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

Percentage Accurate: 91.1% → 93.2%

Time: 6.9s

Alternatives: 9

Speedup: 0.7×

• 27.8% 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: 91.1% 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: 93.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;t_1 \leq 2 \cdot 10^{+283}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{y}{\frac{a}{x}}\right)\\ \end{array} \end{array} \]

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)) a)))
   (if (<= t_1 2e+283) t_1 (fma -1.0 (/ t (/ a z)) (/ y (/ a x))))))

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)) / a;
	double tmp;
	if (t_1 <= 2e+283) {
		tmp = t_1;
	} else {
		tmp = fma(-1.0, (t / (a / z)), (y / (a / x)));
	}
	return tmp;
}

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
	tmp = 0.0
	if (t_1 <= 2e+283)
		tmp = t_1;
	else
		tmp = fma(-1.0, Float64(t / Float64(a / z)), Float64(y / Float64(a / x)));
	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[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+283], t$95$1, N[(-1.0 * N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision] + N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 1.99999999999999991e283

   1. Initial program 98.8%

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

   if 1.99999999999999991e283 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 72.5%

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

   2. Taylor expanded in x around 0 68.3%

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

      1. fma-def 68.3%

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

      2. associate-/l* 78.0%

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

      3. associate-/l* 91.5%

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

   4. Simplified 91.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{y}{\frac{a}{x}}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot t}{a} \leq 2 \cdot 10^{+283}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{t}{\frac{a}{z}}, \frac{y}{\frac{a}{x}}\right)\\ \end{array} \]

Alternative 2: 70.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-152} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-43}\right) \land x \cdot y \leq 5000:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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 y) -5e-114)
   (* y (/ x a))
   (if (or (<= (* x y) 1e-152)
           (and (not (<= (* x y) 5e-43)) (<= (* x y) 5000.0)))
     (/ (* 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 * y) <= -5e-114) {
		tmp = y * (x / a);
	} else if (((x * y) <= 1e-152) || (!((x * y) <= 5e-43) && ((x * y) <= 5000.0))) {
		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 * y) <= (-5d-114)) then
        tmp = y * (x / a)
    else if (((x * y) <= 1d-152) .or. (.not. ((x * y) <= 5d-43)) .and. ((x * y) <= 5000.0d0)) 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 * y) <= -5e-114) {
		tmp = y * (x / a);
	} else if (((x * y) <= 1e-152) || (!((x * y) <= 5e-43) && ((x * y) <= 5000.0))) {
		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 * y) <= -5e-114:
		tmp = y * (x / a)
	elif ((x * y) <= 1e-152) or (not ((x * y) <= 5e-43) and ((x * y) <= 5000.0)):
		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 (Float64(x * y) <= -5e-114)
		tmp = Float64(y * Float64(x / a));
	elseif ((Float64(x * y) <= 1e-152) || (!(Float64(x * y) <= 5e-43) && (Float64(x * y) <= 5000.0)))
		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 * y) <= -5e-114)
		tmp = y * (x / a);
	elseif (((x * y) <= 1e-152) || (~(((x * y) <= 5e-43)) && ((x * y) <= 5000.0)))
		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[N[(x * y), $MachinePrecision], -5e-114], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[N[(x * y), $MachinePrecision], 1e-152], And[N[Not[LessEqual[N[(x * y), $MachinePrecision], 5e-43]], $MachinePrecision], LessEqual[N[(x * y), $MachinePrecision], 5000.0]]], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -4.99999999999999989e-114

   1. Initial program 91.2%

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

   2. Taylor expanded in x around inf 75.9%

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

      1. associate-*r/ 77.0%

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

   4. Simplified 77.0%

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

   if -4.99999999999999989e-114 < (*.f64 x y) < 1.00000000000000007e-152 or 5.00000000000000019e-43 < (*.f64 x y) < 5e3

   1. Initial program 97.8%

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

   2. Taylor expanded in x around 0 87.6%

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

      1. associate-*r/ 87.6%

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

      2. associate-*r* 87.6%

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

      3. neg-mul-1 87.6%

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

   4. Simplified 87.6%

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

   if 1.00000000000000007e-152 < (*.f64 x y) < 5.00000000000000019e-43 or 5e3 < (*.f64 x y)

   1. Initial program 91.9%

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

   2. Taylor expanded in x around inf 81.2%

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

      1. associate-*r/ 78.3%

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

   4. Simplified 78.3%

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

      1. associate-*r/ 81.2%

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

      2. *-commutative 81.2%

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

      3. associate-/l* 82.3%

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

   6. Applied egg-rr 82.3%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{-152} \lor \neg \left(x \cdot y \leq 5 \cdot 10^{-43}\right) \land x \cdot y \leq 5000:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]

Alternative 3: 93.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;t_1 \leq 4 \cdot 10^{+260}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

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 y) (* z t)) a)))
   (if (<= t_1 4e+260) t_1 (- (/ x (/ a y)) (/ 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 * y) - (z * t)) / a;
	double tmp;
	if (t_1 <= 4e+260) {
		tmp = t_1;
	} else {
		tmp = (x / (a / y)) - (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) :: tmp
    t_1 = ((x * y) - (z * t)) / a
    if (t_1 <= 4d+260) then
        tmp = t_1
    else
        tmp = (x / (a / y)) - (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 * y) - (z * t)) / a;
	double tmp;
	if (t_1 <= 4e+260) {
		tmp = t_1;
	} else {
		tmp = (x / (a / y)) - (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 * y) - (z * t)) / a
	tmp = 0
	if t_1 <= 4e+260:
		tmp = t_1
	else:
		tmp = (x / (a / y)) - (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(Float64(Float64(x * y) - Float64(z * t)) / a)
	tmp = 0.0
	if (t_1 <= 4e+260)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / Float64(a / y)) - 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 * y) - (z * t)) / a;
	tmp = 0.0;
	if (t_1 <= 4e+260)
		tmp = t_1;
	else
		tmp = (x / (a / y)) - (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[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, 4e+260], t$95$1, N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 4.00000000000000026e260

   1. Initial program 98.8%

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

   if 4.00000000000000026e260 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 74.1%

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

      1. div-sub 70.1%

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

      2. associate-/l* 82.9%

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

      3. associate-/l* 90.2%

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

   3. Applied egg-rr 90.2%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot t}{a} \leq 4 \cdot 10^{+260}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 4: 66.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \frac{t}{a}\\ \mathbf{if}\;z \leq -1 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -225 \lor \neg \left(z \leq 5.7 \cdot 10^{-21}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (- z) (/ t a))))
   (if (<= z -1e+158)
     t_1
     (if (<= z -7e+122)
       (/ y (/ a x))
       (if (or (<= z -225.0) (not (<= z 5.7e-21))) t_1 (/ (* x y) a))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -z * (t / a);
	double tmp;
	if (z <= -1e+158) {
		tmp = t_1;
	} else if (z <= -7e+122) {
		tmp = y / (a / x);
	} else if ((z <= -225.0) || !(z <= 5.7e-21)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -z * (t / a)
    if (z <= (-1d+158)) then
        tmp = t_1
    else if (z <= (-7d+122)) then
        tmp = y / (a / x)
    else if ((z <= (-225.0d0)) .or. (.not. (z <= 5.7d-21))) then
        tmp = t_1
    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 t_1 = -z * (t / a);
	double tmp;
	if (z <= -1e+158) {
		tmp = t_1;
	} else if (z <= -7e+122) {
		tmp = y / (a / x);
	} else if ((z <= -225.0) || !(z <= 5.7e-21)) {
		tmp = t_1;
	} 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):
	t_1 = -z * (t / a)
	tmp = 0
	if z <= -1e+158:
		tmp = t_1
	elif z <= -7e+122:
		tmp = y / (a / x)
	elif (z <= -225.0) or not (z <= 5.7e-21):
		tmp = t_1
	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)
	t_1 = Float64(Float64(-z) * Float64(t / a))
	tmp = 0.0
	if (z <= -1e+158)
		tmp = t_1;
	elseif (z <= -7e+122)
		tmp = Float64(y / Float64(a / x));
	elseif ((z <= -225.0) || !(z <= 5.7e-21))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * 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)
	t_1 = -z * (t / a);
	tmp = 0.0;
	if (z <= -1e+158)
		tmp = t_1;
	elseif (z <= -7e+122)
		tmp = y / (a / x);
	elseif ((z <= -225.0) || ~((z <= 5.7e-21)))
		tmp = t_1;
	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_] := Block[{t$95$1 = N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+158], t$95$1, If[LessEqual[z, -7e+122], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -225.0], N[Not[LessEqual[z, 5.7e-21]], $MachinePrecision]], t$95$1, N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999953e157 or -7.00000000000000028e122 < z < -225 or 5.6999999999999996e-21 < z

   1. Initial program 90.9%

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

      1. div-sub 86.9%

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

      2. associate-/l* 86.0%

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

      3. associate-/l* 86.8%

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

   3. Applied egg-rr 86.8%

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

   4. Taylor expanded in x around 0 64.4%

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

      1. associate-*l/ 64.7%

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

      2. associate-*r* 64.7%

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

      3. neg-mul-1 64.7%

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

      4. *-commutative 64.7%

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

   6. Simplified 64.7%

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

   if -9.99999999999999953e157 < z < -7.00000000000000028e122

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 75.6%

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

      1. associate-/l* 75.6%

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

   4. Simplified 75.6%

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

   if -225 < z < 5.6999999999999996e-21

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 77.2%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+158}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq -7 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -225 \lor \neg \left(z \leq 5.7 \cdot 10^{-21}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]

Alternative 5: 67.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \left(-t\right) \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -9.8 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -0.41 \lor \neg \left(z \leq 2.55 \cdot 10^{-104}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* (- t) (/ z a))))
   (if (<= z -9.8e+157)
     t_1
     (if (<= z -2.2e+122)
       (/ y (/ a x))
       (if (or (<= z -0.41) (not (<= z 2.55e-104))) t_1 (/ (* x y) a))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -t * (z / a);
	double tmp;
	if (z <= -9.8e+157) {
		tmp = t_1;
	} else if (z <= -2.2e+122) {
		tmp = y / (a / x);
	} else if ((z <= -0.41) || !(z <= 2.55e-104)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -t * (z / a)
    if (z <= (-9.8d+157)) then
        tmp = t_1
    else if (z <= (-2.2d+122)) then
        tmp = y / (a / x)
    else if ((z <= (-0.41d0)) .or. (.not. (z <= 2.55d-104))) then
        tmp = t_1
    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 t_1 = -t * (z / a);
	double tmp;
	if (z <= -9.8e+157) {
		tmp = t_1;
	} else if (z <= -2.2e+122) {
		tmp = y / (a / x);
	} else if ((z <= -0.41) || !(z <= 2.55e-104)) {
		tmp = t_1;
	} 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):
	t_1 = -t * (z / a)
	tmp = 0
	if z <= -9.8e+157:
		tmp = t_1
	elif z <= -2.2e+122:
		tmp = y / (a / x)
	elif (z <= -0.41) or not (z <= 2.55e-104):
		tmp = t_1
	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)
	t_1 = Float64(Float64(-t) * Float64(z / a))
	tmp = 0.0
	if (z <= -9.8e+157)
		tmp = t_1;
	elseif (z <= -2.2e+122)
		tmp = Float64(y / Float64(a / x));
	elseif ((z <= -0.41) || !(z <= 2.55e-104))
		tmp = t_1;
	else
		tmp = Float64(Float64(x * 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)
	t_1 = -t * (z / a);
	tmp = 0.0;
	if (z <= -9.8e+157)
		tmp = t_1;
	elseif (z <= -2.2e+122)
		tmp = y / (a / x);
	elseif ((z <= -0.41) || ~((z <= 2.55e-104)))
		tmp = t_1;
	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_] := Block[{t$95$1 = N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.8e+157], t$95$1, If[LessEqual[z, -2.2e+122], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -0.41], N[Not[LessEqual[z, 2.55e-104]], $MachinePrecision]], t$95$1, N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.8000000000000003e157 or -2.1999999999999999e122 < z < -0.409999999999999976 or 2.54999999999999996e-104 < z

   1. Initial program 92.0%

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

   2. Taylor expanded in x around 0 63.5%

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

      1. associate-*r/ 63.5%

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

      2. mul-1-neg 63.5%

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

      3. distribute-rgt-neg-out 63.5%

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

      4. *-commutative 63.5%

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

      5. associate-/l* 63.0%

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

      6. associate-/r/ 65.1%

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

   4. Simplified 65.1%

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

   if -9.8000000000000003e157 < z < -2.1999999999999999e122

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 75.6%

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

      1. associate-/l* 75.6%

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

   4. Simplified 75.6%

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

   if -0.409999999999999976 < z < 2.54999999999999996e-104

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 80.6%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.8 \cdot 10^{+157}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -0.41 \lor \neg \left(z \leq 2.55 \cdot 10^{-104}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]

Alternative 6: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{t}{\frac{-a}{z}}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -355:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.44 \cdot 10^{-98}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \end{array} \]

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 (/ t (/ (- a) z))))
   (if (<= z -1.2e+158)
     t_1
     (if (<= z -7.5e+122)
       (/ y (/ a x))
       (if (<= z -355.0)
         t_1
         (if (<= z 1.44e-98) (/ (* x y) a) (* (- t) (/ z a))))))))

C

assert(x < y);
assert(z < t);
double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (-a / z);
	double tmp;
	if (z <= -1.2e+158) {
		tmp = t_1;
	} else if (z <= -7.5e+122) {
		tmp = y / (a / x);
	} else if (z <= -355.0) {
		tmp = t_1;
	} else if (z <= 1.44e-98) {
		tmp = (x * y) / a;
	} else {
		tmp = -t * (z / 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 = t / (-a / z)
    if (z <= (-1.2d+158)) then
        tmp = t_1
    else if (z <= (-7.5d+122)) then
        tmp = y / (a / x)
    else if (z <= (-355.0d0)) then
        tmp = t_1
    else if (z <= 1.44d-98) then
        tmp = (x * y) / a
    else
        tmp = -t * (z / 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 = t / (-a / z);
	double tmp;
	if (z <= -1.2e+158) {
		tmp = t_1;
	} else if (z <= -7.5e+122) {
		tmp = y / (a / x);
	} else if (z <= -355.0) {
		tmp = t_1;
	} else if (z <= 1.44e-98) {
		tmp = (x * y) / a;
	} else {
		tmp = -t * (z / a);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[z, t] = sort([z, t])
def code(x, y, z, t, a):
	t_1 = t / (-a / z)
	tmp = 0
	if z <= -1.2e+158:
		tmp = t_1
	elif z <= -7.5e+122:
		tmp = y / (a / x)
	elif z <= -355.0:
		tmp = t_1
	elif z <= 1.44e-98:
		tmp = (x * y) / a
	else:
		tmp = -t * (z / a)
	return tmp

Julia

x, y = sort([x, y])
z, t = sort([z, t])
function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(Float64(-a) / z))
	tmp = 0.0
	if (z <= -1.2e+158)
		tmp = t_1;
	elseif (z <= -7.5e+122)
		tmp = Float64(y / Float64(a / x));
	elseif (z <= -355.0)
		tmp = t_1;
	elseif (z <= 1.44e-98)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(Float64(-t) * Float64(z / 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 = t / (-a / z);
	tmp = 0.0;
	if (z <= -1.2e+158)
		tmp = t_1;
	elseif (z <= -7.5e+122)
		tmp = y / (a / x);
	elseif (z <= -355.0)
		tmp = t_1;
	elseif (z <= 1.44e-98)
		tmp = (x * y) / a;
	else
		tmp = -t * (z / 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[(t / N[((-a) / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+158], t$95$1, If[LessEqual[z, -7.5e+122], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -355.0], t$95$1, If[LessEqual[z, 1.44e-98], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.20000000000000004e158 or -7.5000000000000002e122 < z < -355

   1. Initial program 88.5%

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

      1. div-sub 86.8%

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

      2. associate-/l* 88.2%

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

      3. associate-/l* 93.1%

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

   3. Applied egg-rr 93.1%

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

   4. Taylor expanded in x around 0 71.1%

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

      1. associate-*l/ 74.4%

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

      2. associate-*r* 74.4%

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

      3. neg-mul-1 74.4%

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

      4. *-commutative 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in z around 0 71.1%

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

      1. associate-*r/ 71.1%

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

      2. *-commutative 71.1%

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

      3. neg-mul-1 71.1%

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

      4. distribute-rgt-neg-out 71.1%

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

      5. associate-/l* 74.3%

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

      6. remove-double-neg 74.3%

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

      7. distribute-frac-neg 74.3%

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

      8. neg-mul-1 74.3%

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

      9. neg-mul-1 74.3%

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

      10. times-frac 74.3%

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

      11. metadata-eval 74.3%

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

      12. *-lft-identity 74.3%

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

      13. distribute-frac-neg 74.3%

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

      14. associate-/l* 71.1%

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

      15. *-commutative 71.1%

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

      16. associate-/l* 75.2%

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

   9. Simplified 75.2%

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

   if -1.20000000000000004e158 < z < -7.5000000000000002e122

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 75.6%

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

      1. associate-/l* 75.6%

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

   4. Simplified 75.6%

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

   if -355 < z < 1.44e-98

   1. Initial program 96.1%

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

   2. Taylor expanded in x around inf 79.8%

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

   if 1.44e-98 < z

   1. Initial program 94.3%

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

   2. Taylor expanded in x around 0 57.7%

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

      1. associate-*r/ 57.7%

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

      2. mul-1-neg 57.7%

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

      3. distribute-rgt-neg-out 57.7%

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

      4. *-commutative 57.7%

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

      5. associate-/l* 54.7%

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

      6. associate-/r/ 58.4%

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

   4. Simplified 58.4%

      \[\leadsto \color{blue}{\frac{-z}{a} \cdot t} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+158}:\\ \;\;\;\;\frac{t}{\frac{-a}{z}}\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;z \leq -355:\\ \;\;\;\;\frac{t}{\frac{-a}{z}}\\ \mathbf{elif}\;z \leq 1.44 \cdot 10^{-98}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{z}{a}\\ \end{array} \]

Alternative 7: 93.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+294}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

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) -2e+294) (/ y (/ a x)) (/ (- (* 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) <= -2e+294) {
		tmp = y / (a / x);
	} 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) <= (-2d+294)) then
        tmp = y / (a / x)
    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) <= -2e+294) {
		tmp = y / (a / x);
	} 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) <= -2e+294:
		tmp = y / (a / x)
	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) <= -2e+294)
		tmp = Float64(y / Float64(a / x));
	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) <= -2e+294)
		tmp = y / (a / x);
	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], -2e+294], N[(y / N[(a / x), $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) < -2.00000000000000013e294

   1. Initial program 69.6%

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

   2. Taylor expanded in x around inf 78.7%

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

      1. associate-/l* 95.7%

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

   4. Simplified 95.7%

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

   if -2.00000000000000013e294 < (*.f64 x y)

   1. Initial program 96.2%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+294}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 8: 51.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -0.007:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \end{array} \]

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 (<= z -0.007) (* x (/ y 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 (z <= -0.007) {
		tmp = x * (y / 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 (z <= (-0.007d0)) then
        tmp = x * (y / 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 (z <= -0.007) {
		tmp = x * (y / 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 z <= -0.007:
		tmp = x * (y / 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 (z <= -0.007)
		tmp = Float64(x * Float64(y / a));
	else
		tmp = Float64(Float64(x * 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 (z <= -0.007)
		tmp = x * (y / 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[z, -0.007], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.00700000000000000015

   1. Initial program 90.0%

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

   2. Taylor expanded in x around inf 33.0%

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

      1. associate-*l/ 34.2%

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

   4. Applied egg-rr 34.2%

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

   if -0.00700000000000000015 < z

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 66.2%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.007:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \end{array} \]

Alternative 9: 52.0% 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 93.9%

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

2. Taylor expanded in x around inf 57.4%

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

   1. associate-*r/ 57.4%

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

4. Simplified 57.4%

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

5. Final simplification 57.4%

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

Developer target: 90.9% 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 2023195 
(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))