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

Percentage Accurate: 91.0% → 96.6%

Time: 7.9s

Alternatives: 13

Speedup: 0.4×

• 28.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y \cdot \frac{x}{t} - z}{a}\\ \end{array} \end{array} \]

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 (<= t_1 (- INFINITY))
     (* x (- (/ y a) (* t (/ (/ z x) a))))
     (if (<= t_1 5e+274)
       (/ (fma x y (* t (- z))) a)
       (* t (/ (- (* y (/ x t)) z) 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 <= -((double) INFINITY)) {
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	} else if (t_1 <= 5e+274) {
		tmp = fma(x, y, (t * -z)) / a;
	} else {
		tmp = t * (((y * (x / t)) - z) / 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 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y / a) - Float64(t * Float64(Float64(z / x) / a))));
	elseif (t_1 <= 5e+274)
		tmp = Float64(fma(x, y, Float64(t * Float64(-z))) / a);
	else
		tmp = Float64(t * Float64(Float64(Float64(y * Float64(x / t)) - z) / a));
	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]}, If[LessEqual[t$95$1, (-Infinity)], N[(x * N[(N[(y / a), $MachinePrecision] - N[(t * N[(N[(z / x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+274], N[(N[(x * y + N[(t * (-z)), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(t * N[(N[(N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 72.3%

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

   3. Taylor expanded in x around inf 85.9%

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

      1. +-commutative 85.9%

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

      2. mul-1-neg 85.9%

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

      3. unsub-neg 85.9%

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

      4. associate-/l* 89.7%

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

      5. *-commutative 89.7%

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

      6. associate-/r* 93.3%

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

   5. Simplified 93.3%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999998e274

   1. Initial program 98.8%

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

      1. div-sub 97.2%

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

      2. *-commutative 97.2%

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

      3. div-sub 98.8%

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

      4. *-commutative 98.8%

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

      5. fma-neg 98.8%

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

      6. distribute-rgt-neg-out 98.8%

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

   3. Simplified 98.8%

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

   if 4.9999999999999998e274 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 58.8%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. mul-1-neg 69.1%

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

      3. unsub-neg 69.1%

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

      4. times-frac 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in x around 0 69.1%

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

      1. associate-/l/ 69.6%

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

      2. div-sub 75.4%

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

      3. *-commutative 75.4%

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

      4. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t \cdot \left(-z\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y \cdot \frac{x}{t} - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 72.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -4e-14)
     (/ x (/ a y))
     (if (<= (* x y) 4e-155)
       (/ (* t (- z)) a)
       (if (<= (* x y) 2e-71)
         t_1
         (if (<= (* x y) 2e-36)
           (* z (/ t (- a)))
           (if (<= (* x y) 4e+111) (/ (* x y) a) t_1)))))))

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 / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = x / (a / y);
	} else if ((x * y) <= 4e-155) {
		tmp = (t * -z) / a;
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = z * (t / -a);
	} else if ((x * y) <= 4e+111) {
		tmp = (x * y) / 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.
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) <= (-4d-14)) then
        tmp = x / (a / y)
    else if ((x * y) <= 4d-155) then
        tmp = (t * -z) / a
    else if ((x * y) <= 2d-71) then
        tmp = t_1
    else if ((x * y) <= 2d-36) then
        tmp = z * (t / -a)
    else if ((x * y) <= 4d+111) then
        tmp = (x * y) / a
    else
        tmp = t_1
    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 / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = x / (a / y);
	} else if ((x * y) <= 4e-155) {
		tmp = (t * -z) / a;
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = z * (t / -a);
	} else if ((x * y) <= 4e+111) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	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 / a)
	tmp = 0
	if (x * y) <= -4e-14:
		tmp = x / (a / y)
	elif (x * y) <= 4e-155:
		tmp = (t * -z) / a
	elif (x * y) <= 2e-71:
		tmp = t_1
	elif (x * y) <= 2e-36:
		tmp = z * (t / -a)
	elif (x * y) <= 4e+111:
		tmp = (x * y) / a
	else:
		tmp = t_1
	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(x * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -4e-14)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 4e-155)
		tmp = Float64(Float64(t * Float64(-z)) / a);
	elseif (Float64(x * y) <= 2e-71)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-36)
		tmp = Float64(z * Float64(t / Float64(-a)));
	elseif (Float64(x * y) <= 4e+111)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = t_1;
	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 / a);
	tmp = 0.0;
	if ((x * y) <= -4e-14)
		tmp = x / (a / y);
	elseif ((x * y) <= 4e-155)
		tmp = (t * -z) / a;
	elseif ((x * y) <= 2e-71)
		tmp = t_1;
	elseif ((x * y) <= 2e-36)
		tmp = z * (t / -a);
	elseif ((x * y) <= 4e+111)
		tmp = (x * y) / 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.
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], -4e-14], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-155], N[(N[(t * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-71], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-36], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+111], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4e-14

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 75.4%

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

      1. associate-*r/ 76.9%

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

   5. Simplified 76.9%

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

      1. clear-num 76.8%

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

      2. un-div-inv 77.5%

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

   7. Applied egg-rr 77.5%

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

   if -4e-14 < (*.f64 x y) < 4.00000000000000006e-155

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0 81.9%

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

      1. associate-*r* 81.9%

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

      2. mul-1-neg 81.9%

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

   5. Simplified 81.9%

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

   if 4.00000000000000006e-155 < (*.f64 x y) < 1.9999999999999998e-71 or 3.99999999999999983e111 < (*.f64 x y)

   1. Initial program 85.6%

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

   3. Taylor expanded in x around inf 78.7%

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

      1. associate-*r/ 85.7%

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

   5. Simplified 85.7%

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

   if 1.9999999999999998e-71 < (*.f64 x y) < 1.9999999999999999e-36

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. associate-*r/ 65.9%

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

      3. neg-mul-1 65.9%

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

      4. distribute-rgt-neg-in 65.9%

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

      5. distribute-frac-neg 65.9%

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

   5. Simplified 65.9%

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

   if 1.9999999999999999e-36 < (*.f64 x y) < 3.99999999999999983e111

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 66.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;\frac{t \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -4e-14)
     (/ x (/ a y))
     (if (<= (* x y) 4e-155)
       (/ (- t) (/ a z))
       (if (<= (* x y) 2e-71)
         t_1
         (if (<= (* x y) 2e-36)
           (* z (/ t (- a)))
           (if (<= (* x y) 4e+111) (/ (* x y) a) t_1)))))))

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 / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = x / (a / y);
	} else if ((x * y) <= 4e-155) {
		tmp = -t / (a / z);
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = z * (t / -a);
	} else if ((x * y) <= 4e+111) {
		tmp = (x * y) / 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.
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) <= (-4d-14)) then
        tmp = x / (a / y)
    else if ((x * y) <= 4d-155) then
        tmp = -t / (a / z)
    else if ((x * y) <= 2d-71) then
        tmp = t_1
    else if ((x * y) <= 2d-36) then
        tmp = z * (t / -a)
    else if ((x * y) <= 4d+111) then
        tmp = (x * y) / a
    else
        tmp = t_1
    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 / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = x / (a / y);
	} else if ((x * y) <= 4e-155) {
		tmp = -t / (a / z);
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = z * (t / -a);
	} else if ((x * y) <= 4e+111) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	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 / a)
	tmp = 0
	if (x * y) <= -4e-14:
		tmp = x / (a / y)
	elif (x * y) <= 4e-155:
		tmp = -t / (a / z)
	elif (x * y) <= 2e-71:
		tmp = t_1
	elif (x * y) <= 2e-36:
		tmp = z * (t / -a)
	elif (x * y) <= 4e+111:
		tmp = (x * y) / a
	else:
		tmp = t_1
	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(x * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -4e-14)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 4e-155)
		tmp = Float64(Float64(-t) / Float64(a / z));
	elseif (Float64(x * y) <= 2e-71)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-36)
		tmp = Float64(z * Float64(t / Float64(-a)));
	elseif (Float64(x * y) <= 4e+111)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = t_1;
	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 / a);
	tmp = 0.0;
	if ((x * y) <= -4e-14)
		tmp = x / (a / y);
	elseif ((x * y) <= 4e-155)
		tmp = -t / (a / z);
	elseif ((x * y) <= 2e-71)
		tmp = t_1;
	elseif ((x * y) <= 2e-36)
		tmp = z * (t / -a);
	elseif ((x * y) <= 4e+111)
		tmp = (x * y) / 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.
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], -4e-14], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-155], N[((-t) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-71], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-36], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+111], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4e-14

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 75.4%

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

      1. associate-*r/ 76.9%

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

   5. Simplified 76.9%

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

      1. clear-num 76.8%

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

      2. un-div-inv 77.5%

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

   7. Applied egg-rr 77.5%

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

   if -4e-14 < (*.f64 x y) < 4.00000000000000006e-155

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0 81.9%

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

      1. associate-*r* 81.9%

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

      2. mul-1-neg 81.9%

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

   5. Simplified 81.9%

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

      1. add-sqr-sqrt 40.3%

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

      2. sqrt-unprod 34.8%

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

      3. sqr-neg 34.8%

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

      4. sqrt-unprod 4.4%

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

      5. add-sqr-sqrt 11.1%

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

      6. associate-*l/ 11.2%

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

      7. frac-2neg 11.2%

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

   7. Applied egg-rr 11.2%

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

      1. add-sqr-sqrt 3.3%

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

      2. sqrt-unprod 36.2%

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

      3. sqr-neg 36.2%

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

      4. sqrt-unprod 44.0%

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

      5. add-sqr-sqrt 78.0%

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

      6. distribute-rgt-neg-out 78.0%

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

      7. associate-/r/ 76.3%

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

      8. distribute-neg-frac 76.3%

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

   9. Applied egg-rr 76.3%

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

   if 4.00000000000000006e-155 < (*.f64 x y) < 1.9999999999999998e-71 or 3.99999999999999983e111 < (*.f64 x y)

   1. Initial program 85.6%

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

   3. Taylor expanded in x around inf 78.7%

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

      1. associate-*r/ 85.7%

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

   5. Simplified 85.7%

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

   if 1.9999999999999998e-71 < (*.f64 x y) < 1.9999999999999999e-36

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. associate-*r/ 65.9%

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

      3. neg-mul-1 65.9%

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

      4. distribute-rgt-neg-in 65.9%

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

      5. distribute-frac-neg 65.9%

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

   5. Simplified 65.9%

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

   if 1.9999999999999999e-36 < (*.f64 x y) < 3.99999999999999983e111

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 66.0%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;\frac{-t}{\frac{a}{z}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot \frac{y}{a}\\ \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -4e-14)
     (/ x (/ a y))
     (if (<= (* x y) 4e-155)
       (* t (/ (- z) a))
       (if (<= (* x y) 2e-71)
         t_1
         (if (<= (* x y) 2e-36)
           (* z (/ t (- a)))
           (if (<= (* x y) 4e+111) (/ (* x y) a) t_1)))))))

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 / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = x / (a / y);
	} else if ((x * y) <= 4e-155) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = z * (t / -a);
	} else if ((x * y) <= 4e+111) {
		tmp = (x * y) / 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.
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) <= (-4d-14)) then
        tmp = x / (a / y)
    else if ((x * y) <= 4d-155) then
        tmp = t * (-z / a)
    else if ((x * y) <= 2d-71) then
        tmp = t_1
    else if ((x * y) <= 2d-36) then
        tmp = z * (t / -a)
    else if ((x * y) <= 4d+111) then
        tmp = (x * y) / a
    else
        tmp = t_1
    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 / a);
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = x / (a / y);
	} else if ((x * y) <= 4e-155) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 2e-71) {
		tmp = t_1;
	} else if ((x * y) <= 2e-36) {
		tmp = z * (t / -a);
	} else if ((x * y) <= 4e+111) {
		tmp = (x * y) / a;
	} else {
		tmp = t_1;
	}
	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 / a)
	tmp = 0
	if (x * y) <= -4e-14:
		tmp = x / (a / y)
	elif (x * y) <= 4e-155:
		tmp = t * (-z / a)
	elif (x * y) <= 2e-71:
		tmp = t_1
	elif (x * y) <= 2e-36:
		tmp = z * (t / -a)
	elif (x * y) <= 4e+111:
		tmp = (x * y) / a
	else:
		tmp = t_1
	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(x * Float64(y / a))
	tmp = 0.0
	if (Float64(x * y) <= -4e-14)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 4e-155)
		tmp = Float64(t * Float64(Float64(-z) / a));
	elseif (Float64(x * y) <= 2e-71)
		tmp = t_1;
	elseif (Float64(x * y) <= 2e-36)
		tmp = Float64(z * Float64(t / Float64(-a)));
	elseif (Float64(x * y) <= 4e+111)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = t_1;
	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 / a);
	tmp = 0.0;
	if ((x * y) <= -4e-14)
		tmp = x / (a / y);
	elseif ((x * y) <= 4e-155)
		tmp = t * (-z / a);
	elseif ((x * y) <= 2e-71)
		tmp = t_1;
	elseif ((x * y) <= 2e-36)
		tmp = z * (t / -a);
	elseif ((x * y) <= 4e+111)
		tmp = (x * y) / 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.
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], -4e-14], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-155], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-71], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 2e-36], N[(z * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+111], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -4e-14

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 75.4%

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

      1. associate-*r/ 76.9%

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

   5. Simplified 76.9%

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

      1. clear-num 76.8%

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

      2. un-div-inv 77.5%

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

   7. Applied egg-rr 77.5%

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

   if -4e-14 < (*.f64 x y) < 4.00000000000000006e-155

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. associate-/l* 74.4%

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

      3. distribute-rgt-neg-in 74.4%

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

      4. distribute-neg-frac2 74.4%

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

   5. Simplified 74.4%

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

   if 4.00000000000000006e-155 < (*.f64 x y) < 1.9999999999999998e-71 or 3.99999999999999983e111 < (*.f64 x y)

   1. Initial program 85.6%

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

   3. Taylor expanded in x around inf 78.7%

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

      1. associate-*r/ 85.7%

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

   5. Simplified 85.7%

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

   if 1.9999999999999998e-71 < (*.f64 x y) < 1.9999999999999999e-36

   1. Initial program 89.3%

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

   3. Taylor expanded in x around 0 67.2%

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

      1. *-commutative 67.2%

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

      2. associate-*r/ 65.9%

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

      3. neg-mul-1 65.9%

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

      4. distribute-rgt-neg-in 65.9%

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

      5. distribute-frac-neg 65.9%

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

   5. Simplified 65.9%

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

   if 1.9999999999999999e-36 < (*.f64 x y) < 3.99999999999999983e111

   1. Initial program 96.2%

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

   3. Taylor expanded in x around inf 66.0%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-71}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-36}:\\ \;\;\;\;z \cdot \frac{t}{-a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y \cdot \frac{x}{t} - z}{a}\\ \end{array} \end{array} \]

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 (<= t_1 (- INFINITY))
     (* x (- (/ y a) (* t (/ (/ z x) a))))
     (if (<= t_1 5e+274) (/ t_1 a) (* t (/ (- (* y (/ x t)) z) 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 <= -((double) INFINITY)) {
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	} else if (t_1 <= 5e+274) {
		tmp = t_1 / a;
	} else {
		tmp = t * (((y * (x / t)) - z) / a);
	}
	return tmp;
}

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 <= -Double.POSITIVE_INFINITY) {
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	} else if (t_1 <= 5e+274) {
		tmp = t_1 / a;
	} else {
		tmp = t * (((y * (x / t)) - z) / 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 <= -math.inf:
		tmp = x * ((y / a) - (t * ((z / x) / a)))
	elif t_1 <= 5e+274:
		tmp = t_1 / a
	else:
		tmp = t * (((y * (x / t)) - z) / 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 <= Float64(-Inf))
		tmp = Float64(x * Float64(Float64(y / a) - Float64(t * Float64(Float64(z / x) / a))));
	elseif (t_1 <= 5e+274)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(t * Float64(Float64(Float64(y * Float64(x / t)) - z) / 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 <= -Inf)
		tmp = x * ((y / a) - (t * ((z / x) / a)));
	elseif (t_1 <= 5e+274)
		tmp = t_1 / a;
	else
		tmp = t * (((y * (x / t)) - z) / 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[LessEqual[t$95$1, (-Infinity)], N[(x * N[(N[(y / a), $MachinePrecision] - N[(t * N[(N[(z / x), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+274], N[(t$95$1 / a), $MachinePrecision], N[(t * N[(N[(N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 72.3%

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

   3. Taylor expanded in x around inf 85.9%

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

      1. +-commutative 85.9%

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

      2. mul-1-neg 85.9%

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

      3. unsub-neg 85.9%

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

      4. associate-/l* 89.7%

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

      5. *-commutative 89.7%

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

      6. associate-/r* 93.3%

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

   5. Simplified 93.3%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999998e274

   1. Initial program 98.8%

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

   if 4.9999999999999998e274 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 58.8%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. mul-1-neg 69.1%

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

      3. unsub-neg 69.1%

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

      4. times-frac 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in x around 0 69.1%

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

      1. associate-/l/ 69.6%

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

      2. div-sub 75.4%

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

      3. *-commutative 75.4%

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

      4. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

Alternative 6: 96.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+234}:\\ \;\;\;\;x \cdot \frac{y}{a} - \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y \cdot \frac{x}{t} - z}{a}\\ \end{array} \end{array} \]

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 (<= t_1 -5e+234)
     (- (* x (/ y a)) (/ t (/ a z)))
     (if (<= t_1 5e+274) (/ t_1 a) (* t (/ (- (* y (/ x t)) z) 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 <= -5e+234) {
		tmp = (x * (y / a)) - (t / (a / z));
	} else if (t_1 <= 5e+274) {
		tmp = t_1 / a;
	} else {
		tmp = t * (((y * (x / t)) - z) / 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 <= (-5d+234)) then
        tmp = (x * (y / a)) - (t / (a / z))
    else if (t_1 <= 5d+274) then
        tmp = t_1 / a
    else
        tmp = t * (((y * (x / t)) - z) / 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 <= -5e+234) {
		tmp = (x * (y / a)) - (t / (a / z));
	} else if (t_1 <= 5e+274) {
		tmp = t_1 / a;
	} else {
		tmp = t * (((y * (x / t)) - z) / 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 <= -5e+234:
		tmp = (x * (y / a)) - (t / (a / z))
	elif t_1 <= 5e+274:
		tmp = t_1 / a
	else:
		tmp = t * (((y * (x / t)) - z) / 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 <= -5e+234)
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(t / Float64(a / z)));
	elseif (t_1 <= 5e+274)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(t * Float64(Float64(Float64(y * Float64(x / t)) - z) / 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 <= -5e+234)
		tmp = (x * (y / a)) - (t / (a / z));
	elseif (t_1 <= 5e+274)
		tmp = t_1 / a;
	else
		tmp = t * (((y * (x / t)) - z) / 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[LessEqual[t$95$1, -5e+234], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(t / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+274], N[(t$95$1 / a), $MachinePrecision], N[(t * N[(N[(N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000003e234

   1. Initial program 81.2%

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

      1. div-sub 78.7%

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

      2. associate-/l* 90.6%

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

      3. associate-/l* 97.3%

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

   4. Applied egg-rr 97.3%

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

      1. *-commutative 97.3%

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

      2. div-inv 97.3%

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

      3. associate-*l* 97.3%

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

      4. add-sqr-sqrt 37.3%

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

      5. sqrt-unprod 57.5%

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

      6. sqr-neg 57.5%

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

      7. sqrt-unprod 32.5%

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

      8. add-sqr-sqrt 52.4%

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

      9. associate-/r/ 52.4%

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

      10. un-div-inv 52.4%

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

      11. add-sqr-sqrt 32.5%

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

      12. sqrt-unprod 57.5%

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

      13. sqr-neg 57.5%

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

      14. sqrt-unprod 37.3%

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

      15. add-sqr-sqrt 97.3%

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

   6. Applied egg-rr 97.3%

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

   if -5.0000000000000003e234 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999998e274

   1. Initial program 98.7%

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

   if 4.9999999999999998e274 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 58.8%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. mul-1-neg 69.1%

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

      3. unsub-neg 69.1%

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

      4. times-frac 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in x around 0 69.1%

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

      1. associate-/l/ 69.6%

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

      2. div-sub 75.4%

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

      3. *-commutative 75.4%

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

      4. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

Alternative 7: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+234}:\\ \;\;\;\;x \cdot \frac{y}{a} - z \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y \cdot \frac{x}{t} - z}{a}\\ \end{array} \end{array} \]

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 (<= t_1 -5e+234)
     (- (* x (/ y a)) (* z (/ t a)))
     (if (<= t_1 5e+274) (/ t_1 a) (* t (/ (- (* y (/ x t)) z) 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 <= -5e+234) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else if (t_1 <= 5e+274) {
		tmp = t_1 / a;
	} else {
		tmp = t * (((y * (x / t)) - z) / 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 <= (-5d+234)) then
        tmp = (x * (y / a)) - (z * (t / a))
    else if (t_1 <= 5d+274) then
        tmp = t_1 / a
    else
        tmp = t * (((y * (x / t)) - z) / 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 <= -5e+234) {
		tmp = (x * (y / a)) - (z * (t / a));
	} else if (t_1 <= 5e+274) {
		tmp = t_1 / a;
	} else {
		tmp = t * (((y * (x / t)) - z) / 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 <= -5e+234:
		tmp = (x * (y / a)) - (z * (t / a))
	elif t_1 <= 5e+274:
		tmp = t_1 / a
	else:
		tmp = t * (((y * (x / t)) - z) / 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 <= -5e+234)
		tmp = Float64(Float64(x * Float64(y / a)) - Float64(z * Float64(t / a)));
	elseif (t_1 <= 5e+274)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(t * Float64(Float64(Float64(y * Float64(x / t)) - z) / 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 <= -5e+234)
		tmp = (x * (y / a)) - (z * (t / a));
	elseif (t_1 <= 5e+274)
		tmp = t_1 / a;
	else
		tmp = t * (((y * (x / t)) - z) / 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[LessEqual[t$95$1, -5e+234], N[(N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision] - N[(z * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+274], N[(t$95$1 / a), $MachinePrecision], N[(t * N[(N[(N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000003e234

   1. Initial program 81.2%

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

      1. div-sub 78.7%

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

      2. associate-/l* 90.6%

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

      3. associate-/l* 97.3%

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

   4. Applied egg-rr 97.3%

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

   if -5.0000000000000003e234 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999998e274

   1. Initial program 98.7%

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

   if 4.9999999999999998e274 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 58.8%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. mul-1-neg 69.1%

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

      3. unsub-neg 69.1%

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

      4. times-frac 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in x around 0 69.1%

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

      1. associate-/l/ 69.6%

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

      2. div-sub 75.4%

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

      3. *-commutative 75.4%

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

      4. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

Alternative 8: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

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-14)
   (/ x (/ a y))
   (if (<= (* x y) 4e-155)
     (* t (/ (- z) a))
     (if (<= (* x y) 4e+111) (/ (* x y) a) (* 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) {
	double tmp;
	if ((x * y) <= -4e-14) {
		tmp = x / (a / y);
	} else if ((x * y) <= 4e-155) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 4e+111) {
		tmp = (x * y) / a;
	} else {
		tmp = x * (y / 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-14)) then
        tmp = x / (a / y)
    else if ((x * y) <= 4d-155) then
        tmp = t * (-z / a)
    else if ((x * y) <= 4d+111) then
        tmp = (x * y) / a
    else
        tmp = x * (y / 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-14) {
		tmp = x / (a / y);
	} else if ((x * y) <= 4e-155) {
		tmp = t * (-z / a);
	} else if ((x * y) <= 4e+111) {
		tmp = (x * y) / a;
	} else {
		tmp = x * (y / 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-14:
		tmp = x / (a / y)
	elif (x * y) <= 4e-155:
		tmp = t * (-z / a)
	elif (x * y) <= 4e+111:
		tmp = (x * y) / a
	else:
		tmp = x * (y / 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-14)
		tmp = Float64(x / Float64(a / y));
	elseif (Float64(x * y) <= 4e-155)
		tmp = Float64(t * Float64(Float64(-z) / a));
	elseif (Float64(x * y) <= 4e+111)
		tmp = Float64(Float64(x * y) / a);
	else
		tmp = Float64(x * Float64(y / 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-14)
		tmp = x / (a / y);
	elseif ((x * y) <= 4e-155)
		tmp = t * (-z / a);
	elseif ((x * y) <= 4e+111)
		tmp = (x * y) / a;
	else
		tmp = x * (y / 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-14], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e-155], N[(t * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 4e+111], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -4e-14

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 75.4%

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

      1. associate-*r/ 76.9%

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

   5. Simplified 76.9%

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

      1. clear-num 76.8%

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

      2. un-div-inv 77.5%

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

   7. Applied egg-rr 77.5%

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

   if -4e-14 < (*.f64 x y) < 4.00000000000000006e-155

   1. Initial program 95.3%

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

   3. Taylor expanded in x around 0 81.9%

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

      1. mul-1-neg 81.9%

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

      2. associate-/l* 74.4%

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

      3. distribute-rgt-neg-in 74.4%

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

      4. distribute-neg-frac2 74.4%

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

   5. Simplified 74.4%

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

   if 4.00000000000000006e-155 < (*.f64 x y) < 3.99999999999999983e111

   1. Initial program 95.6%

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

   3. Taylor expanded in x around inf 61.1%

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

   if 3.99999999999999983e111 < (*.f64 x y)

   1. Initial program 83.2%

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

   3. Taylor expanded in x around inf 77.1%

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

      1. associate-*r/ 85.5%

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

   5. Simplified 85.5%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -4 \cdot 10^{-14}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{-155}:\\ \;\;\;\;t \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \cdot y \leq 4 \cdot 10^{+111}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+234}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+164}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \end{array} \]

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) -5e+234)
   (* y (/ x a))
   (if (<= (* x y) 1e+164) (/ (- (* x y) (* z t)) a) (* 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) {
	double tmp;
	if ((x * y) <= -5e+234) {
		tmp = y * (x / a);
	} else if ((x * y) <= 1e+164) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (y / 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) <= (-5d+234)) then
        tmp = y * (x / a)
    else if ((x * y) <= 1d+164) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = x * (y / 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) <= -5e+234) {
		tmp = y * (x / a);
	} else if ((x * y) <= 1e+164) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = x * (y / 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) <= -5e+234:
		tmp = y * (x / a)
	elif (x * y) <= 1e+164:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = x * (y / 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) <= -5e+234)
		tmp = Float64(y * Float64(x / a));
	elseif (Float64(x * y) <= 1e+164)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(x * Float64(y / 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) <= -5e+234)
		tmp = y * (x / a);
	elseif ((x * y) <= 1e+164)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = x * (y / 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], -5e+234], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e+164], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -5.0000000000000003e234

   1. Initial program 71.3%

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

   3. Taylor expanded in x around inf 71.3%

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

      1. associate-*r/ 88.8%

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

   5. Simplified 88.8%

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

   6. Taylor expanded in x around 0 71.3%

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

      1. *-commutative 71.3%

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

      2. associate-*l/ 88.8%

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

      3. associate-/r/ 88.8%

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

   8. Simplified 88.8%

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

      1. clear-num 88.8%

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

      2. associate-/r/ 88.7%

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

      3. clear-num 88.8%

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

   10. Applied egg-rr 88.8%

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

   if -5.0000000000000003e234 < (*.f64 x y) < 1e164

   1. Initial program 95.5%

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

   if 1e164 < (*.f64 x y)

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf 79.8%

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

      1. associate-*r/ 91.4%

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

   5. Simplified 91.4%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+234}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \mathbf{elif}\;x \cdot y \leq 10^{+164}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 93.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+274}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y \cdot \frac{x}{t} - z}{a}\\ \end{array} \end{array} \]

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 (<= t_1 5e+274) (/ t_1 a) (* t (/ (- (* y (/ x t)) z) 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 <= 5e+274) {
		tmp = t_1 / a;
	} else {
		tmp = t * (((y * (x / t)) - z) / 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 <= 5d+274) then
        tmp = t_1 / a
    else
        tmp = t * (((y * (x / t)) - z) / 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 <= 5e+274) {
		tmp = t_1 / a;
	} else {
		tmp = t * (((y * (x / t)) - z) / 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 <= 5e+274:
		tmp = t_1 / a
	else:
		tmp = t * (((y * (x / t)) - z) / 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 <= 5e+274)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(t * Float64(Float64(Float64(y * Float64(x / t)) - z) / 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 <= 5e+274)
		tmp = t_1 / a;
	else
		tmp = t * (((y * (x / t)) - z) / 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[LessEqual[t$95$1, 5e+274], N[(t$95$1 / a), $MachinePrecision], N[(t * N[(N[(N[(y * N[(x / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999998e274

   1. Initial program 95.6%

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

   if 4.9999999999999998e274 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 58.8%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. mul-1-neg 69.1%

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

      3. unsub-neg 69.1%

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

      4. times-frac 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in x around 0 69.1%

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

      1. associate-/l/ 69.6%

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

      2. div-sub 75.4%

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

      3. *-commutative 75.4%

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

      4. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

Alternative 11: 51.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq 8.5 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \end{array} \]

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 8.5e+172) (* 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 <= 8.5e+172) {
		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 <= 8.5d+172) 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 <= 8.5e+172) {
		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 <= 8.5e+172:
		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 <= 8.5e+172)
		tmp = Float64(x * Float64(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 <= 8.5e+172)
		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, 8.5e+172], N[(x * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(x / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < 8.50000000000000053e172

   1. Initial program 92.1%

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

   3. Taylor expanded in x around inf 53.4%

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

      1. associate-*r/ 54.8%

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

   5. Simplified 54.8%

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

   if 8.50000000000000053e172 < a

   1. Initial program 79.3%

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

   3. Taylor expanded in x around inf 48.6%

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

      1. associate-*r/ 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in x around 0 48.6%

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

      1. *-commutative 48.6%

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

      2. associate-*l/ 48.6%

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

      3. associate-/r/ 48.7%

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

   8. Simplified 48.7%

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

      1. clear-num 48.6%

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

      2. associate-/r/ 48.7%

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

      3. clear-num 48.7%

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

   10. Applied egg-rr 48.7%

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

4. Final simplification 54.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq 8.5 \cdot 10^{+172}:\\ \;\;\;\;x \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.5% accurate, 1.8× speedup

Math

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

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 (/ a y)))

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 / (a / y);
}

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 / (a / y)
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 / (a / y);
}

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 / (a / y)

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(a / y))
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 / (a / y);
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[(a / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.5%

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

3. Taylor expanded in x around inf 52.8%

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

   1. associate-*r/ 54.0%

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

5. Simplified 54.0%

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

   1. clear-num 54.0%

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

   2. un-div-inv 54.3%

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

7. Applied egg-rr 54.3%

   \[\leadsto \color{blue}{\frac{x}{\frac{a}{y}}} \]
8. Add Preprocessing

Alternative 13: 51.5% 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 90.5%

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

3. Taylor expanded in x around inf 52.8%

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

   1. associate-*r/ 54.0%

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

5. Simplified 54.0%

   \[\leadsto \color{blue}{x \cdot \frac{y}{a}} \]
6. Add Preprocessing

Developer target: 91.5% accurate, 0.4× 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 2024089 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (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))