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

Percentage Accurate: 91.7% → 97.4%

Time: 8.8s

Alternatives: 11

Speedup: 0.5×

• 28.7% 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: 91.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ t_2 := \frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+304}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+273}:\\ \;\;\;\;\frac{t_1}{a}\\ \mathbf{elif}\;t_1 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot \mathsf{fma}\left(\frac{x}{t}, \frac{y}{z}, -1\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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))) (t_2 (- (/ x (/ a y)) (/ z (/ a t)))))
   (if (<= t_1 -2e+304)
     t_2
     (if (<= t_1 2e+273)
       (/ t_1 a)
       (if (<= t_1 INFINITY)
         t_2
         (* (/ t a) (* z (fma (/ x t) (/ y z) -1.0))))))))

C

assert(x < y && y < z && z < t && t < a);
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 t_2 = (x / (a / y)) - (z / (a / t));
	double tmp;
	if (t_1 <= -2e+304) {
		tmp = t_2;
	} else if (t_1 <= 2e+273) {
		tmp = t_1 / a;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (t / a) * (z * fma((x / t), (y / z), -1.0));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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))
	t_2 = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)))
	tmp = 0.0
	if (t_1 <= -2e+304)
		tmp = t_2;
	elseif (t_1 <= 2e+273)
		tmp = Float64(t_1 / a);
	elseif (t_1 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(t / a) * Float64(z * fma(Float64(x / t), Float64(y / z), -1.0)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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]}, Block[{t$95$2 = N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+304], t$95$2, If[LessEqual[t$95$1, 2e+273], N[(t$95$1 / a), $MachinePrecision], If[LessEqual[t$95$1, Infinity], t$95$2, N[(N[(t / a), $MachinePrecision] * N[(z * N[(N[(x / t), $MachinePrecision] * N[(y / z), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.9999999999999999e304 or 1.99999999999999989e273 < (-.f64 (*.f64 x y) (*.f64 z t)) < +inf.0

   1. Initial program 68.7%

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

      1. div-sub 68.7%

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

      2. associate-/l* 81.4%

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

      3. associate-/l* 98.3%

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

   4. Applied egg-rr 98.3%

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

   if -1.9999999999999999e304 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.99999999999999989e273

   1. Initial program 98.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

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

   1. Initial program 0.0%

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

      1. div-sub 0.0%

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

      2. associate-/l* 14.3%

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

      3. associate-/l* 28.6%

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

   4. Applied egg-rr 28.6%

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

      1. associate-/l* 14.3%

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

      2. clear-num 14.3%

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

      3. frac-sub 14.3%

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

      4. associate-/l/ 0.0%

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

      5. *-commutative 0.0%

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

      6. *-un-lft-identity 0.0%

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

      7. associate-/l/ 0.0%

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

   6. Applied egg-rr 0.0%

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

   7. Taylor expanded in a around 0 0.0%

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

      1. associate-/l* 0.0%

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

      2. associate-/r/ 0.0%

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

      3. times-frac 100.0%

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

      4. fma-neg 100.0%

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

      5. metadata-eval 100.0%

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

   9. Simplified 100.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 2 \cdot 10^{+273}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq \infty:\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(z \cdot \mathsf{fma}\left(\frac{x}{t}, \frac{y}{z}, -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+304} \lor \neg \left(t_1 \leq 2 \cdot 10^{+273}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -2e+304) (not (<= t_1 2e+273)))
     (- (/ x (/ a y)) (* z (/ t a)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
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 <= -2e+304) || !(t_1 <= 2e+273)) {
		tmp = (x / (a / y)) - (z * (t / a));
	} 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.
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 <= (-2d+304)) .or. (.not. (t_1 <= 2d+273))) then
        tmp = (x / (a / y)) - (z * (t / a))
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -2e+304) || !(t_1 <= 2e+273)) {
		tmp = (x / (a / y)) - (z * (t / a));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[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 <= -2e+304) or not (t_1 <= 2e+273):
		tmp = (x / (a / y)) - (z * (t / a))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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 <= -2e+304) || !(t_1 <= 2e+273))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z * Float64(t / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= -2e+304) || ~((t_1 <= 2e+273)))
		tmp = (x / (a / y)) - (z * (t / a));
	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.
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, -2e+304], N[Not[LessEqual[t$95$1, 2e+273]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.9999999999999999e304 or 1.99999999999999989e273 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 62.1%

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

      1. div-sub 62.1%

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

      2. associate-/l* 75.0%

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

      3. associate-/l* 91.6%

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

   4. Applied egg-rr 91.6%

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

      1. div-inv 91.6%

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

      2. clear-num 91.7%

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

      3. *-commutative 91.7%

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

   6. Applied egg-rr 91.7%

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

   if -1.9999999999999999e304 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.99999999999999989e273

   1. Initial program 98.8%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -2 \cdot 10^{+304} \lor \neg \left(x \cdot y - z \cdot t \leq 2 \cdot 10^{+273}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - z \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{+304} \lor \neg \left(t_1 \leq 2 \cdot 10^{+273}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -2e+304) (not (<= t_1 2e+273)))
     (- (/ x (/ a y)) (/ z (/ a t)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
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 <= -2e+304) || !(t_1 <= 2e+273)) {
		tmp = (x / (a / y)) - (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.
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 <= (-2d+304)) .or. (.not. (t_1 <= 2d+273))) then
        tmp = (x / (a / y)) - (z / (a / t))
    else
        tmp = t_1 / a
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 <= -2e+304) || !(t_1 <= 2e+273)) {
		tmp = (x / (a / y)) - (z / (a / t));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[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 <= -2e+304) or not (t_1 <= 2e+273):
		tmp = (x / (a / y)) - (z / (a / t))
	else:
		tmp = t_1 / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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 <= -2e+304) || !(t_1 <= 2e+273))
		tmp = Float64(Float64(x / Float64(a / y)) - Float64(z / Float64(a / t)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 <= -2e+304) || ~((t_1 <= 2e+273)))
		tmp = (x / (a / y)) - (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.
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, -2e+304], N[Not[LessEqual[t$95$1, 2e+273]], $MachinePrecision]], N[(N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -1.9999999999999999e304 or 1.99999999999999989e273 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 62.1%

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

      1. div-sub 62.1%

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

      2. associate-/l* 75.0%

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

      3. associate-/l* 91.6%

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

   4. Applied egg-rr 91.6%

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

   if -1.9999999999999999e304 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1.99999999999999989e273

   1. Initial program 98.8%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -2 \cdot 10^{+304} \lor \neg \left(x \cdot y - z \cdot t \leq 2 \cdot 10^{+273}\right):\\ \;\;\;\;\frac{x}{\frac{a}{y}} - \frac{z}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{t}{a} \cdot \left(-z\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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))))
   (if (<= (* x y) -2e+107)
     (/ x (/ a y))
     (if (<= (* x y) -2e-8)
       t_1
       (if (<= (* x y) -2e-25)
         (/ (* x y) a)
         (if (<= (* x y) 0.0)
           (/ (- t) (/ a z))
           (if (<= (* x y) 5e+62) t_1 (* y (/ x a)))))))))

C

assert(x < y && y < z && z < t && t < a);
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 tmp;
	if ((x * y) <= -2e+107) {
		tmp = x / (a / y);
	} else if ((x * y) <= -2e-8) {
		tmp = t_1;
	} else if ((x * y) <= -2e-25) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 0.0) {
		tmp = -t / (a / z);
	} else if ((x * y) <= 5e+62) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = (t / a) * -z
    if ((x * y) <= (-2d+107)) then
        tmp = x / (a / y)
    else if ((x * y) <= (-2d-8)) then
        tmp = t_1
    else if ((x * y) <= (-2d-25)) then
        tmp = (x * y) / a
    else if ((x * y) <= 0.0d0) then
        tmp = -t / (a / z)
    else if ((x * y) <= 5d+62) then
        tmp = t_1
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 tmp;
	if ((x * y) <= -2e+107) {
		tmp = x / (a / y);
	} else if ((x * y) <= -2e-8) {
		tmp = t_1;
	} else if ((x * y) <= -2e-25) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 0.0) {
		tmp = -t / (a / z);
	} else if ((x * y) <= 5e+62) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (t / a) * -z
	tmp = 0
	if (x * y) <= -2e+107:
		tmp = x / (a / y)
	elif (x * y) <= -2e-8:
		tmp = t_1
	elif (x * y) <= -2e-25:
		tmp = (x * y) / a
	elif (x * y) <= 0.0:
		tmp = -t / (a / z)
	elif (x * y) <= 5e+62:
		tmp = t_1
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / a) * Float64(-z))
	tmp = 0.0
	if (Float64(x * y) <= -2e+107)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= -2e-8)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e-25)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 0.0)
		tmp = Float64(Float64(-t) / Float64(a / z));
	elseif (Float64(x * y) <= 5e+62)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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;
	tmp = 0.0;
	if ((x * y) <= -2e+107)
		tmp = x / (a / y);
	elseif ((x * y) <= -2e-8)
		tmp = t_1;
	elseif ((x * y) <= -2e-25)
		tmp = (x * y) / a;
	elseif ((x * y) <= 0.0)
		tmp = -t / (a / z);
	elseif ((x * y) <= 5e+62)
		tmp = t_1;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(t / a), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+107], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-8], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e-25], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.0], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+62], t$95$1, N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.9999999999999999e107

   1. Initial program 76.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.5%

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

      1. associate-*l/ 91.2%

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

   5. Simplified 91.2%

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

      1. associate-/r/ 91.2%

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

   7. Applied egg-rr 91.2%

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

   if -1.9999999999999999e107 < (*.f64 x y) < -2e-8 or 0.0 < (*.f64 x y) < 5.00000000000000029e62

   1. Initial program 94.5%

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

      1. div-sub 94.5%

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

      2. associate-/l* 85.6%

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

      3. associate-/l* 87.0%

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

   4. Applied egg-rr 87.0%

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

      1. clear-num 87.0%

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

      2. inv-pow 87.0%

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

      3. associate-/l/ 85.5%

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

   6. Applied egg-rr 85.5%

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

      1. unpow-1 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-/r* 87.0%

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

   8. Simplified 87.0%

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

   9. Taylor expanded in x around 0 68.0%

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

       1. mul-1-neg 68.0%

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

       2. associate-*l/ 69.0%

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

       3. *-commutative 69.0%

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

       4. distribute-lft-neg-out 69.0%

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

   11. Simplified 69.0%

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

   if -2e-8 < (*.f64 x y) < -2.00000000000000008e-25

   1. Initial program 100.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 93.2%

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

   if -2.00000000000000008e-25 < (*.f64 x y) < 0.0

   1. Initial program 93.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. associate-/l* 78.2%

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

   5. Simplified 78.2%

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

   if 5.00000000000000029e62 < (*.f64 x y)

   1. Initial program 78.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.4%

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

      1. associate-*l/ 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{t}{a} \cdot \left(-z\right)\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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))))
   (if (<= (* x y) -2e+107)
     (/ x (/ a y))
     (if (<= (* x y) -2e-8)
       t_1
       (if (<= (* x y) -2e-25)
         (/ (* x y) a)
         (if (<= (* x y) 0.0)
           (* t (/ (- z) a))
           (if (<= (* x y) 5e+62) t_1 (* y (/ x a)))))))))

C

assert(x < y && y < z && z < t && t < a);
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 tmp;
	if ((x * y) <= -2e+107) {
		tmp = x / (a / y);
	} else if ((x * y) <= -2e-8) {
		tmp = t_1;
	} else if ((x * y) <= -2e-25) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 0.0) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 5e+62) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 = (t / a) * -z
    if ((x * y) <= (-2d+107)) then
        tmp = x / (a / y)
    else if ((x * y) <= (-2d-8)) then
        tmp = t_1
    else if ((x * y) <= (-2d-25)) then
        tmp = (x * y) / a
    else if ((x * y) <= 0.0d0) then
        tmp = t * (-z / a)
    else if ((x * y) <= 5d+62) then
        tmp = t_1
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 tmp;
	if ((x * y) <= -2e+107) {
		tmp = x / (a / y);
	} else if ((x * y) <= -2e-8) {
		tmp = t_1;
	} else if ((x * y) <= -2e-25) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 0.0) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 5e+62) {
		tmp = t_1;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = (t / a) * -z
	tmp = 0
	if (x * y) <= -2e+107:
		tmp = x / (a / y)
	elif (x * y) <= -2e-8:
		tmp = t_1
	elif (x * y) <= -2e-25:
		tmp = (x * y) / a
	elif (x * y) <= 0.0:
		tmp = t * (-z / a)
	elif (x * y) <= 5e+62:
		tmp = t_1
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / a) * Float64(-z))
	tmp = 0.0
	if (Float64(x * y) <= -2e+107)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= -2e-8)
		tmp = t_1;
	elseif (Float64(x * y) <= -2e-25)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 0.0)
		tmp = Float64(t * Float64(Float64(-z) / a));
	elseif (Float64(x * y) <= 5e+62)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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;
	tmp = 0.0;
	if ((x * y) <= -2e+107)
		tmp = x / (a / y);
	elseif ((x * y) <= -2e-8)
		tmp = t_1;
	elseif ((x * y) <= -2e-25)
		tmp = (x * y) / a;
	elseif ((x * y) <= 0.0)
		tmp = t * (-z / a);
	elseif ((x * y) <= 5e+62)
		tmp = t_1;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(t / a), $MachinePrecision] * (-z)), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+107], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-8], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], -2e-25], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 0.0], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+62], t$95$1, N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.9999999999999999e107

   1. Initial program 76.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.5%

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

      1. associate-*l/ 91.2%

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

   5. Simplified 91.2%

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

      1. associate-/r/ 91.2%

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

   7. Applied egg-rr 91.2%

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

   if -1.9999999999999999e107 < (*.f64 x y) < -2e-8 or 0.0 < (*.f64 x y) < 5.00000000000000029e62

   1. Initial program 94.5%

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

      1. div-sub 94.5%

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

      2. associate-/l* 85.6%

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

      3. associate-/l* 87.0%

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

   4. Applied egg-rr 87.0%

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

      1. clear-num 87.0%

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

      2. inv-pow 87.0%

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

      3. associate-/l/ 85.5%

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

   6. Applied egg-rr 85.5%

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

      1. unpow-1 85.5%

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

      2. *-commutative 85.5%

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

      3. associate-/r* 87.0%

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

   8. Simplified 87.0%

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

   9. Taylor expanded in x around 0 68.0%

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

       1. mul-1-neg 68.0%

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

       2. associate-*l/ 69.0%

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

       3. *-commutative 69.0%

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

       4. distribute-lft-neg-out 69.0%

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

   11. Simplified 69.0%

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

   if -2e-8 < (*.f64 x y) < -2.00000000000000008e-25

   1. Initial program 100.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 93.2%

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

   if -2.00000000000000008e-25 < (*.f64 x y) < 0.0

   1. Initial program 93.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.5%

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

      1. *-commutative 80.5%

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

      2. associate-*l/ 78.7%

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

      3. associate-*r* 78.7%

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

      4. neg-mul-1 78.7%

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

      5. distribute-frac-neg 78.7%

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

   5. Simplified 78.7%

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

   if 5.00000000000000029e62 < (*.f64 x y)

   1. Initial program 78.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.4%

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

      1. associate-*l/ 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-25}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 0:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-38}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -2e+107)
   (/ x (/ a y))
   (if (<= (* x y) -2e-8)
     (* (/ t a) (- z))
     (if (<= (* x y) -5e-38)
       (/ y (/ a x))
       (if (<= (* x y) 5e+62) (/ (* z (- t)) a) (* y (/ x a)))))))

C

assert(x < y && y < z && z < t && t < a);
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) <= -2e+107) {
		tmp = x / (a / y);
	} else if ((x * y) <= -2e-8) {
		tmp = (t / a) * -z;
	} else if ((x * y) <= -5e-38) {
		tmp = y / (a / x);
	} else if ((x * y) <= 5e+62) {
		tmp = (z * -t) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) <= (-2d+107)) then
        tmp = x / (a / y)
    else if ((x * y) <= (-2d-8)) then
        tmp = (t / a) * -z
    else if ((x * y) <= (-5d-38)) then
        tmp = y / (a / x)
    else if ((x * y) <= 5d+62) then
        tmp = (z * -t) / a
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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) <= -2e+107) {
		tmp = x / (a / y);
	} else if ((x * y) <= -2e-8) {
		tmp = (t / a) * -z;
	} else if ((x * y) <= -5e-38) {
		tmp = y / (a / x);
	} else if ((x * y) <= 5e+62) {
		tmp = (z * -t) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+107:
		tmp = x / (a / y)
	elif (x * y) <= -2e-8:
		tmp = (t / a) * -z
	elif (x * y) <= -5e-38:
		tmp = y / (a / x)
	elif (x * y) <= 5e+62:
		tmp = (z * -t) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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) <= -2e+107)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= -2e-8)
		tmp = Float64(Float64(t / a) * Float64(-z));
	elseif (Float64(x * y) <= -5e-38)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 5e+62)
		tmp = Float64(Float64(z * Float64(-t)) / a);
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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) <= -2e+107)
		tmp = x / (a / y);
	elseif ((x * y) <= -2e-8)
		tmp = (t / a) * -z;
	elseif ((x * y) <= -5e-38)
		tmp = y / (a / x);
	elseif ((x * y) <= 5e+62)
		tmp = (z * -t) / a;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], -2e+107], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -2e-8], N[(N[(t / a), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -5e-38], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+62], N[(N[(z * (-t)), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -1.9999999999999999e107

   1. Initial program 76.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 78.5%

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

      1. associate-*l/ 91.2%

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

   5. Simplified 91.2%

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

      1. associate-/r/ 91.2%

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

   7. Applied egg-rr 91.2%

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

   if -1.9999999999999999e107 < (*.f64 x y) < -2e-8

   1. Initial program 88.8%

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

      1. div-sub 88.8%

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

      2. associate-/l* 77.1%

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

      3. associate-/l* 82.2%

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

   4. Applied egg-rr 82.2%

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

      1. clear-num 82.5%

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

      2. inv-pow 82.5%

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

      3. associate-/l/ 77.1%

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

   6. Applied egg-rr 77.1%

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

      1. unpow-1 77.1%

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

      2. *-commutative 77.1%

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

      3. associate-/r* 82.5%

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

   8. Simplified 82.5%

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

   9. Taylor expanded in x around 0 54.2%

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

       1. mul-1-neg 54.2%

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

       2. associate-*l/ 59.6%

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

       3. *-commutative 59.6%

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

       4. distribute-lft-neg-out 59.6%

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

   11. Simplified 59.6%

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

   if -2e-8 < (*.f64 x y) < -5.00000000000000033e-38

   1. Initial program 84.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 79.0%

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

      1. associate-*l/ 67.4%

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

   5. Simplified 67.4%

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

      1. *-commutative 67.4%

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

      2. clear-num 67.7%

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

      3. un-div-inv 67.9%

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

   7. Applied egg-rr 67.9%

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

   if -5.00000000000000033e-38 < (*.f64 x y) < 5.00000000000000029e62

   1. Initial program 95.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. distribute-rgt-neg-in 76.9%

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

   5. Simplified 76.9%

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

   if 5.00000000000000029e62 < (*.f64 x y)

   1. Initial program 78.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.4%

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

      1. associate-*l/ 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+107}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-8}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \cdot y \leq -5 \cdot 10^{-38}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;\frac{z \cdot \left(-t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+202}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -2e+304)
   (/ x (/ a y))
   (if (<= (* x y) 1e+202) (/ (- (* x y) (* z t)) a) (* y (/ x a)))))

C

assert(x < y && y < z && z < t && t < a);
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) <= -2e+304) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e+202) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) <= (-2d+304)) then
        tmp = x / (a / y)
    else if ((x * y) <= 1d+202) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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) <= -2e+304) {
		tmp = x / (a / y);
	} else if ((x * y) <= 1e+202) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -2e+304:
		tmp = x / (a / y)
	elif (x * y) <= 1e+202:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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) <= -2e+304)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 1e+202)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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) <= -2e+304)
		tmp = x / (a / y);
	elseif ((x * y) <= 1e+202)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], -2e+304], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+202], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -1.9999999999999999e304

   1. Initial program 56.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 66.9%

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

      1. associate-*l/ 99.7%

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

   5. Simplified 99.7%

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

      1. associate-/r/ 99.8%

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

   7. Applied egg-rr 99.8%

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

   if -1.9999999999999999e304 < (*.f64 x y) < 9.999999999999999e201

   1. Initial program 94.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 9.999999999999999e201 < (*.f64 x y)

   1. Initial program 59.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 68.0%

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

      1. associate-*l/ 87.3%

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

   5. Simplified 87.3%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+304}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 10^{+202}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -4e+58)
   (/ x (/ a y))
   (if (<= (* x y) 5e+62) (/ (- t) (/ a z)) (* y (/ x a)))))

C

assert(x < y && y < z && z < t && t < a);
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) <= -4e+58) {
		tmp = x / (a / y);
	} else if ((x * y) <= 5e+62) {
		tmp = -t / (a / z);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) <= (-4d+58)) then
        tmp = x / (a / y)
    else if ((x * y) <= 5d+62) then
        tmp = -t / (a / z)
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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) <= -4e+58) {
		tmp = x / (a / y);
	} else if ((x * y) <= 5e+62) {
		tmp = -t / (a / z);
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -4e+58:
		tmp = x / (a / y)
	elif (x * y) <= 5e+62:
		tmp = -t / (a / z)
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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) <= -4e+58)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 5e+62)
		tmp = Float64(Float64(-t) / Float64(a / z));
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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) <= -4e+58)
		tmp = x / (a / y);
	elseif ((x * y) <= 5e+62)
		tmp = -t / (a / z);
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], -4e+58], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e+62], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -3.99999999999999978e58

   1. Initial program 78.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.3%

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

      1. associate-*l/ 84.6%

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

   5. Simplified 84.6%

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

      1. associate-/r/ 86.5%

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

   7. Applied egg-rr 86.5%

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

   if -3.99999999999999978e58 < (*.f64 x y) < 5.00000000000000029e62

   1. Initial program 94.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 72.9%

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

      1. mul-1-neg 72.9%

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

      2. associate-/l* 72.3%

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

   5. Simplified 72.3%

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

   if 5.00000000000000029e62 < (*.f64 x y)

   1. Initial program 78.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 76.4%

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

      1. associate-*l/ 86.9%

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

   5. Simplified 86.9%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{+58}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{+62}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 1.12 \cdot 10^{-123}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= a 1.12e-123) (/ (* x y) a) (* y (/ x a))))

C

assert(x < y && y < z && z < t && t < a);
assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= 1.12e-123) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (a <= 1.12d-123) then
        tmp = (x * y) / a
    else
        tmp = y * (x / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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 (a <= 1.12e-123) {
		tmp = (x * y) / a;
	} else {
		tmp = y * (x / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if a <= 1.12e-123:
		tmp = (x * y) / a
	else:
		tmp = y * (x / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= 1.12e-123)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(y * Float64(x / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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 (a <= 1.12e-123)
		tmp = (x * y) / a;
	else
		tmp = y * (x / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[a, 1.12e-123], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 1.11999999999999999e-123

   1. Initial program 91.0%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 49.2%

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

   if 1.11999999999999999e-123 < a

   1. Initial program 83.9%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 40.2%

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

      1. associate-*l/ 47.4%

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

   5. Simplified 47.4%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 1.12 \cdot 10^{-123}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.7% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 88.4%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 45.8%

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

   1. associate-*l/ 48.9%

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

5. Simplified 48.9%

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

6. Final simplification 48.9%

   \[\leadsto y \cdot \frac{x}{a} \]
7. Add Preprocessing

Alternative 11: 51.4% accurate, 1.8× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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 88.4%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 45.8%

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

   1. associate-/l* 46.9%

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

   2. clear-num 46.8%

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

   3. associate-/r/ 46.5%

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

   4. clear-num 47.1%

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

5. Applied egg-rr 47.1%

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

6. Final simplification 47.1%

   \[\leadsto x \cdot \frac{y}{a} \]
7. Add Preprocessing

Developer target: 92.3% 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 2024010 
(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))