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

Percentage Accurate: 91.8% → 96.8%

Time: 8.6s

Alternatives: 10

Speedup: 0.7×

• 29.2% 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: 91.8% 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: 96.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 10^{+252}\right):\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, -z \cdot t\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 1e+252)))
     (fma -1.0 (/ t (/ a z)) (/ y (/ a x)))
     (/ (fma y x (- (* z t))) a))))

C

assert(x < y);
assert(z < t);
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 <= 1e+252)) {
		tmp = fma(-1.0, (t / (a / z)), (y / (a / x)));
	} else {
		tmp = fma(y, x, -(z * t)) / a;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
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 <= 1e+252))
		tmp = fma(-1.0, Float64(t / Float64(a / z)), Float64(y / Float64(a / x)));
	else
		tmp = Float64(fma(y, x, Float64(-Float64(z * t))) / a);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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, 1e+252]], $MachinePrecision]], N[(-1.0 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * x + (-N[(z * t), $MachinePrecision])), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 1.0000000000000001e252 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 70.1%

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

   2. Taylor expanded in x around 0 68.4%

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

      1. fma-def 68.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{t \cdot z}{a}, \frac{y \cdot x}{a}\right)} \]

      2. associate-/l* 80.8%

         \[\leadsto \mathsf{fma}\left(-1, \color{blue}{\frac{t}{\frac{a}{z}}}, \frac{y \cdot x}{a}\right) \]

      3. associate-/l* 96.5%

         \[\leadsto \mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \color{blue}{\frac{y}{\frac{a}{x}}}\right) \]

   4. Simplified 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{y}{\frac{a}{x}}\right)} \]

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.0000000000000001e252

   1. Initial program 98.7%

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

   2. Taylor expanded in x around 0 97.1%

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

      1. +-commutative 97.1%

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

      2. mul-1-neg 97.1%

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

      3. sub-neg 97.1%

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

      4. div-sub 98.7%

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

      5. fma-neg 98.7%

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

      6. distribute-rgt-neg-out 98.7%

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

   4. Simplified 98.7%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, x, t \cdot \left(-z\right)\right)}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+252}\right):\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{y}{\frac{a}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, -z \cdot t\right)}{a}\\ \end{array} \]

Alternative 2: 96.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+286}:\\ \;\;\;\;t_1 - t \cdot \frac{z}{a}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, -z \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1 - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ a y))) (t_2 (- (* x y) (* z t))))
   (if (<= t_2 -5e+286)
     (- t_1 (* t (/ z a)))
     (if (<= t_2 5e+257) (/ (fma y x (- (* z t))) a) (- t_1 (/ z (/ a t)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (a / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -5e+286) {
		tmp = t_1 - (t * (z / a));
	} else if (t_2 <= 5e+257) {
		tmp = fma(y, x, -(z * t)) / a;
	} else {
		tmp = t_1 - (z / (a / t));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= -5e+286)
		tmp = Float64(t_1 - Float64(t * Float64(z / a)));
	elseif (t_2 <= 5e+257)
		tmp = Float64(fma(y, x, Float64(-Float64(z * t))) / a);
	else
		tmp = Float64(t_1 - Float64(z / Float64(a / t)));
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+286], N[(t$95$1 - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+257], N[(N[(y * x + (-N[(z * t), $MachinePrecision])), $MachinePrecision] / a), $MachinePrecision], N[(t$95$1 - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000004e286

   1. Initial program 65.6%

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

      1. div-sub 65.6%

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

      2. associate-/l* 82.6%

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

      3. associate-/l* 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. associate-/r/ 96.7%

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

   5. Applied egg-rr 96.7%

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

   if -5.0000000000000004e286 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000028e257

   1. Initial program 98.7%

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

   2. Taylor expanded in x around 0 97.1%

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

      1. +-commutative 97.1%

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

      2. mul-1-neg 97.1%

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

      3. sub-neg 97.1%

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

      4. div-sub 98.7%

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

      5. fma-neg 98.7%

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

      6. distribute-rgt-neg-out 98.7%

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

   4. Simplified 98.7%

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

   if 5.00000000000000028e257 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 79.8%

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

      1. div-sub 76.8%

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

      2. associate-/l* 85.6%

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

      3. associate-/l* 96.9%

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

   3. Applied egg-rr 96.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, -z \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 3: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{+286} \lor \neg \left(t_1 \leq 5 \cdot 10^{+257}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 -5e+286) (not (<= t_1 5e+257)))
     (- (/ x (/ a y)) (* t (/ z a)))
     (/ t_1 a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -5e+286) || !(t_1 <= 5e+257)) {
		tmp = (x / (a / y)) - (t * (z / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 = (x * y) - (z * t)
    if ((t_1 <= (-5d+286)) .or. (.not. (t_1 <= 5d+257))) then
        tmp = (x / (a / y)) - (t * (z / a))
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
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 <= -5e+286) || !(t_1 <= 5e+257)) {
		tmp = (x / (a / y)) - (t * (z / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -5e+286) or not (t_1 <= 5e+257):
		tmp = (x / (a / y)) - (t * (z / a))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -5e+286) || !(t_1 <= 5e+257))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(t * Float64(z / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -5e+286) || ~((t_1 <= 5e+257)))
		tmp = (x / (a / y)) - (t * (z / a));
	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.
NOTE: z and t 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, -5e+286], N[Not[LessEqual[t$95$1, 5e+257]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $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)) < -5.0000000000000004e286 or 5.00000000000000028e257 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 72.7%

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

      1. div-sub 71.2%

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

      2. associate-/l* 84.1%

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

      3. associate-/l* 98.3%

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

   3. Applied egg-rr 98.3%

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

      1. associate-/r/ 96.8%

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

   5. Applied egg-rr 96.8%

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

   if -5.0000000000000004e286 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000028e257

   1. Initial program 98.7%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+286} \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+257}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 4: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_2 \leq -5 \cdot 10^{+286}:\\ \;\;\;\;t_1 - t \cdot \frac{z}{a}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{t_2}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1 - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ x (/ a y))) (t_2 (- (* x y) (* z t))))
   (if (<= t_2 -5e+286)
     (- t_1 (* t (/ z a)))
     (if (<= t_2 5e+257) (/ t_2 a) (- t_1 (/ z (/ a t)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (a / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -5e+286) {
		tmp = t_1 - (t * (z / a));
	} else if (t_2 <= 5e+257) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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) :: t_2
    real(8) :: tmp
    t_1 = x / (a / y)
    t_2 = (x * y) - (z * t)
    if (t_2 <= (-5d+286)) then
        tmp = t_1 - (t * (z / a))
    else if (t_2 <= 5d+257) then
        tmp = t_2 / a
    else
        tmp = t_1 - (z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x / (a / y);
	double t_2 = (x * y) - (z * t);
	double tmp;
	if (t_2 <= -5e+286) {
		tmp = t_1 - (t * (z / a));
	} else if (t_2 <= 5e+257) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (z / (a / t));
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	t_2 = (x * y) - (z * t)
	tmp = 0
	if t_2 <= -5e+286:
		tmp = t_1 - (t * (z / a))
	elif t_2 <= 5e+257:
		tmp = t_2 / a
	else:
		tmp = t_1 - (z / (a / t))
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(x / Float64(a / y))
	t_2 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_2 <= -5e+286)
		tmp = Float64(t_1 - Float64(t * Float64(z / a)));
	elseif (t_2 <= 5e+257)
		tmp = Float64(t_2 / a);
	else
		tmp = Float64(t_1 - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x / (a / y);
	t_2 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_2 <= -5e+286)
		tmp = t_1 - (t * (z / a));
	elseif (t_2 <= 5e+257)
		tmp = t_2 / a;
	else
		tmp = t_1 - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+286], N[(t$95$1 - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+257], N[(t$95$2 / a), $MachinePrecision], N[(t$95$1 - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000004e286

   1. Initial program 65.6%

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

      1. div-sub 65.6%

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

      2. associate-/l* 82.6%

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

      3. associate-/l* 99.7%

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

   3. Applied egg-rr 99.7%

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

      1. associate-/r/ 96.7%

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

   5. Applied egg-rr 96.7%

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

   if -5.0000000000000004e286 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.00000000000000028e257

   1. Initial program 98.7%

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

   if 5.00000000000000028e257 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 79.8%

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

      1. div-sub 76.8%

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

      2. associate-/l* 85.6%

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

      3. associate-/l* 96.9%

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

   3. Applied egg-rr 96.9%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -5 \cdot 10^{+286}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+257}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 5: 68.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+252}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-33}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.65e+252)
   (* y (/ x a))
   (if (<= x -2.6e+135)
     (* x (/ y a))
     (if (<= x -1.65e+56)
       (/ y (/ a x))
       (if (<= x 1.85e-33) (* (- z) (/ t a)) (/ x (/ a y)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.65e+252) {
		tmp = y * (x / a);
	} else if (x <= -2.6e+135) {
		tmp = x * (y / a);
	} else if (x <= -1.65e+56) {
		tmp = y / (a / x);
	} else if (x <= 1.85e-33) {
		tmp = -z * (t / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 <= (-1.65d+252)) then
        tmp = y * (x / a)
    else if (x <= (-2.6d+135)) then
        tmp = x * (y / a)
    else if (x <= (-1.65d+56)) then
        tmp = y / (a / x)
    else if (x <= 1.85d-33) then
        tmp = -z * (t / a)
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.65e+252) {
		tmp = y * (x / a);
	} else if (x <= -2.6e+135) {
		tmp = x * (y / a);
	} else if (x <= -1.65e+56) {
		tmp = y / (a / x);
	} else if (x <= 1.85e-33) {
		tmp = -z * (t / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.65e+252:
		tmp = y * (x / a)
	elif x <= -2.6e+135:
		tmp = x * (y / a)
	elif x <= -1.65e+56:
		tmp = y / (a / x)
	elif x <= 1.85e-33:
		tmp = -z * (t / a)
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.65e+252)
		tmp = Float64(y * Float64(x / a));
	elseif (x <= -2.6e+135)
		tmp = Float64(x * Float64(y / a));
	elseif (x <= -1.65e+56)
		tmp = Float64(y / Float64(a / x));
	elseif (x <= 1.85e-33)
		tmp = Float64(Float64(-z) * Float64(t / a));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.65e+252)
		tmp = y * (x / a);
	elseif (x <= -2.6e+135)
		tmp = x * (y / a);
	elseif (x <= -1.65e+56)
		tmp = y / (a / x);
	elseif (x <= 1.85e-33)
		tmp = -z * (t / 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.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.65e+252], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.6e+135], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.65e+56], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.85e-33], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.65e252

   1. Initial program 85.7%

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

   2. Taylor expanded in x around inf 78.3%

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

      1. associate-*r/ 78.9%

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

   4. Simplified 78.9%

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

   if -1.65e252 < x < -2.6e135

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf 78.3%

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

      1. associate-/l* 78.1%

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

      2. associate-/r/ 86.7%

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

   4. Applied egg-rr 86.7%

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

   if -2.6e135 < x < -1.65000000000000001e56

   1. Initial program 74.6%

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

   2. Taylor expanded in x around inf 57.9%

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

      1. associate-/l* 83.2%

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

   4. Simplified 83.2%

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

   if -1.65000000000000001e56 < x < 1.85000000000000007e-33

   1. Initial program 94.8%

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

   2. Taylor expanded in x around 0 94.0%

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

      1. +-commutative 94.0%

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

      2. mul-1-neg 94.0%

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

      3. sub-neg 94.0%

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

      4. div-sub 94.8%

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

      5. fma-neg 94.8%

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

      6. distribute-rgt-neg-out 94.8%

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

   4. Simplified 94.8%

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

   5. Taylor expanded in y around 0 70.3%

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

      1. mul-1-neg 70.3%

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

      2. associate-*l/ 69.5%

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

      3. distribute-rgt-neg-in 69.5%

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

   7. Simplified 69.5%

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

   if 1.85000000000000007e-33 < x

   1. Initial program 92.3%

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

   2. Taylor expanded in x around inf 63.9%

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

      1. associate-*r/ 67.1%

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

   4. Simplified 67.1%

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

      1. associate-*r/ 63.9%

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

      2. *-commutative 63.9%

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

      3. associate-/l* 62.9%

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

   6. Applied egg-rr 62.9%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+252}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+135}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{+56}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-33}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 68.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+251}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+54}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-33}:\\ \;\;\;\;\frac{-z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.3e+251)
   (* y (/ x a))
   (if (<= x -3.05e+134)
     (* x (/ y a))
     (if (<= x -3.9e+54)
       (/ y (/ a x))
       (if (<= x 3.05e-33) (/ (- (* z t)) a) (/ x (/ a y)))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.3e+251) {
		tmp = y * (x / a);
	} else if (x <= -3.05e+134) {
		tmp = x * (y / a);
	} else if (x <= -3.9e+54) {
		tmp = y / (a / x);
	} else if (x <= 3.05e-33) {
		tmp = -(z * t) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 <= (-2.3d+251)) then
        tmp = y * (x / a)
    else if (x <= (-3.05d+134)) then
        tmp = x * (y / a)
    else if (x <= (-3.9d+54)) then
        tmp = y / (a / x)
    else if (x <= 3.05d-33) then
        tmp = -(z * t) / a
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.3e+251) {
		tmp = y * (x / a);
	} else if (x <= -3.05e+134) {
		tmp = x * (y / a);
	} else if (x <= -3.9e+54) {
		tmp = y / (a / x);
	} else if (x <= 3.05e-33) {
		tmp = -(z * t) / a;
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.3e+251:
		tmp = y * (x / a)
	elif x <= -3.05e+134:
		tmp = x * (y / a)
	elif x <= -3.9e+54:
		tmp = y / (a / x)
	elif x <= 3.05e-33:
		tmp = -(z * t) / a
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.3e+251)
		tmp = Float64(y * Float64(x / a));
	elseif (x <= -3.05e+134)
		tmp = Float64(x * Float64(y / a));
	elseif (x <= -3.9e+54)
		tmp = Float64(y / Float64(a / x));
	elseif (x <= 3.05e-33)
		tmp = Float64(Float64(-Float64(z * t)) / a);
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.3e+251)
		tmp = y * (x / a);
	elseif (x <= -3.05e+134)
		tmp = x * (y / a);
	elseif (x <= -3.9e+54)
		tmp = y / (a / x);
	elseif (x <= 3.05e-33)
		tmp = -(z * t) / 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.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.3e+251], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.05e+134], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.9e+54], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.05e-33], N[((-N[(z * t), $MachinePrecision]) / a), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.29999999999999988e251

   1. Initial program 85.7%

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

   2. Taylor expanded in x around inf 78.3%

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

      1. associate-*r/ 78.9%

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

   4. Simplified 78.9%

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

   if -2.29999999999999988e251 < x < -3.04999999999999989e134

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf 78.3%

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

      1. associate-/l* 78.1%

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

      2. associate-/r/ 86.7%

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

   4. Applied egg-rr 86.7%

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

   if -3.04999999999999989e134 < x < -3.9000000000000003e54

   1. Initial program 74.6%

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

   2. Taylor expanded in x around inf 57.9%

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

      1. associate-/l* 83.2%

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

   4. Simplified 83.2%

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

   if -3.9000000000000003e54 < x < 3.0500000000000001e-33

   1. Initial program 94.9%

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

   2. Taylor expanded in x around 0 70.0%

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

      1. associate-*r/ 70.0%

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

      2. associate-*r* 70.0%

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

      3. neg-mul-1 70.0%

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

   4. Simplified 70.0%

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

   if 3.0500000000000001e-33 < x

   1. Initial program 92.1%

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

   2. Taylor expanded in x around inf 63.1%

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

      1. associate-*r/ 66.4%

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

   4. Simplified 66.4%

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

      1. associate-*r/ 63.1%

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

      2. *-commutative 63.1%

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

      3. associate-/l* 63.1%

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

   6. Applied egg-rr 63.1%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+251}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+54}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \leq 3.05 \cdot 10^{-33}:\\ \;\;\;\;\frac{-z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 93.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+286}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) -5e+286) (* x (/ y a)) (/ (- (* x y) (* z t)) a)))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+286) {
		tmp = x * (y / a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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) <= (-5d+286)) then
        tmp = x * (y / a)
    else
        tmp = ((x * y) - (z * t)) / a
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -5e+286) {
		tmp = x * (y / a);
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -5e+286:
		tmp = x * (y / a)
	else:
		tmp = ((x * y) - (z * t)) / a
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= -5e+286)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -5e+286)
		tmp = x * (y / a);
	else
		tmp = ((x * y) - (z * t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], -5e+286], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -5.0000000000000004e286

   1. Initial program 66.9%

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

   2. Taylor expanded in x around inf 70.7%

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

      1. associate-/l* 96.0%

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

      2. associate-/r/ 96.0%

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

   4. Applied egg-rr 96.0%

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

   if -5.0000000000000004e286 < (*.f64 x y)

   1. Initial program 94.8%

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

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+286}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 8: 51.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+250}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.5e+250) (* y (/ x a)) (* x (/ y a))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.5e+250) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 <= (-2.5d+250)) then
        tmp = y * (x / a)
    else
        tmp = x * (y / a)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.5e+250) {
		tmp = y * (x / a);
	} else {
		tmp = x * (y / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.5e+250:
		tmp = y * (x / a)
	else:
		tmp = x * (y / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.5e+250)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(x * Float64(y / a));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.5e+250)
		tmp = y * (x / a);
	else
		tmp = x * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.5e+250], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.5000000000000001e250

   1. Initial program 85.7%

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

   2. Taylor expanded in x around inf 78.3%

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

      1. associate-*r/ 78.9%

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

   4. Simplified 78.9%

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

   if -2.5000000000000001e250 < x

   1. Initial program 92.3%

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

   2. Taylor expanded in x around inf 50.5%

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

      1. associate-/l* 51.7%

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

      2. associate-/r/ 51.8%

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

   4. Applied egg-rr 51.8%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{+250}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 51.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+248}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.5e+248) (* y (/ x a)) (/ x (/ a y))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.5e+248) {
		tmp = y * (x / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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 <= (-7.5d+248)) then
        tmp = y * (x / a)
    else
        tmp = x / (a / y)
    end if
    code = tmp
end function

Java

assert x < y;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.5e+248) {
		tmp = y * (x / a);
	} else {
		tmp = x / (a / y);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.5e+248:
		tmp = y * (x / a)
	else:
		tmp = x / (a / y)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.5e+248)
		tmp = Float64(y * Float64(x / a));
	else
		tmp = Float64(x / Float64(a / y));
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.5e+248)
		tmp = y * (x / 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.
NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.5e+248], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.5000000000000004e248

   1. Initial program 80.4%

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

   2. Taylor expanded in x around inf 73.5%

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

      1. associate-*r/ 80.3%

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

   4. Simplified 80.3%

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

   if -7.5000000000000004e248 < x

   1. Initial program 92.7%

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

   2. Taylor expanded in x around inf 50.7%

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

      1. associate-*r/ 51.6%

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

   4. Simplified 51.6%

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

      1. associate-*r/ 50.7%

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

      2. *-commutative 50.7%

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

      3. associate-/l* 52.2%

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

   6. Applied egg-rr 52.2%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{+248}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 51.4% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: z and t 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);
assert(z < t);
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.
NOTE: z and t 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;
assert z < t;
public static double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Python

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

Julia

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

MATLAB

x, y = num2cell(sort([x, y])){:}
z, t = num2cell(sort([z, t])){:}
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.
NOTE: z and t 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 92.0%

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

2. Taylor expanded in x around inf 52.1%

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

   1. associate-*r/ 53.3%

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

4. Simplified 53.3%

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

5. Final simplification 53.3%

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

Developer target: 91.9% 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 2023257 
(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))