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

Percentage Accurate: 91.7% → 96.3%

Time: 7.6s

Alternatives: 11

Speedup: 0.4×

• 28.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 91.7% 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: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \left(\frac{y}{a} - t \cdot \frac{\frac{z}{x}}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+266}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(x \cdot \frac{y}{t} - z\right)\\ \end{array} \end{array} \]

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))))
   (if (<= t_1 (- INFINITY))
     (* x (- (/ y a) (* t (/ (/ z x) a))))
     (if (<= t_1 1e+266) (/ t_1 a) (* (/ t a) (- (* x (/ y t)) z))))))

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 <= 1e+266) {
		tmp = t_1 / a;
	} else {
		tmp = (t / a) * ((x * (y / t)) - z);
	}
	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 <= 1e+266) {
		tmp = t_1 / a;
	} else {
		tmp = (t / a) * ((x * (y / t)) - z);
	}
	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 <= 1e+266:
		tmp = t_1 / a
	else:
		tmp = (t / a) * ((x * (y / t)) - z)
	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 <= 1e+266)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(t / a) * Float64(Float64(x * Float64(y / t)) - z));
	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 <= 1e+266)
		tmp = t_1 / a;
	else
		tmp = (t / a) * ((x * (y / t)) - z);
	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, 1e+266], N[(t$95$1 / a), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 67.6%

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

   3. Taylor expanded in x around inf 79.5%

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

      1. +-commutative 79.5%

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

      2. mul-1-neg 79.5%

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

      3. unsub-neg 79.5%

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

      4. associate-/l* 83.1%

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

      5. *-commutative 83.1%

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

      6. associate-/r* 89.8%

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

   5. Simplified 89.8%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1e266

   1. Initial program 99.2%

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

   if 1e266 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.5%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. associate-/l* 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. distribute-frac-neg 85.0%

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

      3. +-commutative 85.0%

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

      4. distribute-frac-neg 85.0%

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

      5. sub-neg 85.0%

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

      6. associate-/l/ 87.6%

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

      7. div-sub 90.1%

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

      8. associate-*r/ 95.1%

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

      9. fma-neg 95.1%

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

      10. associate-*r/ 71.7%

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

      11. associate-*l/ 94.9%

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

      12. fma-undefine 94.9%

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

      13. sub-neg 94.9%

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

   8. Simplified 94.9%

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

Alternative 2: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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+29)
   (/ y (/ a x))
   (if (<= (* x y) 2e-126)
     (* (/ z a) (- t))
     (if (<= (* x y) 1e-97)
       (* (* x y) (/ 1.0 a))
       (if (<= (* x y) 5e-8) (* z (/ (- t) a)) (/ 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) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-126) {
		tmp = (z / a) * -t;
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (1.0 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * (-t / a);
	} else {
		tmp = x / (a / y);
	}
	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+29)) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d-126) then
        tmp = (z / a) * -t
    else if ((x * y) <= 1d-97) then
        tmp = (x * y) * (1.0d0 / a)
    else if ((x * y) <= 5d-8) then
        tmp = z * (-t / a)
    else
        tmp = x / (a / y)
    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+29) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-126) {
		tmp = (z / a) * -t;
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) * (1.0 / a);
	} else if ((x * y) <= 5e-8) {
		tmp = z * (-t / a);
	} else {
		tmp = x / (a / y);
	}
	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+29:
		tmp = y / (a / x)
	elif (x * y) <= 2e-126:
		tmp = (z / a) * -t
	elif (x * y) <= 1e-97:
		tmp = (x * y) * (1.0 / a)
	elif (x * y) <= 5e-8:
		tmp = z * (-t / a)
	else:
		tmp = x / (a / y)
	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+29)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e-126)
		tmp = Float64(Float64(z / a) * Float64(-t));
	elseif (Float64(x * y) <= 1e-97)
		tmp = Float64(Float64(x * y) * Float64(1.0 / a));
	elseif (Float64(x * y) <= 5e-8)
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = Float64(x / Float64(a / y));
	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+29)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e-126)
		tmp = (z / a) * -t;
	elseif ((x * y) <= 1e-97)
		tmp = (x * y) * (1.0 / a);
	elseif ((x * y) <= 5e-8)
		tmp = z * (-t / a);
	else
		tmp = x / (a / y);
	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+29], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-126], N[(N[(z / a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-97], N[(N[(x * y), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-8], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -5.0000000000000001e29

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-/l* 82.0%

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

   5. Applied egg-rr 82.0%

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

      1. clear-num 82.0%

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

      2. un-div-inv 82.8%

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

   7. Applied egg-rr 82.8%

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

   if -5.0000000000000001e29 < (*.f64 x y) < 1.9999999999999999e-126

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. associate-/l* 83.8%

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

      3. distribute-rgt-neg-in 83.8%

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

      4. distribute-neg-frac2 83.8%

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

   5. Simplified 83.8%

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

   if 1.9999999999999999e-126 < (*.f64 x y) < 1.00000000000000004e-97

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 99.0%

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

      1. clear-num 99.0%

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

      2. associate-/r/ 99.2%

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

   5. Applied egg-rr 99.2%

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

   if 1.00000000000000004e-97 < (*.f64 x y) < 4.9999999999999998e-8

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-*r/ 68.3%

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

      3. neg-mul-1 68.3%

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

      4. distribute-rgt-neg-in 68.3%

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

      5. distribute-frac-neg 68.3%

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

   5. Simplified 68.3%

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

   if 4.9999999999999998e-8 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. associate-*r/ 74.3%

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

   5. Simplified 74.3%

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

      1. clear-num 74.2%

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

      2. un-div-inv 74.2%

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

   7. Applied egg-rr 74.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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+29)
   (/ y (/ a x))
   (if (<= (* x y) 2e-126)
     (* (/ z a) (- t))
     (if (<= (* x y) 1e-97)
       (/ (* x y) a)
       (if (<= (* x y) 5e-8) (* z (/ (- t) a)) (/ 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) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-126) {
		tmp = (z / a) * -t;
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-8) {
		tmp = z * (-t / a);
	} else {
		tmp = x / (a / y);
	}
	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+29)) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d-126) then
        tmp = (z / a) * -t
    else if ((x * y) <= 1d-97) then
        tmp = (x * y) / a
    else if ((x * y) <= 5d-8) then
        tmp = z * (-t / a)
    else
        tmp = x / (a / y)
    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+29) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-126) {
		tmp = (z / a) * -t;
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-8) {
		tmp = z * (-t / a);
	} else {
		tmp = x / (a / y);
	}
	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+29:
		tmp = y / (a / x)
	elif (x * y) <= 2e-126:
		tmp = (z / a) * -t
	elif (x * y) <= 1e-97:
		tmp = (x * y) / a
	elif (x * y) <= 5e-8:
		tmp = z * (-t / a)
	else:
		tmp = x / (a / y)
	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+29)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e-126)
		tmp = Float64(Float64(z / a) * Float64(-t));
	elseif (Float64(x * y) <= 1e-97)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 5e-8)
		tmp = Float64(z * Float64(Float64(-t) / a));
	else
		tmp = Float64(x / Float64(a / y));
	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+29)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e-126)
		tmp = (z / a) * -t;
	elseif ((x * y) <= 1e-97)
		tmp = (x * y) / a;
	elseif ((x * y) <= 5e-8)
		tmp = z * (-t / a);
	else
		tmp = x / (a / y);
	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+29], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-126], N[(N[(z / a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-97], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-8], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -5.0000000000000001e29

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-/l* 82.0%

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

   5. Applied egg-rr 82.0%

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

      1. clear-num 82.0%

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

      2. un-div-inv 82.8%

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

   7. Applied egg-rr 82.8%

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

   if -5.0000000000000001e29 < (*.f64 x y) < 1.9999999999999999e-126

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. associate-/l* 83.8%

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

      3. distribute-rgt-neg-in 83.8%

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

      4. distribute-neg-frac2 83.8%

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

   5. Simplified 83.8%

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

   if 1.9999999999999999e-126 < (*.f64 x y) < 1.00000000000000004e-97

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 99.0%

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

   if 1.00000000000000004e-97 < (*.f64 x y) < 4.9999999999999998e-8

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-*r/ 68.3%

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

      3. neg-mul-1 68.3%

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

      4. distribute-rgt-neg-in 68.3%

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

      5. distribute-frac-neg 68.3%

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

   5. Simplified 68.3%

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

   if 4.9999999999999998e-8 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. associate-*r/ 74.3%

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

   5. Simplified 74.3%

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

      1. clear-num 74.2%

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

      2. un-div-inv 74.2%

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

   7. Applied egg-rr 74.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\frac{z}{\frac{a}{-t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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+29)
   (/ y (/ a x))
   (if (<= (* x y) 2e-126)
     (* (/ z a) (- t))
     (if (<= (* x y) 1e-97)
       (/ (* x y) a)
       (if (<= (* x y) 5e-8) (/ z (/ a (- t))) (/ 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) {
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-126) {
		tmp = (z / a) * -t;
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-8) {
		tmp = z / (a / -t);
	} else {
		tmp = x / (a / y);
	}
	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+29)) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d-126) then
        tmp = (z / a) * -t
    else if ((x * y) <= 1d-97) then
        tmp = (x * y) / a
    else if ((x * y) <= 5d-8) then
        tmp = z / (a / -t)
    else
        tmp = x / (a / y)
    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+29) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-126) {
		tmp = (z / a) * -t;
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-8) {
		tmp = z / (a / -t);
	} else {
		tmp = x / (a / y);
	}
	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+29:
		tmp = y / (a / x)
	elif (x * y) <= 2e-126:
		tmp = (z / a) * -t
	elif (x * y) <= 1e-97:
		tmp = (x * y) / a
	elif (x * y) <= 5e-8:
		tmp = z / (a / -t)
	else:
		tmp = x / (a / y)
	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+29)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e-126)
		tmp = Float64(Float64(z / a) * Float64(-t));
	elseif (Float64(x * y) <= 1e-97)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 5e-8)
		tmp = Float64(z / Float64(a / Float64(-t)));
	else
		tmp = Float64(x / Float64(a / y));
	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+29)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e-126)
		tmp = (z / a) * -t;
	elseif ((x * y) <= 1e-97)
		tmp = (x * y) / a;
	elseif ((x * y) <= 5e-8)
		tmp = z / (a / -t);
	else
		tmp = x / (a / y);
	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+29], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-126], N[(N[(z / a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 1e-97], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-8], N[(z / N[(a / (-t)), $MachinePrecision]), $MachinePrecision], N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if (*.f64 x y) < -5.0000000000000001e29

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-/l* 82.0%

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

   5. Applied egg-rr 82.0%

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

      1. clear-num 82.0%

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

      2. un-div-inv 82.8%

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

   7. Applied egg-rr 82.8%

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

   if -5.0000000000000001e29 < (*.f64 x y) < 1.9999999999999999e-126

   1. Initial program 92.4%

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

   3. Taylor expanded in x around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. associate-/l* 83.8%

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

      3. distribute-rgt-neg-in 83.8%

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

      4. distribute-neg-frac2 83.8%

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

   5. Simplified 83.8%

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

   if 1.9999999999999999e-126 < (*.f64 x y) < 1.00000000000000004e-97

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 99.0%

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

   if 1.00000000000000004e-97 < (*.f64 x y) < 4.9999999999999998e-8

   1. Initial program 84.6%

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

   3. Taylor expanded in x around 0 58.5%

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

      1. *-commutative 58.5%

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

      2. associate-*r/ 68.3%

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

      3. neg-mul-1 68.3%

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

      4. distribute-rgt-neg-in 68.3%

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

      5. distribute-frac-neg 68.3%

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

   5. Simplified 68.3%

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

      1. distribute-frac-neg 68.3%

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

      2. distribute-rgt-neg-out 68.3%

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

      3. add-sqr-sqrt 45.3%

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

      4. sqrt-unprod 25.1%

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

      5. sqr-neg 25.1%

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

      6. sqrt-unprod 1.2%

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

      7. add-sqr-sqrt 2.6%

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

      8. clear-num 2.6%

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

      9. un-div-inv 2.6%

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

      10. add-sqr-sqrt 1.2%

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

      11. sqrt-unprod 25.1%

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

      12. sqr-neg 25.1%

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

      13. sqrt-unprod 45.1%

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

      14. add-sqr-sqrt 68.3%

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

   7. Applied egg-rr 68.3%

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

   if 4.9999999999999998e-8 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. associate-*r/ 74.3%

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

   5. Simplified 74.3%

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

      1. clear-num 74.2%

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

      2. un-div-inv 74.2%

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

   7. Applied egg-rr 74.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\frac{z}{\frac{a}{-t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{z}{\frac{a}{-t}}\\ \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \end{array} \]

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 (/ z (/ a (- t)))))
   (if (<= (* x y) -5e+29)
     (/ y (/ a x))
     (if (<= (* x y) 2e-126)
       t_1
       (if (<= (* x y) 1e-97)
         (/ (* x y) a)
         (if (<= (* x y) 5e-8) t_1 (/ 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) {
	double t_1 = z / (a / -t);
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-126) {
		tmp = t_1;
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-8) {
		tmp = t_1;
	} else {
		tmp = x / (a / y);
	}
	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 = z / (a / -t)
    if ((x * y) <= (-5d+29)) then
        tmp = y / (a / x)
    else if ((x * y) <= 2d-126) then
        tmp = t_1
    else if ((x * y) <= 1d-97) then
        tmp = (x * y) / a
    else if ((x * y) <= 5d-8) then
        tmp = t_1
    else
        tmp = x / (a / y)
    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 = z / (a / -t);
	double tmp;
	if ((x * y) <= -5e+29) {
		tmp = y / (a / x);
	} else if ((x * y) <= 2e-126) {
		tmp = t_1;
	} else if ((x * y) <= 1e-97) {
		tmp = (x * y) / a;
	} else if ((x * y) <= 5e-8) {
		tmp = t_1;
	} else {
		tmp = x / (a / y);
	}
	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 = z / (a / -t)
	tmp = 0
	if (x * y) <= -5e+29:
		tmp = y / (a / x)
	elif (x * y) <= 2e-126:
		tmp = t_1
	elif (x * y) <= 1e-97:
		tmp = (x * y) / a
	elif (x * y) <= 5e-8:
		tmp = t_1
	else:
		tmp = x / (a / y)
	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(z / Float64(a / Float64(-t)))
	tmp = 0.0
	if (Float64(x * y) <= -5e+29)
		tmp = Float64(y / Float64(a / x));
	elseif (Float64(x * y) <= 2e-126)
		tmp = t_1;
	elseif (Float64(x * y) <= 1e-97)
		tmp = Float64(Float64(x * y) / a);
	elseif (Float64(x * y) <= 5e-8)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(a / y));
	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 = z / (a / -t);
	tmp = 0.0;
	if ((x * y) <= -5e+29)
		tmp = y / (a / x);
	elseif ((x * y) <= 2e-126)
		tmp = t_1;
	elseif ((x * y) <= 1e-97)
		tmp = (x * y) / a;
	elseif ((x * y) <= 5e-8)
		tmp = t_1;
	else
		tmp = x / (a / y);
	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[(z / N[(a / (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -5e+29], N[(y / N[(a / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e-126], t$95$1, If[LessEqual[N[(x * y), $MachinePrecision], 1e-97], N[(N[(x * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 5e-8], t$95$1, N[(x / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -5.0000000000000001e29

   1. Initial program 88.6%

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

   3. Taylor expanded in x around inf 75.8%

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

      1. *-commutative 75.8%

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

      2. associate-/l* 82.0%

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

   5. Applied egg-rr 82.0%

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

      1. clear-num 82.0%

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

      2. un-div-inv 82.8%

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

   7. Applied egg-rr 82.8%

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

   if -5.0000000000000001e29 < (*.f64 x y) < 1.9999999999999999e-126 or 1.00000000000000004e-97 < (*.f64 x y) < 4.9999999999999998e-8

   1. Initial program 91.3%

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

   3. Taylor expanded in x around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*r/ 82.8%

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

      3. neg-mul-1 82.8%

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

      4. distribute-rgt-neg-in 82.8%

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

      5. distribute-frac-neg 82.8%

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

   5. Simplified 82.8%

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

      1. distribute-frac-neg 82.8%

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

      2. distribute-rgt-neg-out 82.8%

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

      3. add-sqr-sqrt 43.2%

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

      4. sqrt-unprod 36.0%

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

      5. sqr-neg 36.0%

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

      6. sqrt-unprod 4.3%

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

      7. add-sqr-sqrt 9.5%

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

      8. clear-num 9.5%

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

      9. un-div-inv 9.5%

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

      10. add-sqr-sqrt 4.3%

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

      11. sqrt-unprod 36.6%

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

      12. sqr-neg 36.6%

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

      13. sqrt-unprod 43.8%

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

      14. add-sqr-sqrt 83.6%

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

   7. Applied egg-rr 83.6%

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

   if 1.9999999999999999e-126 < (*.f64 x y) < 1.00000000000000004e-97

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf 99.0%

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

   if 4.9999999999999998e-8 < (*.f64 x y)

   1. Initial program 90.2%

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

   3. Taylor expanded in x around inf 76.1%

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

      1. associate-*r/ 74.3%

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

   5. Simplified 74.3%

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

      1. clear-num 74.2%

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

      2. un-div-inv 74.2%

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

   7. Applied egg-rr 74.2%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -5 \cdot 10^{+29}:\\ \;\;\;\;\frac{y}{\frac{a}{x}}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-126}:\\ \;\;\;\;\frac{z}{\frac{a}{-t}}\\ \mathbf{elif}\;x \cdot y \leq 10^{-97}:\\ \;\;\;\;\frac{x \cdot y}{a}\\ \mathbf{elif}\;x \cdot y \leq 5 \cdot 10^{-8}:\\ \;\;\;\;\frac{z}{\frac{a}{-t}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t \cdot \left(\frac{y}{t} \cdot \frac{x}{a} - \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+266}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(x \cdot \frac{y}{t} - z\right)\\ \end{array} \end{array} \]

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))))
   (if (<= t_1 (- INFINITY))
     (* t (- (* (/ y t) (/ x a)) (/ z a)))
     (if (<= t_1 1e+266) (/ t_1 a) (* (/ t a) (- (* x (/ y t)) z))))))

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 = t * (((y / t) * (x / a)) - (z / a));
	} else if (t_1 <= 1e+266) {
		tmp = t_1 / a;
	} else {
		tmp = (t / a) * ((x * (y / t)) - z);
	}
	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 = t * (((y / t) * (x / a)) - (z / a));
	} else if (t_1 <= 1e+266) {
		tmp = t_1 / a;
	} else {
		tmp = (t / a) * ((x * (y / t)) - z);
	}
	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 = t * (((y / t) * (x / a)) - (z / a))
	elif t_1 <= 1e+266:
		tmp = t_1 / a
	else:
		tmp = (t / a) * ((x * (y / t)) - z)
	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(t * Float64(Float64(Float64(y / t) * Float64(x / a)) - Float64(z / a)));
	elseif (t_1 <= 1e+266)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(t / a) * Float64(Float64(x * Float64(y / t)) - z));
	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 = t * (((y / t) * (x / a)) - (z / a));
	elseif (t_1 <= 1e+266)
		tmp = t_1 / a;
	else
		tmp = (t / a) * ((x * (y / t)) - z);
	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[(t * N[(N[(N[(y / t), $MachinePrecision] * N[(x / a), $MachinePrecision]), $MachinePrecision] - N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+266], N[(t$95$1 / a), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 67.6%

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

   3. Taylor expanded in t around inf 80.4%

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

      1. +-commutative 80.4%

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

      2. mul-1-neg 80.4%

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

      3. unsub-neg 80.4%

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

      4. times-frac 93.4%

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

   5. Simplified 93.4%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 1e266

   1. Initial program 99.2%

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

   if 1e266 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.5%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. associate-/l* 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. distribute-frac-neg 85.0%

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

      3. +-commutative 85.0%

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

      4. distribute-frac-neg 85.0%

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

      5. sub-neg 85.0%

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

      6. associate-/l/ 87.6%

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

      7. div-sub 90.1%

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

      8. associate-*r/ 95.1%

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

      9. fma-neg 95.1%

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

      10. associate-*r/ 71.7%

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

      11. associate-*l/ 94.9%

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

      12. fma-undefine 94.9%

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

      13. sub-neg 94.9%

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

   8. Simplified 94.9%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty:\\ \;\;\;\;t \cdot \left(\frac{y}{t} \cdot \frac{x}{a} - \frac{z}{a}\right)\\ \mathbf{elif}\;x \cdot y - z \cdot t \leq 10^{+266}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(x \cdot \frac{y}{t} - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 95.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+218}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \end{array} \end{array} \]

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
 (if (<= (* z t) (- INFINITY))
   (* z (/ (- t) a))
   (if (<= (* z t) 2e+218) (/ (- (* x y) (* z t)) a) (* (/ z a) (- t)))))

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 ((z * t) <= -((double) INFINITY)) {
		tmp = z * (-t / a);
	} else if ((z * t) <= 2e+218) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (z / a) * -t;
	}
	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 tmp;
	if ((z * t) <= -Double.POSITIVE_INFINITY) {
		tmp = z * (-t / a);
	} else if ((z * t) <= 2e+218) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (z / a) * -t;
	}
	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 (z * t) <= -math.inf:
		tmp = z * (-t / a)
	elif (z * t) <= 2e+218:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = (z / a) * -t
	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(z * t) <= Float64(-Inf))
		tmp = Float64(z * Float64(Float64(-t) / a));
	elseif (Float64(z * t) <= 2e+218)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(z / a) * Float64(-t));
	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 ((z * t) <= -Inf)
		tmp = z * (-t / a);
	elseif ((z * t) <= 2e+218)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = (z / a) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(z * t), $MachinePrecision], (-Infinity)], N[(z * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+218], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 42.4%

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

   3. Taylor expanded in x around 0 42.4%

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

      1. *-commutative 42.4%

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

      2. associate-*r/ 93.6%

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

      3. neg-mul-1 93.6%

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

      4. distribute-rgt-neg-in 93.6%

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

      5. distribute-frac-neg 93.6%

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

   5. Simplified 93.6%

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

   if -inf.0 < (*.f64 z t) < 2.00000000000000017e218

   1. Initial program 96.3%

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

   if 2.00000000000000017e218 < (*.f64 z t)

   1. Initial program 70.6%

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

   3. Taylor expanded in x around 0 74.9%

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

      1. mul-1-neg 74.9%

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

      2. associate-/l* 95.7%

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

      3. distribute-rgt-neg-in 95.7%

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

      4. distribute-neg-frac2 95.7%

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

   5. Simplified 95.7%

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

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -\infty:\\ \;\;\;\;z \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+218}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 94.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq 10^{+266}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(x \cdot \frac{y}{t} - z\right)\\ \end{array} \end{array} \]

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))))
   (if (<= t_1 1e+266) (/ t_1 a) (* (/ t a) (- (* x (/ y t)) z)))))

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 <= 1e+266) {
		tmp = t_1 / a;
	} else {
		tmp = (t / a) * ((x * (y / t)) - z);
	}
	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 <= 1d+266) then
        tmp = t_1 / a
    else
        tmp = (t / a) * ((x * (y / t)) - z)
    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 <= 1e+266) {
		tmp = t_1 / a;
	} else {
		tmp = (t / a) * ((x * (y / t)) - z);
	}
	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 <= 1e+266:
		tmp = t_1 / a
	else:
		tmp = (t / a) * ((x * (y / t)) - z)
	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 <= 1e+266)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(t / a) * Float64(Float64(x * Float64(y / t)) - z));
	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 <= 1e+266)
		tmp = t_1 / a;
	else
		tmp = (t / a) * ((x * (y / t)) - z);
	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, 1e+266], N[(t$95$1 / a), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * N[(N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < 1e266

   1. Initial program 95.0%

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

   if 1e266 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.5%

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

   3. Taylor expanded in t around inf 69.1%

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

      1. associate-/l* 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in t around inf 85.0%

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

      1. mul-1-neg 85.0%

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

      2. distribute-frac-neg 85.0%

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

      3. +-commutative 85.0%

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

      4. distribute-frac-neg 85.0%

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

      5. sub-neg 85.0%

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

      6. associate-/l/ 87.6%

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

      7. div-sub 90.1%

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

      8. associate-*r/ 95.1%

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

      9. fma-neg 95.1%

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

      10. associate-*r/ 71.7%

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

      11. associate-*l/ 94.9%

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

      12. fma-undefine 94.9%

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

      13. sub-neg 94.9%

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

   8. Simplified 94.9%

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

Alternative 9: 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 90.6%

   \[\frac{x \cdot y - z \cdot t}{a} \]
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/ 47.9%

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

5. Simplified 47.9%

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

   1. clear-num 47.6%

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

   2. un-div-inv 47.4%

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

7. Applied egg-rr 47.4%

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

Alternative 10: 51.7% accurate, 1.8× speedup

Math

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

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 90.6%

   \[\frac{x \cdot y - z \cdot t}{a} \]
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/ 47.9%

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

5. Simplified 47.9%

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

Alternative 11: 8.8% accurate, 1.8× speedup

Math

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

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 (* 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) {
	return t * (z / 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 = t * (z / 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 t * (z / 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 t * (z / 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(t * Float64(z / 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 = t * (z / 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[(t * N[(z / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 90.6%

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

   1. div-inv 90.5%

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

   2. *-commutative 90.5%

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

   3. cancel-sign-sub-inv 90.5%

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

   4. *-commutative 90.5%

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

   5. add-sqr-sqrt 47.6%

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

   6. sqrt-unprod 58.4%

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

   7. sqr-neg 58.4%

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

   8. sqrt-unprod 20.1%

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

   9. add-sqr-sqrt 44.6%

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

   10. fma-define 44.6%

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

4. Applied egg-rr 44.6%

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

5. Taylor expanded in x around 0 8.0%

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

   1. associate-/l* 8.7%

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

7. Simplified 8.7%

   \[\leadsto \color{blue}{t \cdot \frac{z}{a}} \]
8. Add Preprocessing

Developer target: 92.6% 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 2024108 
(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))