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

Percentage Accurate: 91.3% → 96.6%

Time: 7.2s

Alternatives: 9

Speedup: 0.7×

• 27.9% 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: 91.3% 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: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x}{\frac{a}{y}}\\ t_2 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_2 \leq -4 \cdot 10^{+249}:\\ \;\;\;\;t_1 - t \cdot \frac{z}{a}\\ \mathbf{elif}\;t_2 \leq 5 \cdot 10^{+261}:\\ \;\;\;\;\frac{t_2}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1 - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a 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 -4e+249)
     (- t_1 (* t (/ z a)))
     (if (<= t_2 5e+261) (/ t_2 a) (- t_1 (/ z (/ a t)))))))

C

assert(x < y && y < z && z < t && t < a);
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 <= -4e+249) {
		tmp = t_1 - (t * (z / a));
	} else if (t_2 <= 5e+261) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a 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 <= (-4d+249)) then
        tmp = t_1 - (t * (z / a))
    else if (t_2 <= 5d+261) then
        tmp = t_2 / a
    else
        tmp = t_1 - (z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -4e+249) {
		tmp = t_1 - (t * (z / a));
	} else if (t_2 <= 5e+261) {
		tmp = t_2 / a;
	} else {
		tmp = t_1 - (z / (a / t));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x / (a / y)
	t_2 = (x * y) - (z * t)
	tmp = 0
	if t_2 <= -4e+249:
		tmp = t_1 - (t * (z / a))
	elif t_2 <= 5e+261:
		tmp = t_2 / a
	else:
		tmp = t_1 - (z / (a / t))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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 <= -4e+249)
		tmp = Float64(t_1 - Float64(t * Float64(z / a)));
	elseif (t_2 <= 5e+261)
		tmp = Float64(t_2 / a);
	else
		tmp = Float64(t_1 - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= -4e+249)
		tmp = t_1 - (t * (z / a));
	elseif (t_2 <= 5e+261)
		tmp = t_2 / a;
	else
		tmp = t_1 - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a 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, -4e+249], N[(t$95$1 - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 5e+261], 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)) < -3.9999999999999997e249

   1. Initial program 79.8%

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

      1. div-sub 77.7%

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

      2. associate-/l* 85.7%

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

      3. associate-/l* 97.6%

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

   3. Applied egg-rr 97.6%

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

      1. associate-/r/ 97.7%

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

   5. Applied egg-rr 97.7%

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

   if -3.9999999999999997e249 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.0000000000000001e261

   1. Initial program 98.1%

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

   if 5.0000000000000001e261 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 74.2%

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

      1. div-sub 74.2%

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

      2. associate-/l* 89.5%

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

      3. associate-/l* 95.5%

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

   3. Applied egg-rr 95.5%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -4 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+261}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 2: 97.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{+273} \lor \neg \left(t_1 \leq 5 \cdot 10^{+283}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a 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 -1e+273) (not (<= t_1 5e+283)))
     (- (* x (/ y a)) (/ z (/ a t)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -1e+273) || !(t_1 <= 5e+283)) {
		tmp = (x * (y / a)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a 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 <= (-1d+273)) .or. (.not. (t_1 <= 5d+283))) then
        tmp = (x * (y / a)) - (z / (a / t))
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -1e+273) || !(t_1 <= 5e+283)) {
		tmp = (x * (y / a)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if (t_1 <= -1e+273) or not (t_1 <= 5e+283):
		tmp = (x * (y / a)) - (z / (a / t))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= -1e+273) || !(t_1 <= 5e+283))
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z / Float64(a / t)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if ((t_1 <= -1e+273) || ~((t_1 <= 5e+283)))
		tmp = (x * (y / a)) - (z / (a / t));
	else
		tmp = t_1 / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a 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, -1e+273], N[Not[LessEqual[t$95$1, 5e+283]], $MachinePrecision]], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -9.99999999999999945e272 or 5.0000000000000004e283 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 72.5%

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

      1. div-sub 71.0%

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

      2. associate-/l* 84.7%

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

      3. associate-/l* 96.9%

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

   3. Applied egg-rr 96.9%

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

      1. clear-num 96.9%

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

      2. associate-/r/ 96.9%

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

      3. clear-num 96.9%

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

   5. Applied egg-rr 96.9%

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

   if -9.99999999999999945e272 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.0000000000000004e283

   1. Initial program 98.2%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -1 \cdot 10^{+273} \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+283}\right):\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]

Alternative 3: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -4 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+283}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{z}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a 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 (<= t_1 -4e+249)
     (- (/ x (/ a y)) (* t (/ z a)))
     (if (<= t_1 5e+283) (/ t_1 a) (- (* x (/ y a)) (/ z (/ a t)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -4e+249) {
		tmp = (x / (a / y)) - (t * (z / a));
	} else if (t_1 <= 5e+283) {
		tmp = t_1 / a;
	} else {
		tmp = (x * (y / a)) - (z / (a / t));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a 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 <= (-4d+249)) then
        tmp = (x / (a / y)) - (t * (z / a))
    else if (t_1 <= 5d+283) then
        tmp = t_1 / a
    else
        tmp = (x * (y / a)) - (z / (a / t))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -4e+249) {
		tmp = (x / (a / y)) - (t * (z / a));
	} else if (t_1 <= 5e+283) {
		tmp = t_1 / a;
	} else {
		tmp = (x * (y / a)) - (z / (a / t));
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (x * y) - (z * t)
	tmp = 0
	if t_1 <= -4e+249:
		tmp = (x / (a / y)) - (t * (z / a))
	elif t_1 <= 5e+283:
		tmp = t_1 / a
	else:
		tmp = (x * (y / a)) - (z / (a / t))
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= -4e+249)
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(t * Float64(z / a)));
	elseif (t_1 <= 5e+283)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z / Float64(a / t)));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (x * y) - (z * t);
	tmp = 0.0;
	if (t_1 <= -4e+249)
		tmp = (x / (a / y)) - (t * (z / a));
	elseif (t_1 <= 5e+283)
		tmp = t_1 / a;
	else
		tmp = (x * (y / a)) - (z / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a 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[LessEqual[t$95$1, -4e+249], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+283], N[(t$95$1 / a), $MachinePrecision], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -3.9999999999999997e249

   1. Initial program 79.8%

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

      1. div-sub 77.7%

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

      2. associate-/l* 85.7%

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

      3. associate-/l* 97.6%

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

   3. Applied egg-rr 97.6%

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

      1. associate-/r/ 97.7%

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

   5. Applied egg-rr 97.7%

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

   if -3.9999999999999997e249 < (-.f64 (*.f64 x y) (*.f64 z t)) < 5.0000000000000004e283

   1. Initial program 98.2%

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

   if 5.0000000000000004e283 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 67.2%

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

      1. div-sub 67.2%

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

      2. associate-/l* 86.7%

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

      3. associate-/l* 96.5%

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

   3. Applied egg-rr 96.5%

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

      1. clear-num 96.4%

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

      2. associate-/r/ 96.4%

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

      3. clear-num 96.4%

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

   5. Applied egg-rr 96.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -4 \cdot 10^{+249}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - t \cdot \frac{z}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+283}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{z}{\frac{a}{t}}\\ \end{array} \]

Alternative 4: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := -\frac{t}{\frac{a}{z}}\\ t_2 := x \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -10000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (/ t (/ a z)))) (t_2 (* x (/ y a))))
   (if (<= (* x y) -10000000000000.0)
     t_2
     (if (<= (* x y) 5e-57)
       t_1
       (if (<= (* x y) 4e-13)
         (/ (* x y) a)
         (if (<= (* x y) 3e+46) t_1 t_2))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = -(t / (a / z));
	double t_2 = x * (y / a);
	double tmp;
	if ((x * y) <= -10000000000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 5e-57) {
		tmp = t_1;
	} else if ((x * y) <= 4e-13) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 3e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a 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 = -(t / (a / z))
    t_2 = x * (y / a)
    if ((x * y) <= (-10000000000000.0d0)) then
        tmp = t_2
    else if ((x * y) <= 5d-57) then
        tmp = t_1
    else if ((x * y) <= 4d-13) then
        tmp = (x * y) / a
    else if ((x * y) <= 3d+46) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -(t / (a / z));
	double t_2 = x * (y / a);
	double tmp;
	if ((x * y) <= -10000000000000.0) {
		tmp = t_2;
	} else if ((x * y) <= 5e-57) {
		tmp = t_1;
	} else if ((x * y) <= 4e-13) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 3e+46) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = -(t / (a / z))
	t_2 = x * (y / a)
	tmp = 0
	if (x * y) <= -10000000000000.0:
		tmp = t_2
	elif (x * y) <= 5e-57:
		tmp = t_1
	elif (x * y) <= 4e-13:
		tmp = (x * y) / a
	elif (x * y) <= 3e+46:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(-Float64(t / Float64(a / z)))
	t_2 = Float64(x * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -10000000000000.0)
		tmp = t_2;
	elseif (Float64(x * y) <= 5e-57)
		tmp = t_1;
	elseif (Float64(x * y) <= 4e-13)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 3e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = -(t / (a / z));
	t_2 = x * (y / a);
	tmp = 0.0;
	if ((x * y) <= -10000000000000.0)
		tmp = t_2;
	elseif ((x * y) <= 5e-57)
		tmp = t_1;
	elseif ((x * y) <= 4e-13)
		tmp = (x * y) / a;
	elseif ((x * y) <= 3e+46)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a 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])}, Block[{t$95$2 = N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -10000000000000.0], t$95$2, If[LessEqual[N[(x * y), $MachinePrecision], 5e-57], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 4e-13], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3e+46], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1e13 or 3.00000000000000023e46 < (*.f64 x y)

   1. Initial program 87.7%

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

   2. Taylor expanded in x around inf 73.3%

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

      1. associate-/l* 76.2%

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

      2. div-inv 76.1%

         \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{a}{y}}} \]

      3. *-commutative 76.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{y}} \cdot x} \]

      4. clear-num 76.4%

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

   4. Applied egg-rr 76.4%

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

   if -1e13 < (*.f64 x y) < 5.0000000000000002e-57 or 4.0000000000000001e-13 < (*.f64 x y) < 3.00000000000000023e46

   1. Initial program 94.0%

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

   2. Taylor expanded in x around 0 82.5%

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

      1. mul-1-neg 82.5%

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

      2. associate-/l* 79.8%

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

   4. Simplified 79.8%

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

   if 5.0000000000000002e-57 < (*.f64 x y) < 4.0000000000000001e-13

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 87.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -10000000000000:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;-\frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{+46}:\\ \;\;\;\;-\frac{t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -10000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;-\frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y a))))
   (if (<= (* x y) -10000000000000.0)
     t_1
     (if (<= (* x y) 5e-57)
       (- (/ t (/ a z)))
       (if (<= (* x y) 4e-13)
         (/ (* x y) a)
         (if (<= (* x y) 3e+46) (* z (/ (- t) a)) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / a);
	double tmp;
	if ((x * y) <= -10000000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e-57) {
		tmp = -(t / (a / z));
	} else if ((x * y) <= 4e-13) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 3e+46) {
		tmp = z * (-t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a 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 / a)
    if ((x * y) <= (-10000000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 5d-57) then
        tmp = -(t / (a / z))
    else if ((x * y) <= 4d-13) then
        tmp = (x * y) / a
    else if ((x * y) <= 3d+46) then
        tmp = z * (-t / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / a);
	double tmp;
	if ((x * y) <= -10000000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e-57) {
		tmp = -(t / (a / z));
	} else if ((x * y) <= 4e-13) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 3e+46) {
		tmp = z * (-t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * (y / a)
	tmp = 0
	if (x * y) <= -10000000000000.0:
		tmp = t_1
	elif (x * y) <= 5e-57:
		tmp = -(t / (a / z))
	elif (x * y) <= 4e-13:
		tmp = (x * y) / a
	elif (x * y) <= 3e+46:
		tmp = z * (-t / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -10000000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-57)
		tmp = Float64(-Float64(t / Float64(a / z)));
	elseif (Float64(x * y) <= 4e-13)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 3e+46)
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / a);
	tmp = 0.0;
	if ((x * y) <= -10000000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 5e-57)
		tmp = -(t / (a / z));
	elseif ((x * y) <= 4e-13)
		tmp = (x * y) / a;
	elseif ((x * y) <= 3e+46)
		tmp = z * (-t / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -10000000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-57], (-N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), If[LessEqual[N[(x * y), $MachinePrecision], 4e-13], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3e+46], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1e13 or 3.00000000000000023e46 < (*.f64 x y)

   1. Initial program 87.7%

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

   2. Taylor expanded in x around inf 73.3%

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

      1. associate-/l* 76.2%

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

      2. div-inv 76.1%

         \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{a}{y}}} \]

      3. *-commutative 76.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{y}} \cdot x} \]

      4. clear-num 76.4%

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

   4. Applied egg-rr 76.4%

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

   if -1e13 < (*.f64 x y) < 5.0000000000000002e-57

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. associate-/l* 79.0%

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

   4. Simplified 79.0%

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

   if 5.0000000000000002e-57 < (*.f64 x y) < 4.0000000000000001e-13

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 87.6%

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

   if 4.0000000000000001e-13 < (*.f64 x y) < 3.00000000000000023e46

   1. Initial program 99.5%

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

      1. div-sub 88.4%

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

      2. associate-/l* 88.4%

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

      3. associate-/l* 81.2%

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

   3. Applied egg-rr 81.2%

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

      1. clear-num 81.2%

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

      2. associate-/r/ 81.2%

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

      3. clear-num 81.2%

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

   5. Applied egg-rr 81.2%

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

   6. Taylor expanded in y around 0 89.0%

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

      1. associate-*r/ 89.0%

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

      2. mul-1-neg 89.0%

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

      3. *-commutative 89.0%

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

      4. distribute-rgt-neg-in 89.0%

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

      5. associate-*r/ 79.1%

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

   8. Simplified 79.1%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -10000000000000:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;-\frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 6: 74.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -10000000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ y a))))
   (if (<= (* x y) -10000000000000.0)
     t_1
     (if (<= (* x y) 5e-57)
       (/ (* t (- z)) a)
       (if (<= (* x y) 4e-13)
         (/ (* x y) a)
         (if (<= (* x y) 3e+46) (* z (/ (- t) a)) t_1))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / a);
	double tmp;
	if ((x * y) <= -10000000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e-57) {
		tmp = (t * -z) / a;
	} else if ((x * y) <= 4e-13) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 3e+46) {
		tmp = z * (-t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a 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 / a)
    if ((x * y) <= (-10000000000000.0d0)) then
        tmp = t_1
    else if ((x * y) <= 5d-57) then
        tmp = (t * -z) / a
    else if ((x * y) <= 4d-13) then
        tmp = (x * y) / a
    else if ((x * y) <= 3d+46) then
        tmp = z * (-t / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (y / a);
	double tmp;
	if ((x * y) <= -10000000000000.0) {
		tmp = t_1;
	} else if ((x * y) <= 5e-57) {
		tmp = (t * -z) / a;
	} else if ((x * y) <= 4e-13) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 3e+46) {
		tmp = z * (-t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = x * (y / a)
	tmp = 0
	if (x * y) <= -10000000000000.0:
		tmp = t_1
	elif (x * y) <= 5e-57:
		tmp = (t * -z) / a
	elif (x * y) <= 4e-13:
		tmp = (x * y) / a
	elif (x * y) <= 3e+46:
		tmp = z * (-t / a)
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -10000000000000.0)
		tmp = t_1;
	elseif (Float64(x * y) <= 5e-57)
		tmp = Float64(Float64(t * Float64(-z)) / a);
	elseif (Float64(x * y) <= 4e-13)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 3e+46)
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (y / a);
	tmp = 0.0;
	if ((x * y) <= -10000000000000.0)
		tmp = t_1;
	elseif ((x * y) <= 5e-57)
		tmp = (t * -z) / a;
	elseif ((x * y) <= 4e-13)
		tmp = (x * y) / a;
	elseif ((x * y) <= 3e+46)
		tmp = z * (-t / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -10000000000000.0], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 5e-57], N[(N[(t * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-13], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 3e+46], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1e13 or 3.00000000000000023e46 < (*.f64 x y)

   1. Initial program 87.7%

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

   2. Taylor expanded in x around inf 73.3%

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

      1. associate-/l* 76.2%

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

      2. div-inv 76.1%

         \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{a}{y}}} \]

      3. *-commutative 76.1%

         \[\leadsto \color{blue}{\frac{1}{\frac{a}{y}} \cdot x} \]

      4. clear-num 76.4%

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

   4. Applied egg-rr 76.4%

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

   if -1e13 < (*.f64 x y) < 5.0000000000000002e-57

   1. Initial program 93.5%

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

   2. Taylor expanded in x around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. distribute-rgt-neg-in 82.0%

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

   4. Simplified 82.0%

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

   if 5.0000000000000002e-57 < (*.f64 x y) < 4.0000000000000001e-13

   1. Initial program 99.1%

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

   2. Taylor expanded in x around inf 87.6%

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

   if 4.0000000000000001e-13 < (*.f64 x y) < 3.00000000000000023e46

   1. Initial program 99.5%

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

      1. div-sub 88.4%

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

      2. associate-/l* 88.4%

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

      3. associate-/l* 81.2%

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

   3. Applied egg-rr 81.2%

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

      1. clear-num 81.2%

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

      2. associate-/r/ 81.2%

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

      3. clear-num 81.2%

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

   5. Applied egg-rr 81.2%

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

   6. Taylor expanded in y around 0 89.0%

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

      1. associate-*r/ 89.0%

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

      2. mul-1-neg 89.0%

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

      3. *-commutative 89.0%

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

      4. distribute-rgt-neg-in 89.0%

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

      5. associate-*r/ 79.1%

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

   8. Simplified 79.1%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -10000000000000:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-57}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-13}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 3 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 93.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) 5e+285) (/ (- (* x y) (* z t)) a) (/ y (/ a x))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 5e+285) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a 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+285) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = y / (a / x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= 5e+285) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y / (a / x);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= 5e+285:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = y / (a / x)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= 5e+285)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(y / Float64(a / x));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= 5e+285)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = y / (a / x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], 5e+285], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5.00000000000000016e285

   1. Initial program 93.4%

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

   if 5.00000000000000016e285 < (*.f64 x y)

   1. Initial program 64.9%

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

   2. Taylor expanded in x around inf 70.2%

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

      1. associate-*l/ 99.9%

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

   4. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

         \[\leadsto y \cdot \color{blue}{\frac{1}{\frac{a}{x}}} \]

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \end{array} \]

Alternative 8: 50.9% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a 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 && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Fortran

NOTE: x, y, z, t, and a 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 && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return y * (x / a);
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, and a 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 91.3%

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

2. Taylor expanded in x around inf 48.0%

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

   1. associate-*l/ 50.7%

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

4. Simplified 50.7%

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

5. Final simplification 50.7%

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

Alternative 9: 51.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, and a 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 = x * (y / a)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.3%

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

2. Taylor expanded in x around inf 48.0%

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

   1. associate-/l* 49.0%

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

   2. div-inv 48.9%

      \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{a}{y}}} \]

   3. *-commutative 48.9%

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{y}} \cdot x} \]

   4. clear-num 49.0%

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

4. Applied egg-rr 49.0%

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

5. Final simplification 49.0%

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

Developer target: 91.4% 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 2023322 
(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))