}}} \]

      9. clear-num 100.0%

         \[\leadsto -\color{blue}{\frac{z}{\frac{a}{t}}} \]

      10. distribute-neg-frac 100.0%

          \[\leadsto \color{blue}{\frac{-z}{\frac{a}{t}}} \]

   10. Applied egg-rr 100.0%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq 4 \cdot 10^{+252}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{a}{t}}\\ \end{array} \]

Alternative 7: 50.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.5e-256) (* x (/ y a)) (* y (/ x a))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-256) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-5.5d-256)) then
        tmp = x * (y / a)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.5e-256) {
		tmp = x * (y / a);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.5e-256:
		tmp = x * (y / a)
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.5e-256)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.5e-256)
		tmp = x * (y / a);
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.5e-256], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.4999999999999998e-256

   1. Initial program 89.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 39.0%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 42.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   4. Simplified 42.8%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 43.4%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   6. Applied egg-rr 43.4%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   if -5.4999999999999998e-256 < z

   1. Initial program 94.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 57.3%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-*r/ 53.9%

         \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

   4. Simplified 53.9%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.5 \cdot 10^{-256}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]

Alternative 8: 50.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.08e-257) (* x (/ y a)) (/ y (/ a x))))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.08e-257) {
		tmp = x * (y / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.08d-257)) then
        tmp = x * (y / a)
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.08e-257) {
		tmp = x * (y / a);
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.08e-257:
		tmp = x * (y / a)
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.08e-257)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.08e-257)
		tmp = x * (y / a);
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.08e-257], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.07999999999999998e-257

   1. Initial program 89.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 39.0%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 42.8%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   4. Simplified 42.8%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
   5. Step-by-step derivation

      1. associate-/r/ 43.4%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   6. Applied egg-rr 43.4%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot x} \]

   if -1.07999999999999998e-257 < z

   1. Initial program 94.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]

   2. Taylor expanded in x around inf 57.3%

      \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
   3. Step-by-step derivation

      1. associate-/l* 54.6%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]

   4. Simplified 54.6%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-257}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 9: 50.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ y \cdot \frac{x}{a} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* y (/ x a)))

C

assert(x < y);
double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = y * (x / a)
end function

Java

assert x < y;
public static double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Python

[x, y] = sort([x, y])
def code(x, y, z, t, a):
	return y * (x / a)

Julia

x, y = sort([x, y])
function code(x, y, z, t, a)
	return Float64(y * Float64(x / a))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y, z, t, a)
	tmp = y * (x / a);
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.1%

   \[\frac{x \cdot y - z \cdot t}{a} \]

2. Taylor expanded in x around inf 48.7%

   \[\leadsto \color{blue}{\frac{y \cdot x}{a}} \]
3. Step-by-step derivation

   1. associate-*r/ 49.4%

      \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

4. Simplified 49.4%

   \[\leadsto \color{blue}{y \cdot \frac{x}{a}} \]

5. Final simplification 49.4%

   \[\leadsto y \cdot \frac{x}{a} \]

Developer target: 91.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (/ y a) x) (* (/ t a) z))))
   (if (< z -2.468684968699548e+170)
     t_1
     (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y / a) * x) - ((t / a) * z)
	tmp = 0
	if z < -2.468684968699548e+170:
		tmp = t_1
	elif z < 6.309831121978371e-71:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y / a) * x) - Float64(Float64(t / a) * z))
	tmp = 0.0
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y / a) * x) - ((t / a) * z);
	tmp = 0.0;
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.468684968699548e+170], t$95$1, If[Less[z, 6.309831121978371e-71], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2023252 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :herbie-target
  (if (< z -2.468684968699548e+170) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z))))

  (/ (- (* x y) (* z t)) a))