Statistics.Math.RootFinding:ridders from math-functions-0.1.5.2

Percentage Accurate: 61.2% → 90.7%

Time: 17.9s

Alternatives: 13

Speedup: 18.6×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) * z) / sqrt(((z * 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) / sqrt(((z * z) - (t * a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return ((x * y) * z) / sqrt(((z * 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) / sqrt(((z * z) - (t * a)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{z}{\sqrt{z \cdot z - a \cdot t}} \cdot \left(y \cdot x\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \left(e^{-0.5 \cdot \left(\log \left(-t\right) - \log \left(\frac{1}{a}\right)\right)} \cdot \left(z \cdot x\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (sqrt (- (* z z) (* a t)))) (* y x))))
   (if (<= z -1e+140)
     (* y (- x))
     (if (<= z -3.9e-187)
       t_1
       (if (<= z 1.45e-79)
         (* y (* (exp (* -0.5 (- (log (- t)) (log (/ 1.0 a))))) (* z x)))
         (if (<= z 1.55e+122) t_1 (* y x)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / sqrt(((z * z) - (a * t)))) * (y * x);
	double tmp;
	if (z <= -1e+140) {
		tmp = y * -x;
	} else if (z <= -3.9e-187) {
		tmp = t_1;
	} else if (z <= 1.45e-79) {
		tmp = y * (exp((-0.5 * (log(-t) - log((1.0 / a))))) * (z * x));
	} else if (z <= 1.55e+122) {
		tmp = t_1;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 / sqrt(((z * z) - (a * t)))) * (y * x)
    if (z <= (-1d+140)) then
        tmp = y * -x
    else if (z <= (-3.9d-187)) then
        tmp = t_1
    else if (z <= 1.45d-79) then
        tmp = y * (exp(((-0.5d0) * (log(-t) - log((1.0d0 / a))))) * (z * x))
    else if (z <= 1.55d+122) then
        tmp = t_1
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z / Math.sqrt(((z * z) - (a * t)))) * (y * x);
	double tmp;
	if (z <= -1e+140) {
		tmp = y * -x;
	} else if (z <= -3.9e-187) {
		tmp = t_1;
	} else if (z <= 1.45e-79) {
		tmp = y * (Math.exp((-0.5 * (Math.log(-t) - Math.log((1.0 / a))))) * (z * x));
	} else if (z <= 1.55e+122) {
		tmp = t_1;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	t_1 = (z / math.sqrt(((z * z) - (a * t)))) * (y * x)
	tmp = 0
	if z <= -1e+140:
		tmp = y * -x
	elif z <= -3.9e-187:
		tmp = t_1
	elif z <= 1.45e-79:
		tmp = y * (math.exp((-0.5 * (math.log(-t) - math.log((1.0 / a))))) * (z * x))
	elif z <= 1.55e+122:
		tmp = t_1
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(z / sqrt(Float64(Float64(z * z) - Float64(a * t)))) * Float64(y * x))
	tmp = 0.0
	if (z <= -1e+140)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -3.9e-187)
		tmp = t_1;
	elseif (z <= 1.45e-79)
		tmp = Float64(y * Float64(exp(Float64(-0.5 * Float64(log(Float64(-t)) - log(Float64(1.0 / a))))) * Float64(z * x)));
	elseif (z <= 1.55e+122)
		tmp = t_1;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = (z / sqrt(((z * z) - (a * t)))) * (y * x);
	tmp = 0.0;
	if (z <= -1e+140)
		tmp = y * -x;
	elseif (z <= -3.9e-187)
		tmp = t_1;
	elseif (z <= 1.45e-79)
		tmp = y * (exp((-0.5 * (log(-t) - log((1.0 / a))))) * (z * x));
	elseif (z <= 1.55e+122)
		tmp = t_1;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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[(z / N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+140], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -3.9e-187], t$95$1, If[LessEqual[z, 1.45e-79], N[(y * N[(N[Exp[N[(-0.5 * N[(N[Log[(-t)], $MachinePrecision] - N[Log[N[(1.0 / a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.55e+122], t$95$1, N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.00000000000000006e140

   1. Initial program 17.4%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 17.4%

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

      2. associate-*l* 16.9%

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

      3. associate-*r/ 17.0%

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

   3. Simplified 17.0%

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

   4. Taylor expanded in z around -inf 98.5%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 98.5%

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

   6. Simplified 98.5%

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

   if -1.00000000000000006e140 < z < -3.8999999999999999e-187 or 1.45e-79 < z < 1.54999999999999999e122

   1. Initial program 90.7%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 90.7%

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

      2. associate-*l* 86.4%

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

      3. associate-*r/ 86.0%

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

   3. Simplified 86.0%

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

      1. associate-*r/ 86.4%

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

      2. associate-*r* 90.7%

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

      3. *-commutative 90.7%

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

      4. expm1-log1p-u 71.9%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}}\right)\right)} \]

      5. associate-*l/ 67.3%

         \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\color{blue}{\frac{x \cdot y}{\sqrt{z \cdot z - t \cdot a}} \cdot z}\right)\right) \]

      6. expm1-udef 36.7%

         \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{x \cdot y}{\sqrt{z \cdot z - t \cdot a}} \cdot z\right)} - 1} \]

      7. *-commutative 36.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{z \cdot \frac{x \cdot y}{\sqrt{z \cdot z - t \cdot a}}}\right)} - 1 \]

      8. clear-num 36.7%

         \[\leadsto e^{\mathsf{log1p}\left(z \cdot \color{blue}{\frac{1}{\frac{\sqrt{z \cdot z - t \cdot a}}{x \cdot y}}}\right)} - 1 \]

      9. un-div-inv 36.7%

         \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{z}{\frac{\sqrt{z \cdot z - t \cdot a}}{x \cdot y}}}\right)} - 1 \]

   5. Applied egg-rr 36.7%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{z}{\frac{\sqrt{z \cdot z - t \cdot a}}{x \cdot y}}\right)} - 1} \]
   6. Step-by-step derivation

      1. expm1-def 67.2%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{z}{\frac{\sqrt{z \cdot z - t \cdot a}}{x \cdot y}}\right)\right)} \]

      2. expm1-log1p 86.0%

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

      3. associate-/r/ 93.9%

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

      4. *-commutative 93.9%

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

   7. Simplified 93.9%

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

   if -3.8999999999999999e-187 < z < 1.45e-79

   1. Initial program 66.7%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 66.7%

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

      2. associate-*l* 74.1%

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

      3. associate-*r/ 70.5%

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

   3. Simplified 70.5%

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

      1. clear-num 70.5%

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

      2. associate-/r/ 70.5%

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

      3. pow1/2 70.5%

         \[\leadsto y \cdot \left(\frac{1}{\color{blue}{{\left(z \cdot z - t \cdot a\right)}^{0.5}}} \cdot \left(x \cdot z\right)\right) \]

      4. pow-flip 70.6%

         \[\leadsto y \cdot \left(\color{blue}{{\left(z \cdot z - t \cdot a\right)}^{\left(-0.5\right)}} \cdot \left(x \cdot z\right)\right) \]

      5. metadata-eval 70.6%

         \[\leadsto y \cdot \left({\left(z \cdot z - t \cdot a\right)}^{\color{blue}{-0.5}} \cdot \left(x \cdot z\right)\right) \]

      6. *-commutative 70.6%

         \[\leadsto y \cdot \left({\left(z \cdot z - t \cdot a\right)}^{-0.5} \cdot \color{blue}{\left(z \cdot x\right)}\right) \]

   5. Applied egg-rr 70.6%

      \[\leadsto y \cdot \color{blue}{\left({\left(z \cdot z - t \cdot a\right)}^{-0.5} \cdot \left(z \cdot x\right)\right)} \]

   6. Taylor expanded in a around inf 36.5%

      \[\leadsto y \cdot \left(\color{blue}{e^{-0.5 \cdot \left(\log \left(-t\right) + -1 \cdot \log \left(\frac{1}{a}\right)\right)}} \cdot \left(z \cdot x\right)\right) \]

   if 1.54999999999999999e122 < z

   1. Initial program 33.5%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 33.5%

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

      2. associate-*l* 32.9%

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

      3. associate-*r/ 33.1%

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

   3. Simplified 33.1%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-187}:\\ \;\;\;\;\frac{z}{\sqrt{z \cdot z - a \cdot t}} \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \left(e^{-0.5 \cdot \left(\log \left(-t\right) - \log \left(\frac{1}{a}\right)\right)} \cdot \left(z \cdot x\right)\right)\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;\frac{z}{\sqrt{z \cdot z - a \cdot t}} \cdot \left(y \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2: 90.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{z \cdot x}{\sqrt{z \cdot z - a \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4e+71)
   (* y (- x))
   (if (<= z 5.1e+115) (* y (/ (* z x) (sqrt (- (* z z) (* a t))))) (* y x))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+71) {
		tmp = y * -x;
	} else if (z <= 5.1e+115) {
		tmp = y * ((z * x) / sqrt(((z * z) - (a * t))));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= (-4d+71)) then
        tmp = y * -x
    else if (z <= 5.1d+115) then
        tmp = y * ((z * x) / sqrt(((z * z) - (a * t))))
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4e+71) {
		tmp = y * -x;
	} else if (z <= 5.1e+115) {
		tmp = y * ((z * x) / Math.sqrt(((z * z) - (a * t))));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -4e+71:
		tmp = y * -x
	elif z <= 5.1e+115:
		tmp = y * ((z * x) / math.sqrt(((z * z) - (a * t))))
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4e+71)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 5.1e+115)
		tmp = Float64(y * Float64(Float64(z * x) / sqrt(Float64(Float64(z * z) - Float64(a * t)))));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4e+71)
		tmp = y * -x;
	elseif (z <= 5.1e+115)
		tmp = y * ((z * x) / sqrt(((z * z) - (a * t))));
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4e+71], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 5.1e+115], N[(y * N[(N[(z * x), $MachinePrecision] / N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.0000000000000002e71

   1. Initial program 29.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 29.8%

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

      2. associate-*l* 29.4%

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

      3. associate-*r/ 29.4%

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

   3. Simplified 29.4%

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

   4. Taylor expanded in z around -inf 98.7%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 98.7%

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

   6. Simplified 98.7%

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

   if -4.0000000000000002e71 < z < 5.0999999999999996e115

   1. Initial program 81.5%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 81.5%

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

      2. associate-*l* 81.2%

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

      3. associate-*r/ 79.6%

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

   3. Simplified 79.6%

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

   if 5.0999999999999996e115 < z

   1. Initial program 33.5%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 33.5%

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

      2. associate-*l* 32.9%

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

      3. associate-*r/ 33.1%

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

   3. Simplified 33.1%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+71}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{+115}:\\ \;\;\;\;y \cdot \frac{z \cdot x}{\sqrt{z \cdot z - a \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+117}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{\sqrt{z \cdot z - a \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.3e+51)
   (* y (- x))
   (if (<= z 9.4e+117) (/ (* z (* y x)) (sqrt (- (* z z) (* a t)))) (* y x))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+51) {
		tmp = y * -x;
	} else if (z <= 9.4e+117) {
		tmp = (z * (y * x)) / sqrt(((z * z) - (a * t)));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= (-2.3d+51)) then
        tmp = y * -x
    else if (z <= 9.4d+117) then
        tmp = (z * (y * x)) / sqrt(((z * z) - (a * t)))
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.3e+51) {
		tmp = y * -x;
	} else if (z <= 9.4e+117) {
		tmp = (z * (y * x)) / Math.sqrt(((z * z) - (a * t)));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.3e+51:
		tmp = y * -x
	elif z <= 9.4e+117:
		tmp = (z * (y * x)) / math.sqrt(((z * z) - (a * t)))
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.3e+51)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 9.4e+117)
		tmp = Float64(Float64(z * Float64(y * x)) / sqrt(Float64(Float64(z * z) - Float64(a * t))));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.3e+51)
		tmp = y * -x;
	elseif (z <= 9.4e+117)
		tmp = (z * (y * x)) / sqrt(((z * z) - (a * t)));
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.3e+51], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 9.4e+117], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.30000000000000005e51

   1. Initial program 33.2%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 33.2%

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

      2. associate-*l* 32.7%

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

      3. associate-*r/ 32.8%

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

   3. Simplified 32.8%

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

   4. Taylor expanded in z around -inf 98.8%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 98.8%

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

   6. Simplified 98.8%

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

   if -2.30000000000000005e51 < z < 9.40000000000000011e117

   1. Initial program 81.5%

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

   if 9.40000000000000011e117 < z

   1. Initial program 33.5%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 33.5%

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

      2. associate-*l* 32.9%

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

      3. associate-*r/ 33.1%

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

   3. Simplified 33.1%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 9.4 \cdot 10^{+117}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{\sqrt{z \cdot z - a \cdot t}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 81.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -23000000000:\\ \;\;\;\;y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \frac{t}{\frac{z}{a}} - z}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \frac{z \cdot x}{\sqrt{t \cdot \left(-a\right)}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -23000000000.0)
   (* y (* x (/ z (- (* -0.5 (/ t (/ z a))) z))))
   (if (<= z 9e-77) (* y (/ (* z x) (sqrt (* t (- a))))) (* y x))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -23000000000.0) {
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)));
	} else if (z <= 9e-77) {
		tmp = y * ((z * x) / sqrt((t * -a)));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= (-23000000000.0d0)) then
        tmp = y * (x * (z / (((-0.5d0) * (t / (z / a))) - z)))
    else if (z <= 9d-77) then
        tmp = y * ((z * x) / sqrt((t * -a)))
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -23000000000.0) {
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)));
	} else if (z <= 9e-77) {
		tmp = y * ((z * x) / Math.sqrt((t * -a)));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -23000000000.0:
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)))
	elif z <= 9e-77:
		tmp = y * ((z * x) / math.sqrt((t * -a)))
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -23000000000.0)
		tmp = Float64(y * Float64(x * Float64(z / Float64(Float64(-0.5 * Float64(t / Float64(z / a))) - z))));
	elseif (z <= 9e-77)
		tmp = Float64(y * Float64(Float64(z * x) / sqrt(Float64(t * Float64(-a)))));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -23000000000.0)
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)));
	elseif (z <= 9e-77)
		tmp = y * ((z * x) / sqrt((t * -a)));
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -23000000000.0], N[(y * N[(x * N[(z / N[(N[(-0.5 * N[(t / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9e-77], N[(y * N[(N[(z * x), $MachinePrecision] / N[Sqrt[N[(t * (-a)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e10

   1. Initial program 39.3%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 39.3%

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

      2. associate-*l* 38.9%

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

      3. associate-*r/ 39.0%

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

   3. Simplified 39.0%

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

   4. Taylor expanded in z around -inf 74.3%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{0.5 \cdot \frac{a \cdot t}{z} + -1 \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{0.5 \cdot \left(a \cdot t\right)}{z}} + -1 \cdot z} \]

      2. frac-2neg 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{-0.5 \cdot \left(a \cdot t\right)}{-z}} + -1 \cdot z} \]

      3. *-commutative 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \color{blue}{\left(t \cdot a\right)}}{-z} + -1 \cdot z} \]

      4. mul-1-neg 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{-1 \cdot z}} + -1 \cdot z} \]

      5. add-sqr-sqrt 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{-1 \cdot z} \cdot \sqrt{-1 \cdot z}}} + -1 \cdot z} \]

      6. sqrt-unprod 73.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{\left(-1 \cdot z\right) \cdot \left(-1 \cdot z\right)}}} + -1 \cdot z} \]

      7. mul-1-neg 73.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\color{blue}{\left(-z\right)} \cdot \left(-1 \cdot z\right)}} + -1 \cdot z} \]

      8. mul-1-neg 73.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\left(-z\right) \cdot \color{blue}{\left(-z\right)}}} + -1 \cdot z} \]

      9. sqr-neg 73.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\color{blue}{z \cdot z}}} + -1 \cdot z} \]

      10. sqrt-prod 0.0%

          \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} + -1 \cdot z} \]

      11. add-sqr-sqrt 74.3%

          \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{z}} + -1 \cdot z} \]

   6. Applied egg-rr 74.3%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{-0.5 \cdot \left(t \cdot a\right)}{z}} + -1 \cdot z} \]
   7. Step-by-step derivation

      1. distribute-frac-neg 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-\frac{0.5 \cdot \left(t \cdot a\right)}{z}\right)} + -1 \cdot z} \]

      2. *-commutative 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-\frac{0.5 \cdot \color{blue}{\left(a \cdot t\right)}}{z}\right) + -1 \cdot z} \]

      3. associate-*r/ 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-\color{blue}{0.5 \cdot \frac{a \cdot t}{z}}\right) + -1 \cdot z} \]

      4. associate-/l* 78.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-0.5 \cdot \color{blue}{\frac{a}{\frac{z}{t}}}\right) + -1 \cdot z} \]

      5. distribute-lft-neg-in 78.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-0.5\right) \cdot \frac{a}{\frac{z}{t}}} + -1 \cdot z} \]

      6. metadata-eval 78.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5} \cdot \frac{a}{\frac{z}{t}} + -1 \cdot z} \]

   8. Simplified 78.7%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5 \cdot \frac{a}{\frac{z}{t}}} + -1 \cdot z} \]

   9. Taylor expanded in x around 0 74.3%

      \[\leadsto y \cdot \color{blue}{\frac{z \cdot x}{-1 \cdot z + -0.5 \cdot \frac{a \cdot t}{z}}} \]
   10. Step-by-step derivation

       1. *-commutative 74.3%

          \[\leadsto y \cdot \frac{\color{blue}{x \cdot z}}{-1 \cdot z + -0.5 \cdot \frac{a \cdot t}{z}} \]

       2. neg-mul-1 74.3%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-z\right)} + -0.5 \cdot \frac{a \cdot t}{z}} \]

       3. +-commutative 74.3%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5 \cdot \frac{a \cdot t}{z} + \left(-z\right)}} \]

       4. associate-*l/ 78.7%

          \[\leadsto y \cdot \frac{x \cdot z}{-0.5 \cdot \color{blue}{\left(\frac{a}{z} \cdot t\right)} + \left(-z\right)} \]

       5. fma-udef 78.7%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}} \]

       6. *-lft-identity 78.7%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{1 \cdot \mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}} \]

       7. times-frac 95.1%

          \[\leadsto y \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{z}{\mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}\right)} \]

       8. /-rgt-identity 95.1%

          \[\leadsto y \cdot \left(\color{blue}{x} \cdot \frac{z}{\mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}\right) \]

       9. fma-neg 95.1%

          \[\leadsto y \cdot \left(x \cdot \frac{z}{\color{blue}{-0.5 \cdot \left(\frac{a}{z} \cdot t\right) - z}}\right) \]

       10. associate-*l/ 90.7%

           \[\leadsto y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \color{blue}{\frac{a \cdot t}{z}} - z}\right) \]

       11. *-commutative 90.7%

           \[\leadsto y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \frac{\color{blue}{t \cdot a}}{z} - z}\right) \]

       12. associate-/l* 95.1%

           \[\leadsto y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \color{blue}{\frac{t}{\frac{z}{a}}} - z}\right) \]

   11. Simplified 95.1%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot \frac{z}{-0.5 \cdot \frac{t}{\frac{z}{a}} - z}\right)} \]

   if -2.3e10 < z < 9.0000000000000001e-77

   1. Initial program 72.7%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 72.7%

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

      2. associate-*l* 75.3%

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

      3. associate-*r/ 72.9%

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

   3. Simplified 72.9%

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

   4. Taylor expanded in z around 0 65.3%

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

      1. mul-1-neg 65.3%

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

      2. distribute-rgt-neg-out 65.3%

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

   6. Simplified 65.3%

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

   if 9.0000000000000001e-77 < z

   1. Initial program 62.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 62.8%

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

      2. associate-*l* 60.3%

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

      3. associate-*r/ 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around inf 95.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -23000000000:\\ \;\;\;\;y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \frac{t}{\frac{z}{a}} - z}\right)\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \frac{z \cdot x}{\sqrt{t \cdot \left(-a\right)}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 5: 81.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -23000000000:\\ \;\;\;\;y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \frac{t}{\frac{z}{a}} - z}\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{z \cdot x}{\frac{\sqrt{t \cdot \left(-a\right)}}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -23000000000.0)
   (* y (* x (/ z (- (* -0.5 (/ t (/ z a))) z))))
   (if (<= z 1.4e-77) (/ (* z x) (/ (sqrt (* t (- a))) y)) (* y x))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -23000000000.0) {
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)));
	} else if (z <= 1.4e-77) {
		tmp = (z * x) / (sqrt((t * -a)) / y);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= (-23000000000.0d0)) then
        tmp = y * (x * (z / (((-0.5d0) * (t / (z / a))) - z)))
    else if (z <= 1.4d-77) then
        tmp = (z * x) / (sqrt((t * -a)) / y)
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -23000000000.0) {
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)));
	} else if (z <= 1.4e-77) {
		tmp = (z * x) / (Math.sqrt((t * -a)) / y);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -23000000000.0:
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)))
	elif z <= 1.4e-77:
		tmp = (z * x) / (math.sqrt((t * -a)) / y)
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -23000000000.0)
		tmp = Float64(y * Float64(x * Float64(z / Float64(Float64(-0.5 * Float64(t / Float64(z / a))) - z))));
	elseif (z <= 1.4e-77)
		tmp = Float64(Float64(z * x) / Float64(sqrt(Float64(t * Float64(-a))) / y));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -23000000000.0)
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)));
	elseif (z <= 1.4e-77)
		tmp = (z * x) / (sqrt((t * -a)) / y);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -23000000000.0], N[(y * N[(x * N[(z / N[(N[(-0.5 * N[(t / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e-77], N[(N[(z * x), $MachinePrecision] / N[(N[Sqrt[N[(t * (-a)), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3e10

   1. Initial program 39.3%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 39.3%

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

      2. associate-*l* 38.9%

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

      3. associate-*r/ 39.0%

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

   3. Simplified 39.0%

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

   4. Taylor expanded in z around -inf 74.3%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{0.5 \cdot \frac{a \cdot t}{z} + -1 \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{0.5 \cdot \left(a \cdot t\right)}{z}} + -1 \cdot z} \]

      2. frac-2neg 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{-0.5 \cdot \left(a \cdot t\right)}{-z}} + -1 \cdot z} \]

      3. *-commutative 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \color{blue}{\left(t \cdot a\right)}}{-z} + -1 \cdot z} \]

      4. mul-1-neg 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{-1 \cdot z}} + -1 \cdot z} \]

      5. add-sqr-sqrt 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{-1 \cdot z} \cdot \sqrt{-1 \cdot z}}} + -1 \cdot z} \]

      6. sqrt-unprod 73.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{\left(-1 \cdot z\right) \cdot \left(-1 \cdot z\right)}}} + -1 \cdot z} \]

      7. mul-1-neg 73.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\color{blue}{\left(-z\right)} \cdot \left(-1 \cdot z\right)}} + -1 \cdot z} \]

      8. mul-1-neg 73.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\left(-z\right) \cdot \color{blue}{\left(-z\right)}}} + -1 \cdot z} \]

      9. sqr-neg 73.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\color{blue}{z \cdot z}}} + -1 \cdot z} \]

      10. sqrt-prod 0.0%

          \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} + -1 \cdot z} \]

      11. add-sqr-sqrt 74.3%

          \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{z}} + -1 \cdot z} \]

   6. Applied egg-rr 74.3%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{-0.5 \cdot \left(t \cdot a\right)}{z}} + -1 \cdot z} \]
   7. Step-by-step derivation

      1. distribute-frac-neg 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-\frac{0.5 \cdot \left(t \cdot a\right)}{z}\right)} + -1 \cdot z} \]

      2. *-commutative 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-\frac{0.5 \cdot \color{blue}{\left(a \cdot t\right)}}{z}\right) + -1 \cdot z} \]

      3. associate-*r/ 74.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-\color{blue}{0.5 \cdot \frac{a \cdot t}{z}}\right) + -1 \cdot z} \]

      4. associate-/l* 78.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-0.5 \cdot \color{blue}{\frac{a}{\frac{z}{t}}}\right) + -1 \cdot z} \]

      5. distribute-lft-neg-in 78.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-0.5\right) \cdot \frac{a}{\frac{z}{t}}} + -1 \cdot z} \]

      6. metadata-eval 78.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5} \cdot \frac{a}{\frac{z}{t}} + -1 \cdot z} \]

   8. Simplified 78.7%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5 \cdot \frac{a}{\frac{z}{t}}} + -1 \cdot z} \]

   9. Taylor expanded in x around 0 74.3%

      \[\leadsto y \cdot \color{blue}{\frac{z \cdot x}{-1 \cdot z + -0.5 \cdot \frac{a \cdot t}{z}}} \]
   10. Step-by-step derivation

       1. *-commutative 74.3%

          \[\leadsto y \cdot \frac{\color{blue}{x \cdot z}}{-1 \cdot z + -0.5 \cdot \frac{a \cdot t}{z}} \]

       2. neg-mul-1 74.3%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-z\right)} + -0.5 \cdot \frac{a \cdot t}{z}} \]

       3. +-commutative 74.3%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5 \cdot \frac{a \cdot t}{z} + \left(-z\right)}} \]

       4. associate-*l/ 78.7%

          \[\leadsto y \cdot \frac{x \cdot z}{-0.5 \cdot \color{blue}{\left(\frac{a}{z} \cdot t\right)} + \left(-z\right)} \]

       5. fma-udef 78.7%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}} \]

       6. *-lft-identity 78.7%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{1 \cdot \mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}} \]

       7. times-frac 95.1%

          \[\leadsto y \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{z}{\mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}\right)} \]

       8. /-rgt-identity 95.1%

          \[\leadsto y \cdot \left(\color{blue}{x} \cdot \frac{z}{\mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}\right) \]

       9. fma-neg 95.1%

          \[\leadsto y \cdot \left(x \cdot \frac{z}{\color{blue}{-0.5 \cdot \left(\frac{a}{z} \cdot t\right) - z}}\right) \]

       10. associate-*l/ 90.7%

           \[\leadsto y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \color{blue}{\frac{a \cdot t}{z}} - z}\right) \]

       11. *-commutative 90.7%

           \[\leadsto y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \frac{\color{blue}{t \cdot a}}{z} - z}\right) \]

       12. associate-/l* 95.1%

           \[\leadsto y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \color{blue}{\frac{t}{\frac{z}{a}}} - z}\right) \]

   11. Simplified 95.1%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot \frac{z}{-0.5 \cdot \frac{t}{\frac{z}{a}} - z}\right)} \]

   if -2.3e10 < z < 1.4e-77

   1. Initial program 72.7%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 72.7%

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

      2. associate-*l* 75.3%

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

      3. associate-*r/ 72.9%

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

   3. Simplified 72.9%

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

      1. associate-*r/ 75.3%

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

      2. associate-*r* 72.7%

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

      3. *-commutative 72.7%

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

      4. associate-*l/ 68.1%

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

      5. *-commutative 68.1%

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

      6. associate-/l* 72.0%

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

      7. associate-*r/ 73.3%

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

   5. Applied egg-rr 73.3%

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

   6. Taylor expanded in z around 0 66.9%

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

      1. mul-1-neg 65.3%

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

      2. distribute-rgt-neg-out 65.3%

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

   8. Simplified 66.9%

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

   if 1.4e-77 < z

   1. Initial program 62.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 62.8%

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

      2. associate-*l* 60.3%

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

      3. associate-*r/ 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around inf 95.9%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -23000000000:\\ \;\;\;\;y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \frac{t}{\frac{z}{a}} - z}\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{z \cdot x}{\frac{\sqrt{t \cdot \left(-a\right)}}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 6: 75.5% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-170}:\\ \;\;\;\;-2 \cdot \left(\frac{y}{a} \cdot \left(z \cdot \frac{z \cdot x}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e-288)
   (* y (- x))
   (if (<= z 1.45e-170) (* -2.0 (* (/ y a) (* z (/ (* z x) t)))) (* y x))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-288) {
		tmp = y * -x;
	} else if (z <= 1.45e-170) {
		tmp = -2.0 * ((y / a) * (z * ((z * x) / t)));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= (-2.4d-288)) then
        tmp = y * -x
    else if (z <= 1.45d-170) then
        tmp = (-2.0d0) * ((y / a) * (z * ((z * x) / t)))
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-288) {
		tmp = y * -x;
	} else if (z <= 1.45e-170) {
		tmp = -2.0 * ((y / a) * (z * ((z * x) / t)));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e-288:
		tmp = y * -x
	elif z <= 1.45e-170:
		tmp = -2.0 * ((y / a) * (z * ((z * x) / t)))
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e-288)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.45e-170)
		tmp = Float64(-2.0 * Float64(Float64(y / a) * Float64(z * Float64(Float64(z * x) / t))));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e-288)
		tmp = y * -x;
	elseif (z <= 1.45e-170)
		tmp = -2.0 * ((y / a) * (z * ((z * x) / t)));
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e-288], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.45e-170], N[(-2.0 * N[(N[(y / a), $MachinePrecision] * N[(z * N[(N[(z * x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999998e-288

   1. Initial program 47.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 47.8%

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

      2. associate-*l* 47.5%

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

      3. associate-*r/ 46.9%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in z around -inf 79.7%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 79.7%

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

   6. Simplified 79.7%

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

   if -2.3999999999999998e-288 < z < 1.45e-170

   1. Initial program 80.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in z around inf 57.7%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z + -0.5 \cdot \frac{a \cdot t}{z}}} \cdot z \]
   5. Step-by-step derivation

      1. associate-/l* 58.8%

         \[\leadsto \frac{x \cdot y}{z + -0.5 \cdot \color{blue}{\frac{a}{\frac{z}{t}}}} \cdot z \]

   6. Simplified 58.8%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z + -0.5 \cdot \frac{a}{\frac{z}{t}}}} \cdot z \]

   7. Taylor expanded in z around 0 55.7%

      \[\leadsto \color{blue}{-2 \cdot \frac{y \cdot \left({z}^{2} \cdot x\right)}{a \cdot t}} \]
   8. Step-by-step derivation

      1. times-frac 55.8%

         \[\leadsto -2 \cdot \color{blue}{\left(\frac{y}{a} \cdot \frac{{z}^{2} \cdot x}{t}\right)} \]

      2. unpow2 55.8%

         \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \frac{\color{blue}{\left(z \cdot z\right)} \cdot x}{t}\right) \]

   9. Simplified 55.8%

      \[\leadsto \color{blue}{-2 \cdot \left(\frac{y}{a} \cdot \frac{\left(z \cdot z\right) \cdot x}{t}\right)} \]

   10. Taylor expanded in z around 0 55.8%

       \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \color{blue}{\frac{{z}^{2} \cdot x}{t}}\right) \]
   11. Step-by-step derivation

       1. unpow2 55.8%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \frac{\color{blue}{\left(z \cdot z\right)} \cdot x}{t}\right) \]

       2. associate-*r* 55.8%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \frac{\color{blue}{z \cdot \left(z \cdot x\right)}}{t}\right) \]

       3. *-rgt-identity 55.8%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \frac{\color{blue}{\left(z \cdot \left(z \cdot x\right)\right) \cdot 1}}{t}\right) \]

       4. associate-*r/ 55.8%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \color{blue}{\left(\left(z \cdot \left(z \cdot x\right)\right) \cdot \frac{1}{t}\right)}\right) \]

       5. associate-*l* 56.4%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \color{blue}{\left(z \cdot \left(\left(z \cdot x\right) \cdot \frac{1}{t}\right)\right)}\right) \]

       6. associate-*r/ 56.4%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \left(z \cdot \color{blue}{\frac{\left(z \cdot x\right) \cdot 1}{t}}\right)\right) \]

       7. *-rgt-identity 56.4%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \left(z \cdot \frac{\color{blue}{z \cdot x}}{t}\right)\right) \]

   12. Simplified 56.4%

       \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \color{blue}{\left(z \cdot \frac{z \cdot x}{t}\right)}\right) \]

   if 1.45e-170 < z

   1. Initial program 62.4%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 62.4%

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

      2. associate-*l* 61.1%

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

      3. associate-*r/ 60.8%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in z around inf 85.6%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-170}:\\ \;\;\;\;-2 \cdot \left(\frac{y}{a} \cdot \left(z \cdot \frac{z \cdot x}{t}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 7: 75.5% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-169}:\\ \;\;\;\;-2 \cdot \frac{y \cdot \left(z \cdot \frac{z}{\frac{t}{x}}\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e-288)
   (* y (- x))
   (if (<= z 1.28e-169) (* -2.0 (/ (* y (* z (/ z (/ t x)))) a)) (* y x))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-288) {
		tmp = y * -x;
	} else if (z <= 1.28e-169) {
		tmp = -2.0 * ((y * (z * (z / (t / x)))) / a);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= (-2.4d-288)) then
        tmp = y * -x
    else if (z <= 1.28d-169) then
        tmp = (-2.0d0) * ((y * (z * (z / (t / x)))) / a)
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-288) {
		tmp = y * -x;
	} else if (z <= 1.28e-169) {
		tmp = -2.0 * ((y * (z * (z / (t / x)))) / a);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e-288:
		tmp = y * -x
	elif z <= 1.28e-169:
		tmp = -2.0 * ((y * (z * (z / (t / x)))) / a)
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e-288)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.28e-169)
		tmp = Float64(-2.0 * Float64(Float64(y * Float64(z * Float64(z / Float64(t / x)))) / a));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e-288)
		tmp = y * -x;
	elseif (z <= 1.28e-169)
		tmp = -2.0 * ((y * (z * (z / (t / x)))) / a);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e-288], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.28e-169], N[(-2.0 * N[(N[(y * N[(z * N[(z / N[(t / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999998e-288

   1. Initial program 47.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 47.8%

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

      2. associate-*l* 47.5%

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

      3. associate-*r/ 46.9%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in z around -inf 79.7%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 79.7%

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

   6. Simplified 79.7%

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

   if -2.3999999999999998e-288 < z < 1.28e-169

   1. Initial program 80.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. associate-*l/ 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in z around inf 57.7%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z + -0.5 \cdot \frac{a \cdot t}{z}}} \cdot z \]
   5. Step-by-step derivation

      1. associate-/l* 58.8%

         \[\leadsto \frac{x \cdot y}{z + -0.5 \cdot \color{blue}{\frac{a}{\frac{z}{t}}}} \cdot z \]

   6. Simplified 58.8%

      \[\leadsto \frac{x \cdot y}{\color{blue}{z + -0.5 \cdot \frac{a}{\frac{z}{t}}}} \cdot z \]

   7. Taylor expanded in z around 0 55.7%

      \[\leadsto \color{blue}{-2 \cdot \frac{y \cdot \left({z}^{2} \cdot x\right)}{a \cdot t}} \]
   8. Step-by-step derivation

      1. times-frac 55.8%

         \[\leadsto -2 \cdot \color{blue}{\left(\frac{y}{a} \cdot \frac{{z}^{2} \cdot x}{t}\right)} \]

      2. unpow2 55.8%

         \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \frac{\color{blue}{\left(z \cdot z\right)} \cdot x}{t}\right) \]

   9. Simplified 55.8%

      \[\leadsto \color{blue}{-2 \cdot \left(\frac{y}{a} \cdot \frac{\left(z \cdot z\right) \cdot x}{t}\right)} \]

   10. Taylor expanded in z around 0 55.8%

       \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \color{blue}{\frac{{z}^{2} \cdot x}{t}}\right) \]
   11. Step-by-step derivation

       1. unpow2 55.8%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \frac{\color{blue}{\left(z \cdot z\right)} \cdot x}{t}\right) \]

       2. associate-*r* 55.8%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \frac{\color{blue}{z \cdot \left(z \cdot x\right)}}{t}\right) \]

       3. *-rgt-identity 55.8%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \frac{\color{blue}{\left(z \cdot \left(z \cdot x\right)\right) \cdot 1}}{t}\right) \]

       4. associate-*r/ 55.8%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \color{blue}{\left(\left(z \cdot \left(z \cdot x\right)\right) \cdot \frac{1}{t}\right)}\right) \]

       5. associate-*l* 56.4%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \color{blue}{\left(z \cdot \left(\left(z \cdot x\right) \cdot \frac{1}{t}\right)\right)}\right) \]

       6. associate-*r/ 56.4%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \left(z \cdot \color{blue}{\frac{\left(z \cdot x\right) \cdot 1}{t}}\right)\right) \]

       7. *-rgt-identity 56.4%

          \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \left(z \cdot \frac{\color{blue}{z \cdot x}}{t}\right)\right) \]

   12. Simplified 56.4%

       \[\leadsto -2 \cdot \left(\frac{y}{a} \cdot \color{blue}{\left(z \cdot \frac{z \cdot x}{t}\right)}\right) \]
   13. Step-by-step derivation

       1. associate-*l/ 56.4%

          \[\leadsto -2 \cdot \color{blue}{\frac{y \cdot \left(z \cdot \frac{z \cdot x}{t}\right)}{a}} \]

       2. associate-/l* 52.4%

          \[\leadsto -2 \cdot \frac{y \cdot \left(z \cdot \color{blue}{\frac{z}{\frac{t}{x}}}\right)}{a} \]

   14. Applied egg-rr 52.4%

       \[\leadsto -2 \cdot \color{blue}{\frac{y \cdot \left(z \cdot \frac{z}{\frac{t}{x}}\right)}{a}} \]

   if 1.28e-169 < z

   1. Initial program 62.4%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 62.4%

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

      2. associate-*l* 61.1%

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

      3. associate-*r/ 60.8%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in z around inf 85.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-169}:\\ \;\;\;\;-2 \cdot \frac{y \cdot \left(z \cdot \frac{z}{\frac{t}{x}}\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 8: 75.5% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-169}:\\ \;\;\;\;y \cdot \frac{z \cdot x}{-0.5 \cdot \left(t \cdot \frac{a}{z}\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e-288)
   (* y (- x))
   (if (<= z 3.5e-169) (* y (/ (* z x) (* -0.5 (* t (/ a z))))) (* y x))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-288) {
		tmp = y * -x;
	} else if (z <= 3.5e-169) {
		tmp = y * ((z * x) / (-0.5 * (t * (a / z))));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= (-2.4d-288)) then
        tmp = y * -x
    else if (z <= 3.5d-169) then
        tmp = y * ((z * x) / ((-0.5d0) * (t * (a / z))))
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-288) {
		tmp = y * -x;
	} else if (z <= 3.5e-169) {
		tmp = y * ((z * x) / (-0.5 * (t * (a / z))));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e-288:
		tmp = y * -x
	elif z <= 3.5e-169:
		tmp = y * ((z * x) / (-0.5 * (t * (a / z))))
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e-288)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 3.5e-169)
		tmp = Float64(y * Float64(Float64(z * x) / Float64(-0.5 * Float64(t * Float64(a / z)))));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e-288)
		tmp = y * -x;
	elseif (z <= 3.5e-169)
		tmp = y * ((z * x) / (-0.5 * (t * (a / z))));
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e-288], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 3.5e-169], N[(y * N[(N[(z * x), $MachinePrecision] / N[(-0.5 * N[(t * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999998e-288

   1. Initial program 47.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 47.8%

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

      2. associate-*l* 47.5%

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

      3. associate-*r/ 46.9%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in z around -inf 79.7%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 79.7%

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

   6. Simplified 79.7%

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

   if -2.3999999999999998e-288 < z < 3.5000000000000003e-169

   1. Initial program 80.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 80.8%

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

      2. associate-*l* 84.2%

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

      3. associate-*r/ 80.6%

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

   3. Simplified 80.6%

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

   4. Taylor expanded in z around -inf 55.7%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{0.5 \cdot \frac{a \cdot t}{z} + -1 \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 55.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{0.5 \cdot \left(a \cdot t\right)}{z}} + -1 \cdot z} \]

      2. frac-2neg 55.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{-0.5 \cdot \left(a \cdot t\right)}{-z}} + -1 \cdot z} \]

      3. *-commutative 55.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \color{blue}{\left(t \cdot a\right)}}{-z} + -1 \cdot z} \]

      4. mul-1-neg 55.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{-1 \cdot z}} + -1 \cdot z} \]

      5. add-sqr-sqrt 9.6%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{-1 \cdot z} \cdot \sqrt{-1 \cdot z}}} + -1 \cdot z} \]

      6. sqrt-unprod 55.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{\left(-1 \cdot z\right) \cdot \left(-1 \cdot z\right)}}} + -1 \cdot z} \]

      7. mul-1-neg 55.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\color{blue}{\left(-z\right)} \cdot \left(-1 \cdot z\right)}} + -1 \cdot z} \]

      8. mul-1-neg 55.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\left(-z\right) \cdot \color{blue}{\left(-z\right)}}} + -1 \cdot z} \]

      9. sqr-neg 55.7%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\color{blue}{z \cdot z}}} + -1 \cdot z} \]

      10. sqrt-prod 46.3%

          \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} + -1 \cdot z} \]

      11. add-sqr-sqrt 55.9%

          \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{z}} + -1 \cdot z} \]

   6. Applied egg-rr 55.9%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{-0.5 \cdot \left(t \cdot a\right)}{z}} + -1 \cdot z} \]
   7. Step-by-step derivation

      1. distribute-frac-neg 55.9%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-\frac{0.5 \cdot \left(t \cdot a\right)}{z}\right)} + -1 \cdot z} \]

      2. *-commutative 55.9%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-\frac{0.5 \cdot \color{blue}{\left(a \cdot t\right)}}{z}\right) + -1 \cdot z} \]

      3. associate-*r/ 55.9%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-\color{blue}{0.5 \cdot \frac{a \cdot t}{z}}\right) + -1 \cdot z} \]

      4. associate-/l* 56.4%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-0.5 \cdot \color{blue}{\frac{a}{\frac{z}{t}}}\right) + -1 \cdot z} \]

      5. distribute-lft-neg-in 56.4%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-0.5\right) \cdot \frac{a}{\frac{z}{t}}} + -1 \cdot z} \]

      6. metadata-eval 56.4%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5} \cdot \frac{a}{\frac{z}{t}} + -1 \cdot z} \]

   8. Simplified 56.4%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5 \cdot \frac{a}{\frac{z}{t}}} + -1 \cdot z} \]

   9. Taylor expanded in a around inf 56.0%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5 \cdot \frac{a \cdot t}{z}}} \]
   10. Step-by-step derivation

       1. associate-*l/ 56.4%

          \[\leadsto y \cdot \frac{x \cdot z}{-0.5 \cdot \color{blue}{\left(\frac{a}{z} \cdot t\right)}} \]

       2. *-commutative 56.4%

          \[\leadsto y \cdot \frac{x \cdot z}{-0.5 \cdot \color{blue}{\left(t \cdot \frac{a}{z}\right)}} \]

   11. Simplified 56.4%

       \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5 \cdot \left(t \cdot \frac{a}{z}\right)}} \]

   if 3.5000000000000003e-169 < z

   1. Initial program 62.4%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 62.4%

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

      2. associate-*l* 61.1%

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

      3. associate-*r/ 60.8%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in z around inf 85.6%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{-169}:\\ \;\;\;\;y \cdot \frac{z \cdot x}{-0.5 \cdot \left(t \cdot \frac{a}{z}\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 9: 77.4% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \frac{t}{\frac{z}{a}} - z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z 1.7e-170) (* y (* x (/ z (- (* -0.5 (/ t (/ z a))) z)))) (* y x)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.7e-170) {
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= 1.7d-170) then
        tmp = y * (x * (z / (((-0.5d0) * (t / (z / a))) - z)))
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.7e-170) {
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.7e-170:
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)))
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.7e-170)
		tmp = Float64(y * Float64(x * Float64(z / Float64(Float64(-0.5 * Float64(t / Float64(z / a))) - z))));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.7e-170)
		tmp = y * (x * (z / ((-0.5 * (t / (z / a))) - z)));
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, 1.7e-170], N[(y * N[(x * N[(z / N[(N[(-0.5 * N[(t / N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.70000000000000006e-170

   1. Initial program 53.9%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 53.9%

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

      2. associate-*l* 54.3%

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

      3. associate-*r/ 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in z around -inf 64.1%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{0.5 \cdot \frac{a \cdot t}{z} + -1 \cdot z}} \]
   5. Step-by-step derivation

      1. associate-*r/ 64.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{0.5 \cdot \left(a \cdot t\right)}{z}} + -1 \cdot z} \]

      2. frac-2neg 64.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{-0.5 \cdot \left(a \cdot t\right)}{-z}} + -1 \cdot z} \]

      3. *-commutative 64.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \color{blue}{\left(t \cdot a\right)}}{-z} + -1 \cdot z} \]

      4. mul-1-neg 64.1%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{-1 \cdot z}} + -1 \cdot z} \]

      5. add-sqr-sqrt 55.6%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{-1 \cdot z} \cdot \sqrt{-1 \cdot z}}} + -1 \cdot z} \]

      6. sqrt-unprod 61.9%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{\left(-1 \cdot z\right) \cdot \left(-1 \cdot z\right)}}} + -1 \cdot z} \]

      7. mul-1-neg 61.9%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\color{blue}{\left(-z\right)} \cdot \left(-1 \cdot z\right)}} + -1 \cdot z} \]

      8. mul-1-neg 61.9%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\left(-z\right) \cdot \color{blue}{\left(-z\right)}}} + -1 \cdot z} \]

      9. sqr-neg 61.9%

         \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\sqrt{\color{blue}{z \cdot z}}} + -1 \cdot z} \]

      10. sqrt-prod 8.6%

          \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{\sqrt{z} \cdot \sqrt{z}}} + -1 \cdot z} \]

      11. add-sqr-sqrt 63.3%

          \[\leadsto y \cdot \frac{x \cdot z}{\frac{-0.5 \cdot \left(t \cdot a\right)}{\color{blue}{z}} + -1 \cdot z} \]

   6. Applied egg-rr 63.3%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\frac{-0.5 \cdot \left(t \cdot a\right)}{z}} + -1 \cdot z} \]
   7. Step-by-step derivation

      1. distribute-frac-neg 63.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-\frac{0.5 \cdot \left(t \cdot a\right)}{z}\right)} + -1 \cdot z} \]

      2. *-commutative 63.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-\frac{0.5 \cdot \color{blue}{\left(a \cdot t\right)}}{z}\right) + -1 \cdot z} \]

      3. associate-*r/ 63.3%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-\color{blue}{0.5 \cdot \frac{a \cdot t}{z}}\right) + -1 \cdot z} \]

      4. associate-/l* 66.0%

         \[\leadsto y \cdot \frac{x \cdot z}{\left(-0.5 \cdot \color{blue}{\frac{a}{\frac{z}{t}}}\right) + -1 \cdot z} \]

      5. distribute-lft-neg-in 66.0%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-0.5\right) \cdot \frac{a}{\frac{z}{t}}} + -1 \cdot z} \]

      6. metadata-eval 66.0%

         \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5} \cdot \frac{a}{\frac{z}{t}} + -1 \cdot z} \]

   8. Simplified 66.0%

      \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5 \cdot \frac{a}{\frac{z}{t}}} + -1 \cdot z} \]

   9. Taylor expanded in x around 0 63.3%

      \[\leadsto y \cdot \color{blue}{\frac{z \cdot x}{-1 \cdot z + -0.5 \cdot \frac{a \cdot t}{z}}} \]
   10. Step-by-step derivation

       1. *-commutative 63.3%

          \[\leadsto y \cdot \frac{\color{blue}{x \cdot z}}{-1 \cdot z + -0.5 \cdot \frac{a \cdot t}{z}} \]

       2. neg-mul-1 63.3%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\left(-z\right)} + -0.5 \cdot \frac{a \cdot t}{z}} \]

       3. +-commutative 63.3%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{-0.5 \cdot \frac{a \cdot t}{z} + \left(-z\right)}} \]

       4. associate-*l/ 66.0%

          \[\leadsto y \cdot \frac{x \cdot z}{-0.5 \cdot \color{blue}{\left(\frac{a}{z} \cdot t\right)} + \left(-z\right)} \]

       5. fma-udef 66.0%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{\mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}} \]

       6. *-lft-identity 66.0%

          \[\leadsto y \cdot \frac{x \cdot z}{\color{blue}{1 \cdot \mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}} \]

       7. times-frac 76.5%

          \[\leadsto y \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{z}{\mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}\right)} \]

       8. /-rgt-identity 76.5%

          \[\leadsto y \cdot \left(\color{blue}{x} \cdot \frac{z}{\mathsf{fma}\left(-0.5, \frac{a}{z} \cdot t, -z\right)}\right) \]

       9. fma-neg 76.5%

          \[\leadsto y \cdot \left(x \cdot \frac{z}{\color{blue}{-0.5 \cdot \left(\frac{a}{z} \cdot t\right) - z}}\right) \]

       10. associate-*l/ 73.9%

           \[\leadsto y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \color{blue}{\frac{a \cdot t}{z}} - z}\right) \]

       11. *-commutative 73.9%

           \[\leadsto y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \frac{\color{blue}{t \cdot a}}{z} - z}\right) \]

       12. associate-/l* 76.5%

           \[\leadsto y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \color{blue}{\frac{t}{\frac{z}{a}}} - z}\right) \]

   11. Simplified 76.5%

       \[\leadsto y \cdot \color{blue}{\left(x \cdot \frac{z}{-0.5 \cdot \frac{t}{\frac{z}{a}} - z}\right)} \]

   if 1.70000000000000006e-170 < z

   1. Initial program 62.4%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 62.4%

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

      2. associate-*l* 61.1%

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

      3. associate-*r/ 60.8%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in z around inf 85.6%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{-170}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{z}{-0.5 \cdot \frac{t}{\frac{z}{a}} - z}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 10: 75.6% accurate, 9.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-192}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{-z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e-47)
   (* y (- x))
   (if (<= z 1.48e-192) (/ (* z (* y x)) (- z)) (* y x))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-47) {
		tmp = y * -x;
	} else if (z <= 1.48e-192) {
		tmp = (z * (y * x)) / -z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= (-2d-47)) then
        tmp = y * -x
    else if (z <= 1.48d-192) then
        tmp = (z * (y * x)) / -z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-47) {
		tmp = y * -x;
	} else if (z <= 1.48e-192) {
		tmp = (z * (y * x)) / -z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e-47:
		tmp = y * -x
	elif z <= 1.48e-192:
		tmp = (z * (y * x)) / -z
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e-47)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.48e-192)
		tmp = Float64(Float64(z * Float64(y * x)) / Float64(-z));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e-47)
		tmp = y * -x;
	elseif (z <= 1.48e-192)
		tmp = (z * (y * x)) / -z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e-47], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.48e-192], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] / (-z)), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.9999999999999999e-47

   1. Initial program 44.3%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 44.3%

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

      2. associate-*l* 43.0%

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

      3. associate-*r/ 43.1%

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

   3. Simplified 43.1%

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

   4. Taylor expanded in z around -inf 92.3%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 92.3%

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

   6. Simplified 92.3%

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

   if -1.9999999999999999e-47 < z < 1.4800000000000001e-192

   1. Initial program 73.1%

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

   2. Taylor expanded in z around -inf 32.2%

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

      1. mul-1-neg 32.2%

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

   4. Simplified 32.2%

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

   if 1.4800000000000001e-192 < z

   1. Initial program 62.3%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 62.3%

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

      2. associate-*l* 60.9%

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

      3. associate-*r/ 60.7%

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

   3. Simplified 60.7%

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

   4. Taylor expanded in z around inf 84.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-47}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.48 \cdot 10^{-192}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{-z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 11: 74.4% accurate, 10.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \frac{z \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e-288)
   (* y (- x))
   (if (<= z 3.7e-236) (* y (/ (* z x) z)) (* y x))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-288) {
		tmp = y * -x;
	} else if (z <= 3.7e-236) {
		tmp = y * ((z * x) / z);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= (-2.4d-288)) then
        tmp = y * -x
    else if (z <= 3.7d-236) then
        tmp = y * ((z * x) / z)
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-288) {
		tmp = y * -x;
	} else if (z <= 3.7e-236) {
		tmp = y * ((z * x) / z);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e-288:
		tmp = y * -x
	elif z <= 3.7e-236:
		tmp = y * ((z * x) / z)
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e-288)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 3.7e-236)
		tmp = Float64(y * Float64(Float64(z * x) / z));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e-288)
		tmp = y * -x;
	elseif (z <= 3.7e-236)
		tmp = y * ((z * x) / z);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e-288], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 3.7e-236], N[(y * N[(N[(z * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.3999999999999998e-288

   1. Initial program 47.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 47.8%

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

      2. associate-*l* 47.5%

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

      3. associate-*r/ 46.9%

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

   3. Simplified 46.9%

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

   4. Taylor expanded in z around -inf 79.7%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 79.7%

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

   6. Simplified 79.7%

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

   if -2.3999999999999998e-288 < z < 3.70000000000000021e-236

   1. Initial program 91.9%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 91.9%

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

      2. associate-*l* 91.9%

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

      3. associate-*r/ 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in z around inf 43.4%

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

   if 3.70000000000000021e-236 < z

   1. Initial program 62.4%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 62.4%

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

      2. associate-*l* 61.9%

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

      3. associate-*r/ 61.7%

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

   3. Simplified 61.7%

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

   4. Taylor expanded in z around inf 79.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-288}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \frac{z \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 12: 73.4% accurate, 18.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6.2e-306) (* y (- x)) (* y x)))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e-306) {
		tmp = y * -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: 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 (z <= (-6.2d-306)) then
        tmp = y * -x
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

assert x < y;
assert t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6.2e-306) {
		tmp = y * -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	tmp = 0
	if z <= -6.2e-306:
		tmp = y * -x
	else:
		tmp = y * x
	return tmp

Julia

x, y = sort([x, y])
t, a = sort([t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6.2e-306)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
t, a = num2cell(sort([t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6.2e-306)
		tmp = y * -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6.2e-306], N[(y * (-x)), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.19999999999999995e-306

   1. Initial program 48.3%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 48.3%

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

      2. associate-*l* 48.1%

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

      3. associate-*r/ 47.4%

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

   3. Simplified 47.4%

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

   4. Taylor expanded in z around -inf 78.4%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot x\right)} \]
   5. Step-by-step derivation

      1. neg-mul-1 78.4%

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

   6. Simplified 78.4%

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

   if -6.19999999999999995e-306 < z

   1. Initial program 65.8%

      \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
   2. Step-by-step derivation

      1. *-commutative 65.8%

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

      2. associate-*l* 65.4%

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

      3. associate-*r/ 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in z around inf 72.2%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 13: 44.2% accurate, 37.7× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
NOTE: t and a should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = y * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 57.6%

   \[\frac{\left(x \cdot y\right) \cdot z}{\sqrt{z \cdot z - t \cdot a}} \]
2. Step-by-step derivation

   1. *-commutative 57.6%

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

   2. associate-*l* 57.2%

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

   3. associate-*r/ 56.4%

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

3. Simplified 56.4%

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

4. Taylor expanded in z around inf 43.3%

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

5. Final simplification 43.3%

   \[\leadsto y \cdot x \]

Developer target: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < -3.1921305903852764 \cdot 10^{+46}:\\ \;\;\;\;-y \cdot x\\ \mathbf{elif}\;z < 5.976268120920894 \cdot 10^{+90}:\\ \;\;\;\;\frac{x \cdot z}{\frac{\sqrt{z \cdot z - a \cdot t}}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (< z -3.1921305903852764e+46)
   (- (* y x))
   (if (< z 5.976268120920894e+90)
     (/ (* x z) (/ (sqrt (- (* z z) (* a t))) y))
     (* y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z < -3.1921305903852764e+46) {
		tmp = -(y * x);
	} else if (z < 5.976268120920894e+90) {
		tmp = (x * z) / (sqrt(((z * z) - (a * t))) / y);
	} else {
		tmp = y * x;
	}
	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) :: tmp
    if (z < (-3.1921305903852764d+46)) then
        tmp = -(y * x)
    else if (z < 5.976268120920894d+90) then
        tmp = (x * z) / (sqrt(((z * z) - (a * t))) / y)
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z < -3.1921305903852764e+46) {
		tmp = -(y * x);
	} else if (z < 5.976268120920894e+90) {
		tmp = (x * z) / (Math.sqrt(((z * z) - (a * t))) / y);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z < -3.1921305903852764e+46:
		tmp = -(y * x)
	elif z < 5.976268120920894e+90:
		tmp = (x * z) / (math.sqrt(((z * z) - (a * t))) / y)
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z < -3.1921305903852764e+46)
		tmp = Float64(-Float64(y * x));
	elseif (z < 5.976268120920894e+90)
		tmp = Float64(Float64(x * z) / Float64(sqrt(Float64(Float64(z * z) - Float64(a * t))) / y));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z < -3.1921305903852764e+46)
		tmp = -(y * x);
	elseif (z < 5.976268120920894e+90)
		tmp = (x * z) / (sqrt(((z * z) - (a * t))) / y);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Less[z, -3.1921305903852764e+46], (-N[(y * x), $MachinePrecision]), If[Less[z, 5.976268120920894e+90], N[(N[(x * z), $MachinePrecision] / N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y z t a)
  :name "Statistics.Math.RootFinding:ridders from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z -3.1921305903852764e+46) (- (* y x)) (if (< z 5.976268120920894e+90) (/ (* x z) (/ (sqrt (- (* z z) (* a t))) y)) (* y x)))

  (/ (* (* x y) z) (sqrt (- (* z z) (* t a)))))