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

Percentage Accurate: 61.6% → 91.3%

Time: 27.8s

Alternatives: 22

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: 61.6% 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: 91.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \sqrt{z \cdot z - t \cdot a}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-206}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{t_1}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-156}:\\ \;\;\;\;\left(x \cdot e^{-0.5 \cdot \left(\log \left(-t\right) - \log \left(\frac{1}{a}\right)\right)}\right) \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+137}:\\ \;\;\;\;\frac{y}{\frac{\frac{t_1}{z}}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 (sqrt (- (* z z) (* t a)))))
   (if (<= z -6.5e+99)
     (* y (- x))
     (if (<= z -1.9e-206)
       (/ (* z (* y x)) t_1)
       (if (<= z 6e-156)
         (* (* x (exp (* -0.5 (- (log (- t)) (log (/ 1.0 a)))))) (* z y))
         (if (<= z 1.7e+137) (/ y (/ (/ t_1 z) x)) (* y x)))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = sqrt(((z * z) - (t * a)));
	double tmp;
	if (z <= -6.5e+99) {
		tmp = y * -x;
	} else if (z <= -1.9e-206) {
		tmp = (z * (y * x)) / t_1;
	} else if (z <= 6e-156) {
		tmp = (x * exp((-0.5 * (log(-t) - log((1.0 / a)))))) * (z * y);
	} else if (z <= 1.7e+137) {
		tmp = y / ((t_1 / z) / 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) :: t_1
    real(8) :: tmp
    t_1 = sqrt(((z * z) - (t * a)))
    if (z <= (-6.5d+99)) then
        tmp = y * -x
    else if (z <= (-1.9d-206)) then
        tmp = (z * (y * x)) / t_1
    else if (z <= 6d-156) then
        tmp = (x * exp(((-0.5d0) * (log(-t) - log((1.0d0 / a)))))) * (z * y)
    else if (z <= 1.7d+137) then
        tmp = y / ((t_1 / z) / 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 t_1 = Math.sqrt(((z * z) - (t * a)));
	double tmp;
	if (z <= -6.5e+99) {
		tmp = y * -x;
	} else if (z <= -1.9e-206) {
		tmp = (z * (y * x)) / t_1;
	} else if (z <= 6e-156) {
		tmp = (x * Math.exp((-0.5 * (Math.log(-t) - Math.log((1.0 / a)))))) * (z * y);
	} else if (z <= 1.7e+137) {
		tmp = y / ((t_1 / z) / 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):
	t_1 = math.sqrt(((z * z) - (t * a)))
	tmp = 0
	if z <= -6.5e+99:
		tmp = y * -x
	elif z <= -1.9e-206:
		tmp = (z * (y * x)) / t_1
	elif z <= 6e-156:
		tmp = (x * math.exp((-0.5 * (math.log(-t) - math.log((1.0 / a)))))) * (z * y)
	elif z <= 1.7e+137:
		tmp = y / ((t_1 / z) / 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)
	t_1 = sqrt(Float64(Float64(z * z) - Float64(t * a)))
	tmp = 0.0
	if (z <= -6.5e+99)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -1.9e-206)
		tmp = Float64(Float64(z * Float64(y * x)) / t_1);
	elseif (z <= 6e-156)
		tmp = Float64(Float64(x * exp(Float64(-0.5 * Float64(log(Float64(-t)) - log(Float64(1.0 / a)))))) * Float64(z * y));
	elseif (z <= 1.7e+137)
		tmp = Float64(y / Float64(Float64(t_1 / z) / 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)
	t_1 = sqrt(((z * z) - (t * a)));
	tmp = 0.0;
	if (z <= -6.5e+99)
		tmp = y * -x;
	elseif (z <= -1.9e-206)
		tmp = (z * (y * x)) / t_1;
	elseif (z <= 6e-156)
		tmp = (x * exp((-0.5 * (log(-t) - log((1.0 / a)))))) * (z * y);
	elseif (z <= 1.7e+137)
		tmp = y / ((t_1 / z) / 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_] := Block[{t$95$1 = N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, -6.5e+99], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -1.9e-206], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[z, 6e-156], N[(N[(x * N[Exp[N[(-0.5 * N[(N[Log[(-t)], $MachinePrecision] - N[Log[N[(1.0 / a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+137], N[(y / N[(N[(t$95$1 / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.5000000000000004e99

   1. Initial program 38.4%

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

      1. associate-*l* 36.0%

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

      2. associate-*r/ 38.2%

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

      3. *-commutative 38.2%

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

      4. associate-/l* 36.7%

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

   3. Simplified 36.7%

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

   4. Taylor expanded in z around -inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. distribute-rgt-neg-out 98.0%

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

   6. Simplified 98.0%

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

   if -6.5000000000000004e99 < z < -1.90000000000000001e-206

   1. Initial program 92.1%

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

   if -1.90000000000000001e-206 < z < 6e-156

   1. Initial program 67.3%

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

      1. associate-*l* 72.0%

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

      2. associate-*r/ 74.1%

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

      3. *-commutative 74.1%

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

      4. div-inv 74.1%

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

      5. associate-*l* 71.9%

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

      6. *-commutative 71.9%

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

      7. pow1/2 71.9%

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

      8. pow-flip 72.0%

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

      9. metadata-eval 72.0%

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

   3. Applied egg-rr 72.0%

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

   4. Taylor expanded in a around inf 39.4%

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

   if 6e-156 < z < 1.69999999999999993e137

   1. Initial program 87.8%

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

      1. associate-*l* 79.0%

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

      2. associate-*r/ 83.8%

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

      3. *-commutative 83.8%

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

      4. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

      1. associate-*r/ 89.0%

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

      2. associate-*l/ 87.5%

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

      3. associate-/l* 91.3%

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

      4. associate-/r/ 91.2%

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

      5. *-commutative 91.2%

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

      6. associate-/l* 92.8%

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

   5. Applied egg-rr 92.8%

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

   if 1.69999999999999993e137 < z

   1. Initial program 21.5%

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

      1. associate-*l* 18.9%

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

      2. associate-*r/ 21.0%

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

      3. *-commutative 21.0%

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

      4. associate-/l* 20.1%

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

   3. Simplified 20.1%

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

   4. Taylor expanded in z around inf 98.1%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+99}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-206}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{\sqrt{z \cdot z - t \cdot a}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-156}:\\ \;\;\;\;\left(x \cdot e^{-0.5 \cdot \left(\log \left(-t\right) - \log \left(\frac{1}{a}\right)\right)}\right) \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+137}:\\ \;\;\;\;\frac{y}{\frac{\frac{\sqrt{z \cdot z - t \cdot a}}{z}}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 2: 89.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(z \cdot \frac{y}{\sqrt{z \cdot z - t \cdot a}}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -5e+92)
   (* y (- x))
   (if (<= z 1.6e+36) (* x (* z (/ y (sqrt (- (* z z) (* 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 <= -5e+92) {
		tmp = y * -x;
	} else if (z <= 1.6e+36) {
		tmp = x * (z * (y / sqrt(((z * z) - (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 <= (-5d+92)) then
        tmp = y * -x
    else if (z <= 1.6d+36) then
        tmp = x * (z * (y / sqrt(((z * z) - (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 <= -5e+92) {
		tmp = y * -x;
	} else if (z <= 1.6e+36) {
		tmp = x * (z * (y / Math.sqrt(((z * z) - (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 <= -5e+92:
		tmp = y * -x
	elif z <= 1.6e+36:
		tmp = x * (z * (y / math.sqrt(((z * z) - (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 <= -5e+92)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.6e+36)
		tmp = Float64(x * Float64(z * Float64(y / sqrt(Float64(Float64(z * z) - Float64(t * 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 <= -5e+92)
		tmp = y * -x;
	elseif (z <= 1.6e+36)
		tmp = x * (z * (y / sqrt(((z * z) - (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, -5e+92], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.6e+36], N[(x * N[(z * N[(y / N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.00000000000000022e92

   1. Initial program 42.2%

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

      1. associate-*l* 39.8%

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

      2. associate-*r/ 41.9%

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

      3. *-commutative 41.9%

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

      4. associate-/l* 38.7%

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

   3. Simplified 38.7%

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

   4. Taylor expanded in z around -inf 96.2%

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

      1. mul-1-neg 96.2%

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

      2. distribute-rgt-neg-out 96.2%

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

   6. Simplified 96.2%

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

   if -5.00000000000000022e92 < z < 1.5999999999999999e36

   1. Initial program 83.5%

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

      1. associate-*l* 82.8%

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

      2. associate-*r/ 84.0%

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

      3. *-commutative 84.0%

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

      4. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

      1. clear-num 84.6%

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

      2. associate-/r/ 84.2%

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

      3. clear-num 84.2%

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

   5. Applied egg-rr 84.2%

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

   if 1.5999999999999999e36 < z

   1. Initial program 40.0%

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

      1. associate-*l* 33.9%

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

      2. associate-*r/ 36.9%

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

      3. *-commutative 36.9%

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

      4. associate-/l* 37.6%

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

   3. Simplified 37.6%

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

   4. Taylor expanded in z around inf 94.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \left(z \cdot \frac{y}{\sqrt{z \cdot z - t \cdot a}}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 90.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{z}{\frac{\sqrt{z \cdot z - t \cdot a}}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -1.55e+93)
   (* y (- x))
   (if (<= z 1.6e+36) (* x (/ z (/ (sqrt (- (* z z) (* 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 <= -1.55e+93) {
		tmp = y * -x;
	} else if (z <= 1.6e+36) {
		tmp = x * (z / (sqrt(((z * z) - (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 <= (-1.55d+93)) then
        tmp = y * -x
    else if (z <= 1.6d+36) then
        tmp = x * (z / (sqrt(((z * z) - (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 <= -1.55e+93) {
		tmp = y * -x;
	} else if (z <= 1.6e+36) {
		tmp = x * (z / (Math.sqrt(((z * z) - (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 <= -1.55e+93:
		tmp = y * -x
	elif z <= 1.6e+36:
		tmp = x * (z / (math.sqrt(((z * z) - (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 <= -1.55e+93)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.6e+36)
		tmp = Float64(x * Float64(z / Float64(sqrt(Float64(Float64(z * z) - Float64(t * 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 <= -1.55e+93)
		tmp = y * -x;
	elseif (z <= 1.6e+36)
		tmp = x * (z / (sqrt(((z * z) - (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, -1.55e+93], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.6e+36], N[(x * N[(z / N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5500000000000001e93

   1. Initial program 42.2%

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

      1. associate-*l* 39.8%

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

      2. associate-*r/ 41.9%

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

      3. *-commutative 41.9%

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

      4. associate-/l* 38.7%

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

   3. Simplified 38.7%

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

   4. Taylor expanded in z around -inf 96.2%

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

      1. mul-1-neg 96.2%

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

      2. distribute-rgt-neg-out 96.2%

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

   6. Simplified 96.2%

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

   if -1.5500000000000001e93 < z < 1.5999999999999999e36

   1. Initial program 83.5%

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

      1. associate-*l* 82.8%

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

      2. associate-*r/ 84.0%

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

      3. *-commutative 84.0%

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

      4. associate-/l* 84.7%

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

   3. Simplified 84.7%

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

   if 1.5999999999999999e36 < z

   1. Initial program 40.0%

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

      1. associate-*l* 33.9%

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

      2. associate-*r/ 36.9%

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

      3. *-commutative 36.9%

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

      4. associate-/l* 37.6%

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

   3. Simplified 37.6%

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

   4. Taylor expanded in z around inf 94.6%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{z}{\frac{\sqrt{z \cdot z - t \cdot a}}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 4: 90.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{z \cdot y}{\sqrt{z \cdot z - t \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -2e+101)
   (* y (- x))
   (if (<= z 1.6e+36) (* x (/ (* z y) (sqrt (- (* z z) (* 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 <= -2e+101) {
		tmp = y * -x;
	} else if (z <= 1.6e+36) {
		tmp = x * ((z * y) / sqrt(((z * z) - (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 <= (-2d+101)) then
        tmp = y * -x
    else if (z <= 1.6d+36) then
        tmp = x * ((z * y) / sqrt(((z * z) - (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 <= -2e+101) {
		tmp = y * -x;
	} else if (z <= 1.6e+36) {
		tmp = x * ((z * y) / Math.sqrt(((z * z) - (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 <= -2e+101:
		tmp = y * -x
	elif z <= 1.6e+36:
		tmp = x * ((z * y) / math.sqrt(((z * z) - (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 <= -2e+101)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.6e+36)
		tmp = Float64(x * Float64(Float64(z * y) / sqrt(Float64(Float64(z * z) - Float64(t * 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 <= -2e+101)
		tmp = y * -x;
	elseif (z <= 1.6e+36)
		tmp = x * ((z * y) / sqrt(((z * z) - (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, -2e+101], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.6e+36], N[(x * N[(N[(z * y), $MachinePrecision] / N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e101

   1. Initial program 38.4%

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

      1. associate-*l* 36.0%

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

      2. associate-*r/ 38.2%

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

      3. *-commutative 38.2%

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

      4. associate-/l* 36.7%

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

   3. Simplified 36.7%

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

   4. Taylor expanded in z around -inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. distribute-rgt-neg-out 98.0%

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

   6. Simplified 98.0%

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

   if -2e101 < z < 1.5999999999999999e36

   1. Initial program 83.8%

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

      1. associate-*l* 83.1%

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

      2. associate-*r/ 84.4%

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

   3. Simplified 84.4%

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

   if 1.5999999999999999e36 < z

   1. Initial program 40.0%

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

      1. associate-*l* 33.9%

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

      2. associate-*r/ 36.9%

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

      3. *-commutative 36.9%

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

      4. associate-/l* 37.6%

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

   3. Simplified 37.6%

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

   4. Taylor expanded in z around inf 94.6%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+101}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{z \cdot y}{\sqrt{z \cdot z - t \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 5: 80.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-169}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{\frac{t \cdot 0.5}{\frac{z}{a}} - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(z \cdot \frac{y}{\sqrt{t \cdot \left(-a\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \end{array} \]

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 -1.55e+140)
   (* y (- x))
   (if (<= z -1.16e-169)
     (/ (* z (* y x)) (- (/ (* t 0.5) (/ z a)) z))
     (if (<= z 9.5e-36)
       (* x (* z (/ y (sqrt (* t (- a))))))
       (/ y (/ (/ (+ z (* -0.5 (/ (* t a) z))) z) x))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+140) {
		tmp = y * -x;
	} else if (z <= -1.16e-169) {
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z);
	} else if (z <= 9.5e-36) {
		tmp = x * (z * (y / sqrt((t * -a))));
	} else {
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= (-1.55d+140)) then
        tmp = y * -x
    else if (z <= (-1.16d-169)) then
        tmp = (z * (y * x)) / (((t * 0.5d0) / (z / a)) - z)
    else if (z <= 9.5d-36) then
        tmp = x * (z * (y / sqrt((t * -a))))
    else
        tmp = y / (((z + ((-0.5d0) * ((t * a) / z))) / z) / 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 <= -1.55e+140) {
		tmp = y * -x;
	} else if (z <= -1.16e-169) {
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z);
	} else if (z <= 9.5e-36) {
		tmp = x * (z * (y / Math.sqrt((t * -a))));
	} else {
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= -1.55e+140:
		tmp = y * -x
	elif z <= -1.16e-169:
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z)
	elif z <= 9.5e-36:
		tmp = x * (z * (y / math.sqrt((t * -a))))
	else:
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= -1.55e+140)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -1.16e-169)
		tmp = Float64(Float64(z * Float64(y * x)) / Float64(Float64(Float64(t * 0.5) / Float64(z / a)) - z));
	elseif (z <= 9.5e-36)
		tmp = Float64(x * Float64(z * Float64(y / sqrt(Float64(t * Float64(-a))))));
	else
		tmp = Float64(y / Float64(Float64(Float64(z + Float64(-0.5 * Float64(Float64(t * a) / z))) / z) / 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 <= -1.55e+140)
		tmp = y * -x;
	elseif (z <= -1.16e-169)
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z);
	elseif (z <= 9.5e-36)
		tmp = x * (z * (y / sqrt((t * -a))));
	else
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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, -1.55e+140], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -1.16e-169], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(t * 0.5), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.5e-36], N[(x * N[(z * N[(y / N[Sqrt[N[(t * (-a)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(N[(z + N[(-0.5 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.55e140

   1. Initial program 28.1%

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

      1. associate-*l* 27.7%

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

      2. associate-*r/ 30.3%

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

      3. *-commutative 30.3%

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

      4. associate-/l* 28.5%

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

   3. Simplified 28.5%

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

   4. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

   6. Simplified 100.0%

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

   if -1.55e140 < z < -1.16e-169

   1. Initial program 91.6%

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

   2. Taylor expanded in z around -inf 83.4%

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

      1. expm1-log1p-u 81.7%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.5 \cdot \frac{a \cdot t}{z}\right)\right)} + -1 \cdot z} \]

      2. expm1-udef 81.7%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\left(e^{\mathsf{log1p}\left(0.5 \cdot \frac{a \cdot t}{z}\right)} - 1\right)} + -1 \cdot z} \]

      3. associate-/l* 83.4%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\left(e^{\mathsf{log1p}\left(0.5 \cdot \color{blue}{\frac{a}{\frac{z}{t}}}\right)} - 1\right) + -1 \cdot z} \]

   4. Applied egg-rr 83.4%

      \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\left(e^{\mathsf{log1p}\left(0.5 \cdot \frac{a}{\frac{z}{t}}\right)} - 1\right)} + -1 \cdot z} \]
   5. Step-by-step derivation

      1. expm1-def 83.4%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.5 \cdot \frac{a}{\frac{z}{t}}\right)\right)} + -1 \cdot z} \]

      2. expm1-log1p 85.2%

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

      3. associate-/l* 83.4%

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

      4. *-commutative 83.4%

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

      5. associate-*r/ 83.4%

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

      6. associate-*r* 83.4%

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

      7. associate-/l* 85.1%

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

   6. Simplified 85.1%

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

   if -1.16e-169 < z < 9.5000000000000003e-36

   1. Initial program 75.1%

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

      1. associate-*l* 74.0%

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

      2. associate-*r/ 77.5%

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

      3. *-commutative 77.5%

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

      4. associate-/l* 78.7%

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

   3. Simplified 78.7%

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

      1. clear-num 78.7%

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

      2. associate-/r/ 77.9%

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

      3. clear-num 77.9%

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

   5. Applied egg-rr 77.9%

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

   6. Taylor expanded in z around 0 69.9%

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

      1. mul-1-neg 69.9%

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

      2. distribute-rgt-neg-out 69.9%

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

   8. Simplified 69.9%

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

   if 9.5000000000000003e-36 < z

   1. Initial program 51.8%

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

      1. associate-*l* 47.0%

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

      2. associate-*r/ 49.4%

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

      3. *-commutative 49.4%

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

      4. associate-/l* 50.0%

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

   3. Simplified 50.0%

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

      1. associate-*r/ 49.2%

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

      2. associate-*l/ 49.8%

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

      3. associate-/l* 53.1%

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

      4. associate-/r/ 54.2%

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

      5. *-commutative 54.2%

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

      6. associate-/l* 54.2%

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

   5. Applied egg-rr 54.2%

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

   6. Taylor expanded in z around inf 92.7%

      \[\leadsto \frac{y}{\frac{\frac{\color{blue}{z + -0.5 \cdot \frac{a \cdot t}{z}}}{z}}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-169}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{\frac{t \cdot 0.5}{\frac{z}{a}} - z}\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \left(z \cdot \frac{y}{\sqrt{t \cdot \left(-a\right)}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \]

Alternative 6: 80.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-174}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{\frac{t \cdot 0.5}{\frac{z}{a}} - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{z \cdot y}{\sqrt{t \cdot \left(-a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \end{array} \]

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 -1.55e+140)
   (* y (- x))
   (if (<= z -3.4e-174)
     (/ (* z (* y x)) (- (/ (* t 0.5) (/ z a)) z))
     (if (<= z 8.8e-36)
       (* x (/ (* z y) (sqrt (* t (- a)))))
       (/ y (/ (/ (+ z (* -0.5 (/ (* t a) z))) z) x))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+140) {
		tmp = y * -x;
	} else if (z <= -3.4e-174) {
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z);
	} else if (z <= 8.8e-36) {
		tmp = x * ((z * y) / sqrt((t * -a)));
	} else {
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= (-1.55d+140)) then
        tmp = y * -x
    else if (z <= (-3.4d-174)) then
        tmp = (z * (y * x)) / (((t * 0.5d0) / (z / a)) - z)
    else if (z <= 8.8d-36) then
        tmp = x * ((z * y) / sqrt((t * -a)))
    else
        tmp = y / (((z + ((-0.5d0) * ((t * a) / z))) / z) / 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 <= -1.55e+140) {
		tmp = y * -x;
	} else if (z <= -3.4e-174) {
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z);
	} else if (z <= 8.8e-36) {
		tmp = x * ((z * y) / Math.sqrt((t * -a)));
	} else {
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= -1.55e+140:
		tmp = y * -x
	elif z <= -3.4e-174:
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z)
	elif z <= 8.8e-36:
		tmp = x * ((z * y) / math.sqrt((t * -a)))
	else:
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= -1.55e+140)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -3.4e-174)
		tmp = Float64(Float64(z * Float64(y * x)) / Float64(Float64(Float64(t * 0.5) / Float64(z / a)) - z));
	elseif (z <= 8.8e-36)
		tmp = Float64(x * Float64(Float64(z * y) / sqrt(Float64(t * Float64(-a)))));
	else
		tmp = Float64(y / Float64(Float64(Float64(z + Float64(-0.5 * Float64(Float64(t * a) / z))) / z) / 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 <= -1.55e+140)
		tmp = y * -x;
	elseif (z <= -3.4e-174)
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z);
	elseif (z <= 8.8e-36)
		tmp = x * ((z * y) / sqrt((t * -a)));
	else
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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, -1.55e+140], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -3.4e-174], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(t * 0.5), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.8e-36], N[(x * N[(N[(z * y), $MachinePrecision] / N[Sqrt[N[(t * (-a)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(N[(z + N[(-0.5 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.55e140

   1. Initial program 28.1%

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

      1. associate-*l* 27.7%

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

      2. associate-*r/ 30.3%

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

      3. *-commutative 30.3%

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

      4. associate-/l* 28.5%

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

   3. Simplified 28.5%

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

   4. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

   6. Simplified 100.0%

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

   if -1.55e140 < z < -3.4000000000000002e-174

   1. Initial program 91.6%

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

   2. Taylor expanded in z around -inf 83.4%

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

      1. expm1-log1p-u 81.7%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.5 \cdot \frac{a \cdot t}{z}\right)\right)} + -1 \cdot z} \]

      2. expm1-udef 81.7%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\left(e^{\mathsf{log1p}\left(0.5 \cdot \frac{a \cdot t}{z}\right)} - 1\right)} + -1 \cdot z} \]

      3. associate-/l* 83.4%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\left(e^{\mathsf{log1p}\left(0.5 \cdot \color{blue}{\frac{a}{\frac{z}{t}}}\right)} - 1\right) + -1 \cdot z} \]

   4. Applied egg-rr 83.4%

      \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\left(e^{\mathsf{log1p}\left(0.5 \cdot \frac{a}{\frac{z}{t}}\right)} - 1\right)} + -1 \cdot z} \]
   5. Step-by-step derivation

      1. expm1-def 83.4%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.5 \cdot \frac{a}{\frac{z}{t}}\right)\right)} + -1 \cdot z} \]

      2. expm1-log1p 85.2%

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

      3. associate-/l* 83.4%

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

      4. *-commutative 83.4%

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

      5. associate-*r/ 83.4%

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

      6. associate-*r* 83.4%

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

      7. associate-/l* 85.1%

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

   6. Simplified 85.1%

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

   if -3.4000000000000002e-174 < z < 8.7999999999999997e-36

   1. Initial program 75.1%

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

      1. associate-*l* 74.0%

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

      2. associate-*r/ 77.5%

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

   3. Simplified 77.5%

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

   4. Taylor expanded in z around 0 72.0%

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

      1. mul-1-neg 69.9%

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

      2. distribute-rgt-neg-out 69.9%

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

   6. Simplified 72.0%

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

   if 8.7999999999999997e-36 < z

   1. Initial program 51.8%

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

      1. associate-*l* 47.0%

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

      2. associate-*r/ 49.4%

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

      3. *-commutative 49.4%

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

      4. associate-/l* 50.0%

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

   3. Simplified 50.0%

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

      1. associate-*r/ 49.2%

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

      2. associate-*l/ 49.8%

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

      3. associate-/l* 53.1%

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

      4. associate-/r/ 54.2%

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

      5. *-commutative 54.2%

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

      6. associate-/l* 54.2%

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

   5. Applied egg-rr 54.2%

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

   6. Taylor expanded in z around inf 92.7%

      \[\leadsto \frac{y}{\frac{\frac{\color{blue}{z + -0.5 \cdot \frac{a \cdot t}{z}}}{z}}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-174}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{\frac{t \cdot 0.5}{\frac{z}{a}} - z}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-36}:\\ \;\;\;\;x \cdot \frac{z \cdot y}{\sqrt{t \cdot \left(-a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \]

Alternative 7: 77.3% accurate, 5.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{z \cdot y}{z + -0.5 \cdot \frac{t \cdot a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -1.7e-175)
   (* y (- x))
   (if (<= z 1.1e+36) (* x (/ (* z y) (+ z (* -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 <= -1.7e-175) {
		tmp = y * -x;
	} else if (z <= 1.1e+36) {
		tmp = x * ((z * y) / (z + (-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 <= (-1.7d-175)) then
        tmp = y * -x
    else if (z <= 1.1d+36) then
        tmp = x * ((z * y) / (z + ((-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 <= -1.7e-175) {
		tmp = y * -x;
	} else if (z <= 1.1e+36) {
		tmp = x * ((z * y) / (z + (-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 <= -1.7e-175:
		tmp = y * -x
	elif z <= 1.1e+36:
		tmp = x * ((z * y) / (z + (-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 <= -1.7e-175)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.1e+36)
		tmp = Float64(x * Float64(Float64(z * y) / Float64(z + Float64(-0.5 * Float64(Float64(t * 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-175)
		tmp = y * -x;
	elseif (z <= 1.1e+36)
		tmp = x * ((z * y) / (z + (-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, -1.7e-175], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.1e+36], N[(x * N[(N[(z * y), $MachinePrecision] / N[(z + N[(-0.5 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7e-175

   1. Initial program 66.5%

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

      1. associate-*l* 65.2%

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

      2. associate-*r/ 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-/l* 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in z around -inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-out 84.5%

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

   6. Simplified 84.5%

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

   if -1.7e-175 < z < 1.1e36

   1. Initial program 79.1%

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

      1. associate-*l* 78.2%

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

      2. associate-*r/ 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in z around inf 57.1%

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

   if 1.1e36 < z

   1. Initial program 40.0%

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

      1. associate-*l* 33.9%

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

      2. associate-*r/ 36.9%

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

      3. *-commutative 36.9%

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

      4. associate-/l* 37.6%

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

   3. Simplified 37.6%

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

   4. Taylor expanded in z around inf 94.6%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{-175}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+36}:\\ \;\;\;\;x \cdot \frac{z \cdot y}{z + -0.5 \cdot \frac{t \cdot a}{z}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 8: 77.5% accurate, 5.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-291}:\\ \;\;\;\;\frac{z}{\frac{\frac{t \cdot 0.5}{\frac{z}{a}} - z}{y \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \end{array} \]

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 -2.8e+83)
   (* y (- x))
   (if (<= z -2.6e-291)
     (/ z (/ (- (/ (* t 0.5) (/ z a)) z) (* y x)))
     (/ y (/ (/ (+ z (* -0.5 (/ (* t a) z))) z) x)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e+83) {
		tmp = y * -x;
	} else if (z <= -2.6e-291) {
		tmp = z / ((((t * 0.5) / (z / a)) - z) / (y * x));
	} else {
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= (-2.8d+83)) then
        tmp = y * -x
    else if (z <= (-2.6d-291)) then
        tmp = z / ((((t * 0.5d0) / (z / a)) - z) / (y * x))
    else
        tmp = y / (((z + ((-0.5d0) * ((t * a) / z))) / z) / 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 <= -2.8e+83) {
		tmp = y * -x;
	} else if (z <= -2.6e-291) {
		tmp = z / ((((t * 0.5) / (z / a)) - z) / (y * x));
	} else {
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= -2.8e+83:
		tmp = y * -x
	elif z <= -2.6e-291:
		tmp = z / ((((t * 0.5) / (z / a)) - z) / (y * x))
	else:
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= -2.8e+83)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -2.6e-291)
		tmp = Float64(z / Float64(Float64(Float64(Float64(t * 0.5) / Float64(z / a)) - z) / Float64(y * x)));
	else
		tmp = Float64(y / Float64(Float64(Float64(z + Float64(-0.5 * Float64(Float64(t * a) / z))) / z) / 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 <= -2.8e+83)
		tmp = y * -x;
	elseif (z <= -2.6e-291)
		tmp = z / ((((t * 0.5) / (z / a)) - z) / (y * x));
	else
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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, -2.8e+83], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -2.6e-291], N[(z / N[(N[(N[(N[(t * 0.5), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision] / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(N[(z + N[(-0.5 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e83

   1. Initial program 43.6%

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

      1. associate-*l* 41.4%

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

      2. associate-*r/ 43.4%

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

      3. *-commutative 43.4%

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

      4. associate-/l* 40.3%

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

   3. Simplified 40.3%

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

   4. Taylor expanded in z around -inf 92.8%

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

      1. mul-1-neg 92.8%

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

      2. distribute-rgt-neg-out 92.8%

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

   6. Simplified 92.8%

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

   if -2.8e83 < z < -2.5999999999999999e-291

   1. Initial program 89.3%

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

   2. Taylor expanded in z around -inf 76.0%

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

   3. Taylor expanded in x around 0 75.0%

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

      1. *-commutative 75.0%

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

      2. associate-*r* 76.0%

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

      3. /-rgt-identity 76.0%

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

      4. associate-/l* 73.8%

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

      5. associate-/l* 73.7%

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

      6. mul-1-neg 73.7%

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

      7. unsub-neg 73.7%

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

      8. associate-/l* 73.8%

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

      9. *-commutative 73.8%

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

      10. associate-*r/ 73.8%

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

      11. associate-*r* 73.8%

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

      12. associate-/l* 73.7%

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

      13. /-rgt-identity 73.7%

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

   5. Simplified 73.7%

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

   if -2.5999999999999999e-291 < z

   1. Initial program 59.9%

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

      1. associate-*l* 56.3%

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

      2. associate-*r/ 59.6%

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

      3. *-commutative 59.6%

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

      4. associate-/l* 60.6%

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

   3. Simplified 60.6%

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

      1. associate-*r/ 60.0%

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

      2. associate-*l/ 58.1%

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

      3. associate-/l* 60.6%

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

      4. associate-/r/ 62.1%

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

      5. *-commutative 62.1%

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

      6. associate-/l* 61.5%

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

   5. Applied egg-rr 61.5%

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

   6. Taylor expanded in z around inf 78.4%

      \[\leadsto \frac{y}{\frac{\frac{\color{blue}{z + -0.5 \cdot \frac{a \cdot t}{z}}}{z}}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+83}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-291}:\\ \;\;\;\;\frac{z}{\frac{\frac{t \cdot 0.5}{\frac{z}{a}} - z}{y \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \]

Alternative 9: 77.3% accurate, 5.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot a}{z}\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \left(z \cdot \frac{y}{0.5 \cdot t_1 - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot t_1}{z}}{x}}\\ \end{array} \end{array} \]

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 (/ (* t a) z)))
   (if (<= z -4.5e+82)
     (* y (- x))
     (if (<= z -1.05e-259)
       (* x (* z (/ y (- (* 0.5 t_1) z))))
       (/ y (/ (/ (+ z (* -0.5 t_1)) z) x))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * a) / z;
	double tmp;
	if (z <= -4.5e+82) {
		tmp = y * -x;
	} else if (z <= -1.05e-259) {
		tmp = x * (z * (y / ((0.5 * t_1) - z)));
	} else {
		tmp = y / (((z + (-0.5 * t_1)) / z) / 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 = (t * a) / z
    if (z <= (-4.5d+82)) then
        tmp = y * -x
    else if (z <= (-1.05d-259)) then
        tmp = x * (z * (y / ((0.5d0 * t_1) - z)))
    else
        tmp = y / (((z + ((-0.5d0) * t_1)) / z) / 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 = (t * a) / z;
	double tmp;
	if (z <= -4.5e+82) {
		tmp = y * -x;
	} else if (z <= -1.05e-259) {
		tmp = x * (z * (y / ((0.5 * t_1) - z)));
	} else {
		tmp = y / (((z + (-0.5 * t_1)) / z) / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	t_1 = (t * a) / z
	tmp = 0
	if z <= -4.5e+82:
		tmp = y * -x
	elif z <= -1.05e-259:
		tmp = x * (z * (y / ((0.5 * t_1) - z)))
	else:
		tmp = y / (((z + (-0.5 * t_1)) / z) / 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(t * a) / z)
	tmp = 0.0
	if (z <= -4.5e+82)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -1.05e-259)
		tmp = Float64(x * Float64(z * Float64(y / Float64(Float64(0.5 * t_1) - z))));
	else
		tmp = Float64(y / Float64(Float64(Float64(z + Float64(-0.5 * t_1)) / z) / 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 = (t * a) / z;
	tmp = 0.0;
	if (z <= -4.5e+82)
		tmp = y * -x;
	elseif (z <= -1.05e-259)
		tmp = x * (z * (y / ((0.5 * t_1) - z)));
	else
		tmp = y / (((z + (-0.5 * t_1)) / z) / 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[(t * a), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -4.5e+82], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -1.05e-259], N[(x * N[(z * N[(y / N[(N[(0.5 * t$95$1), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(N[(z + N[(-0.5 * t$95$1), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.4999999999999997e82

   1. Initial program 43.6%

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

      1. associate-*l* 41.4%

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

      2. associate-*r/ 43.4%

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

      3. *-commutative 43.4%

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

      4. associate-/l* 40.3%

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

   3. Simplified 40.3%

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

   4. Taylor expanded in z around -inf 92.8%

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

      1. mul-1-neg 92.8%

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

      2. distribute-rgt-neg-out 92.8%

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

   6. Simplified 92.8%

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

   if -4.4999999999999997e82 < z < -1.04999999999999999e-259

   1. Initial program 89.0%

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

      1. associate-*l* 89.0%

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

      2. associate-*r/ 87.5%

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

      3. *-commutative 87.5%

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

      4. associate-/l* 87.5%

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

   3. Simplified 87.5%

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

      1. clear-num 87.4%

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

      2. associate-/r/ 87.5%

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

      3. clear-num 87.5%

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

   5. Applied egg-rr 87.5%

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

   6. Taylor expanded in z around -inf 73.6%

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

   if -1.04999999999999999e-259 < z

   1. Initial program 60.5%

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

      1. associate-*l* 56.9%

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

      2. associate-*r/ 60.1%

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

      3. *-commutative 60.1%

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

      4. associate-/l* 61.2%

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

   3. Simplified 61.2%

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

      1. associate-*r/ 59.9%

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

      2. associate-*l/ 58.7%

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

      3. associate-/l* 61.1%

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

      4. associate-/r/ 62.7%

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

      5. *-commutative 62.7%

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

      6. associate-/l* 61.4%

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

   5. Applied egg-rr 61.4%

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

   6. Taylor expanded in z around inf 78.0%

      \[\leadsto \frac{y}{\frac{\frac{\color{blue}{z + -0.5 \cdot \frac{a \cdot t}{z}}}{z}}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-259}:\\ \;\;\;\;x \cdot \left(z \cdot \frac{y}{0.5 \cdot \frac{t \cdot a}{z} - z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \]

Alternative 10: 77.7% accurate, 5.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} t_1 := \frac{t \cdot a}{z}\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-259}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{0.5 \cdot t_1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot t_1}{z}}{x}}\\ \end{array} \end{array} \]

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 (/ (* t a) z)))
   (if (<= z -1.75e+64)
     (* y (- x))
     (if (<= z -2e-259)
       (/ (* z (* y x)) (- (* 0.5 t_1) z))
       (/ y (/ (/ (+ z (* -0.5 t_1)) z) x))))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (t * a) / z;
	double tmp;
	if (z <= -1.75e+64) {
		tmp = y * -x;
	} else if (z <= -2e-259) {
		tmp = (z * (y * x)) / ((0.5 * t_1) - z);
	} else {
		tmp = y / (((z + (-0.5 * t_1)) / z) / 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 = (t * a) / z
    if (z <= (-1.75d+64)) then
        tmp = y * -x
    else if (z <= (-2d-259)) then
        tmp = (z * (y * x)) / ((0.5d0 * t_1) - z)
    else
        tmp = y / (((z + ((-0.5d0) * t_1)) / z) / 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 = (t * a) / z;
	double tmp;
	if (z <= -1.75e+64) {
		tmp = y * -x;
	} else if (z <= -2e-259) {
		tmp = (z * (y * x)) / ((0.5 * t_1) - z);
	} else {
		tmp = y / (((z + (-0.5 * t_1)) / z) / x);
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
[t, a] = sort([t, a])
def code(x, y, z, t, a):
	t_1 = (t * a) / z
	tmp = 0
	if z <= -1.75e+64:
		tmp = y * -x
	elif z <= -2e-259:
		tmp = (z * (y * x)) / ((0.5 * t_1) - z)
	else:
		tmp = y / (((z + (-0.5 * t_1)) / z) / 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(t * a) / z)
	tmp = 0.0
	if (z <= -1.75e+64)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -2e-259)
		tmp = Float64(Float64(z * Float64(y * x)) / Float64(Float64(0.5 * t_1) - z));
	else
		tmp = Float64(y / Float64(Float64(Float64(z + Float64(-0.5 * t_1)) / z) / 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 = (t * a) / z;
	tmp = 0.0;
	if (z <= -1.75e+64)
		tmp = y * -x;
	elseif (z <= -2e-259)
		tmp = (z * (y * x)) / ((0.5 * t_1) - z);
	else
		tmp = y / (((z + (-0.5 * t_1)) / z) / 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[(t * a), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[z, -1.75e+64], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -2e-259], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(N[(0.5 * t$95$1), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(N[(z + N[(-0.5 * t$95$1), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7499999999999999e64

   1. Initial program 47.6%

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

      1. associate-*l* 45.5%

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

      2. associate-*r/ 47.4%

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

      3. *-commutative 47.4%

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

      4. associate-/l* 44.6%

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

   3. Simplified 44.6%

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

   4. Taylor expanded in z around -inf 93.3%

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

      1. mul-1-neg 93.3%

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

      2. distribute-rgt-neg-out 93.3%

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

   6. Simplified 93.3%

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

   if -1.7499999999999999e64 < z < -2.0000000000000001e-259

   1. Initial program 88.3%

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

   2. Taylor expanded in z around -inf 75.1%

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

   if -2.0000000000000001e-259 < z

   1. Initial program 60.5%

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

      1. associate-*l* 56.9%

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

      2. associate-*r/ 60.1%

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

      3. *-commutative 60.1%

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

      4. associate-/l* 61.2%

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

   3. Simplified 61.2%

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

      1. associate-*r/ 59.9%

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

      2. associate-*l/ 58.7%

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

      3. associate-/l* 61.1%

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

      4. associate-/r/ 62.7%

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

      5. *-commutative 62.7%

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

      6. associate-/l* 61.4%

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

   5. Applied egg-rr 61.4%

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

   6. Taylor expanded in z around inf 78.0%

      \[\leadsto \frac{y}{\frac{\frac{\color{blue}{z + -0.5 \cdot \frac{a \cdot t}{z}}}{z}}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-259}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{0.5 \cdot \frac{t \cdot a}{z} - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \]

Alternative 11: 77.1% accurate, 5.9× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-286}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{\frac{t \cdot 0.5}{\frac{z}{a}} - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \end{array} \]

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 -1.55e+140)
   (* y (- x))
   (if (<= z -2.8e-286)
     (/ (* z (* y x)) (- (/ (* t 0.5) (/ z a)) z))
     (/ y (/ (/ (+ z (* -0.5 (/ (* t a) z))) z) x)))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e+140) {
		tmp = y * -x;
	} else if (z <= -2.8e-286) {
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z);
	} else {
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= (-1.55d+140)) then
        tmp = y * -x
    else if (z <= (-2.8d-286)) then
        tmp = (z * (y * x)) / (((t * 0.5d0) / (z / a)) - z)
    else
        tmp = y / (((z + ((-0.5d0) * ((t * a) / z))) / z) / 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 <= -1.55e+140) {
		tmp = y * -x;
	} else if (z <= -2.8e-286) {
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z);
	} else {
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= -1.55e+140:
		tmp = y * -x
	elif z <= -2.8e-286:
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z)
	else:
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= -1.55e+140)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -2.8e-286)
		tmp = Float64(Float64(z * Float64(y * x)) / Float64(Float64(Float64(t * 0.5) / Float64(z / a)) - z));
	else
		tmp = Float64(y / Float64(Float64(Float64(z + Float64(-0.5 * Float64(Float64(t * a) / z))) / z) / 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 <= -1.55e+140)
		tmp = y * -x;
	elseif (z <= -2.8e-286)
		tmp = (z * (y * x)) / (((t * 0.5) / (z / a)) - z);
	else
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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, -1.55e+140], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -2.8e-286], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(t * 0.5), $MachinePrecision] / N[(z / a), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(N[(z + N[(-0.5 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55e140

   1. Initial program 28.1%

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

      1. associate-*l* 27.7%

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

      2. associate-*r/ 30.3%

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

      3. *-commutative 30.3%

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

      4. associate-/l* 28.5%

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

   3. Simplified 28.5%

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

   4. Taylor expanded in z around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-out 100.0%

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

   6. Simplified 100.0%

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

   if -1.55e140 < z < -2.8e-286

   1. Initial program 88.7%

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

   2. Taylor expanded in z around -inf 75.3%

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

      1. expm1-log1p-u 74.0%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.5 \cdot \frac{a \cdot t}{z}\right)\right)} + -1 \cdot z} \]

      2. expm1-udef 74.0%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\left(e^{\mathsf{log1p}\left(0.5 \cdot \frac{a \cdot t}{z}\right)} - 1\right)} + -1 \cdot z} \]

      3. associate-/l* 75.2%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\left(e^{\mathsf{log1p}\left(0.5 \cdot \color{blue}{\frac{a}{\frac{z}{t}}}\right)} - 1\right) + -1 \cdot z} \]

   4. Applied egg-rr 75.2%

      \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\left(e^{\mathsf{log1p}\left(0.5 \cdot \frac{a}{\frac{z}{t}}\right)} - 1\right)} + -1 \cdot z} \]
   5. Step-by-step derivation

      1. expm1-def 75.2%

         \[\leadsto \frac{\left(x \cdot y\right) \cdot z}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(0.5 \cdot \frac{a}{\frac{z}{t}}\right)\right)} + -1 \cdot z} \]

      2. expm1-log1p 76.5%

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

      3. associate-/l* 75.3%

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

      4. *-commutative 75.3%

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

      5. associate-*r/ 75.3%

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

      6. associate-*r* 75.3%

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

      7. associate-/l* 76.6%

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

   6. Simplified 76.6%

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

   if -2.8e-286 < z

   1. Initial program 59.9%

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

      1. associate-*l* 56.3%

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

      2. associate-*r/ 59.6%

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

      3. *-commutative 59.6%

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

      4. associate-/l* 60.6%

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

   3. Simplified 60.6%

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

      1. associate-*r/ 60.0%

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

      2. associate-*l/ 58.1%

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

      3. associate-/l* 60.6%

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

      4. associate-/r/ 62.1%

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

      5. *-commutative 62.1%

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

      6. associate-/l* 61.5%

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

   5. Applied egg-rr 61.5%

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

   6. Taylor expanded in z around inf 78.4%

      \[\leadsto \frac{y}{\frac{\frac{\color{blue}{z + -0.5 \cdot \frac{a \cdot t}{z}}}{z}}{x}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{+140}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-286}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{\frac{t \cdot 0.5}{\frac{z}{a}} - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \]

Alternative 12: 74.6% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-183}:\\ \;\;\;\;-2 \cdot \left(\frac{y}{a} \cdot \frac{x \cdot \left(z \cdot z\right)}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -1.9e-57)
   (* y (- x))
   (if (<= z 2.9e-183) (* -2.0 (* (/ y a) (/ (* x (* z z)) 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 <= -1.9e-57) {
		tmp = y * -x;
	} else if (z <= 2.9e-183) {
		tmp = -2.0 * ((y / a) * ((x * (z * z)) / 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 <= (-1.9d-57)) then
        tmp = y * -x
    else if (z <= 2.9d-183) then
        tmp = (-2.0d0) * ((y / a) * ((x * (z * z)) / 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 <= -1.9e-57) {
		tmp = y * -x;
	} else if (z <= 2.9e-183) {
		tmp = -2.0 * ((y / a) * ((x * (z * z)) / 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 <= -1.9e-57:
		tmp = y * -x
	elif z <= 2.9e-183:
		tmp = -2.0 * ((y / a) * ((x * (z * z)) / 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 <= -1.9e-57)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 2.9e-183)
		tmp = Float64(-2.0 * Float64(Float64(y / a) * Float64(Float64(x * Float64(z * z)) / 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 <= -1.9e-57)
		tmp = y * -x;
	elseif (z <= 2.9e-183)
		tmp = -2.0 * ((y / a) * ((x * (z * z)) / 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, -1.9e-57], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 2.9e-183], N[(-2.0 * N[(N[(y / a), $MachinePrecision] * N[(N[(x * N[(z * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e-57

   1. Initial program 61.0%

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

      1. associate-*l* 59.4%

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

      2. associate-*r/ 60.7%

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

      3. *-commutative 60.7%

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

      4. associate-/l* 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around -inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. distribute-rgt-neg-out 90.1%

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

   6. Simplified 90.1%

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

   if -1.8999999999999999e-57 < z < 2.9e-183

   1. Initial program 77.5%

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

      1. associate-*l* 77.8%

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

      2. associate-*r/ 77.8%

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

      3. *-commutative 77.8%

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

      4. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

      1. associate-*r/ 72.8%

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

      2. associate-*l/ 70.9%

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

      3. associate-/l* 74.3%

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

      4. associate-/r/ 77.7%

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

      5. *-commutative 77.7%

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

      6. associate-/l* 73.6%

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

   5. Applied egg-rr 73.6%

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

   6. Taylor expanded in z around inf 53.6%

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

   7. Taylor expanded in z around 0 50.5%

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

      1. times-frac 50.4%

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

      2. unpow2 50.4%

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

   9. Simplified 50.4%

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

   if 2.9e-183 < z

   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. associate-*l* 52.8%

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

      2. associate-*r/ 56.2%

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

      3. *-commutative 56.2%

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

      4. associate-/l* 58.7%

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

   3. Simplified 58.7%

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

   4. Taylor expanded in z around inf 82.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-183}:\\ \;\;\;\;-2 \cdot \left(\frac{y}{a} \cdot \frac{x \cdot \left(z \cdot z\right)}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 13: 74.6% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-179}:\\ \;\;\;\;-2 \cdot \left(x \cdot \left(\frac{z}{\frac{t}{z}} \cdot \frac{y}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -1.9e-57)
   (* y (- x))
   (if (<= z 1.7e-179) (* -2.0 (* x (* (/ z (/ t z)) (/ y 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 <= -1.9e-57) {
		tmp = y * -x;
	} else if (z <= 1.7e-179) {
		tmp = -2.0 * (x * ((z / (t / z)) * (y / 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 <= (-1.9d-57)) then
        tmp = y * -x
    else if (z <= 1.7d-179) then
        tmp = (-2.0d0) * (x * ((z / (t / z)) * (y / 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 <= -1.9e-57) {
		tmp = y * -x;
	} else if (z <= 1.7e-179) {
		tmp = -2.0 * (x * ((z / (t / z)) * (y / 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 <= -1.9e-57:
		tmp = y * -x
	elif z <= 1.7e-179:
		tmp = -2.0 * (x * ((z / (t / z)) * (y / 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 <= -1.9e-57)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.7e-179)
		tmp = Float64(-2.0 * Float64(x * Float64(Float64(z / Float64(t / z)) * Float64(y / 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 <= -1.9e-57)
		tmp = y * -x;
	elseif (z <= 1.7e-179)
		tmp = -2.0 * (x * ((z / (t / z)) * (y / 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, -1.9e-57], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.7e-179], N[(-2.0 * N[(x * N[(N[(z / N[(t / z), $MachinePrecision]), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e-57

   1. Initial program 61.0%

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

      1. associate-*l* 59.4%

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

      2. associate-*r/ 60.7%

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

      3. *-commutative 60.7%

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

      4. associate-/l* 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around -inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. distribute-rgt-neg-out 90.1%

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

   6. Simplified 90.1%

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

   if -1.8999999999999999e-57 < z < 1.6999999999999999e-179

   1. Initial program 77.5%

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

      1. associate-*l* 77.8%

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

      2. associate-*r/ 77.8%

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

      3. *-commutative 77.8%

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

      4. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

      1. associate-*r/ 72.8%

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

      2. associate-*l/ 70.9%

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

      3. associate-/l* 74.3%

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

      4. associate-/r/ 77.7%

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

      5. *-commutative 77.7%

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

      6. associate-/l* 73.6%

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

   5. Applied egg-rr 73.6%

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

   6. Taylor expanded in z around inf 48.8%

      \[\leadsto \frac{y}{\color{blue}{-0.5 \cdot \frac{a \cdot t}{{z}^{2} \cdot x} + \frac{1}{x}}} \]
   7. Step-by-step derivation

      1. fma-def 48.8%

         \[\leadsto \frac{y}{\color{blue}{\mathsf{fma}\left(-0.5, \frac{a \cdot t}{{z}^{2} \cdot x}, \frac{1}{x}\right)}} \]

      2. associate-/l* 49.3%

         \[\leadsto \frac{y}{\mathsf{fma}\left(-0.5, \color{blue}{\frac{a}{\frac{{z}^{2} \cdot x}{t}}}, \frac{1}{x}\right)} \]

      3. associate-/l* 47.6%

         \[\leadsto \frac{y}{\mathsf{fma}\left(-0.5, \frac{a}{\color{blue}{\frac{{z}^{2}}{\frac{t}{x}}}}, \frac{1}{x}\right)} \]

      4. unpow2 47.6%

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

   8. Simplified 47.6%

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

   9. Taylor expanded in a around inf 50.5%

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

       1. *-commutative 50.5%

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

       2. times-frac 50.4%

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

       3. associate-*l/ 50.4%

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

       4. unpow2 50.4%

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

       5. associate-*r* 50.5%

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

       6. unpow2 50.5%

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

       7. times-frac 50.5%

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

       8. *-commutative 50.5%

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

       9. *-commutative 50.5%

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

       10. times-frac 50.5%

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

       11. unpow2 50.5%

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

       12. associate-/l* 50.8%

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

   11. Simplified 50.8%

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

   if 1.6999999999999999e-179 < z

   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. associate-*l* 52.8%

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

      2. associate-*r/ 56.2%

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

      3. *-commutative 56.2%

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

      4. associate-/l* 58.7%

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

   3. Simplified 58.7%

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

   4. Taylor expanded in z around inf 82.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-179}:\\ \;\;\;\;-2 \cdot \left(x \cdot \left(\frac{z}{\frac{t}{z}} \cdot \frac{y}{a}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 14: 74.8% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{-2}{t} \cdot \frac{x \cdot \left(y \cdot \left(z \cdot z\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -1.9e-57)
   (* y (- x))
   (if (<= z 1.8e-175) (* (/ -2.0 t) (/ (* x (* y (* z z))) 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 <= -1.9e-57) {
		tmp = y * -x;
	} else if (z <= 1.8e-175) {
		tmp = (-2.0 / t) * ((x * (y * (z * z))) / 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 <= (-1.9d-57)) then
        tmp = y * -x
    else if (z <= 1.8d-175) then
        tmp = ((-2.0d0) / t) * ((x * (y * (z * z))) / 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 <= -1.9e-57) {
		tmp = y * -x;
	} else if (z <= 1.8e-175) {
		tmp = (-2.0 / t) * ((x * (y * (z * z))) / 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 <= -1.9e-57:
		tmp = y * -x
	elif z <= 1.8e-175:
		tmp = (-2.0 / t) * ((x * (y * (z * z))) / 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 <= -1.9e-57)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.8e-175)
		tmp = Float64(Float64(-2.0 / t) * Float64(Float64(x * Float64(y * Float64(z * z))) / 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 <= -1.9e-57)
		tmp = y * -x;
	elseif (z <= 1.8e-175)
		tmp = (-2.0 / t) * ((x * (y * (z * z))) / 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, -1.9e-57], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.8e-175], N[(N[(-2.0 / t), $MachinePrecision] * N[(N[(x * N[(y * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e-57

   1. Initial program 61.0%

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

      1. associate-*l* 59.4%

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

      2. associate-*r/ 60.7%

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

      3. *-commutative 60.7%

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

      4. associate-/l* 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around -inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. distribute-rgt-neg-out 90.1%

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

   6. Simplified 90.1%

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

   if -1.8999999999999999e-57 < z < 1.8e-175

   1. Initial program 77.5%

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

      1. associate-*l* 77.8%

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

      2. associate-*r/ 77.8%

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

      3. *-commutative 77.8%

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

      4. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

      1. associate-*r/ 72.8%

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

      2. associate-*l/ 70.9%

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

      3. associate-/l* 74.3%

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

      4. associate-/r/ 77.7%

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

      5. *-commutative 77.7%

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

      6. associate-/l* 73.6%

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

   5. Applied egg-rr 73.6%

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

   6. Taylor expanded in z around inf 53.6%

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

   7. Taylor expanded in z around 0 50.5%

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

      1. associate-*r/ 50.5%

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

      2. *-commutative 50.5%

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

      3. times-frac 51.0%

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

      4. *-commutative 51.0%

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

      5. *-commutative 51.0%

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

      6. associate-*l* 51.0%

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

      7. unpow2 51.0%

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

   9. Simplified 51.0%

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

   if 1.8e-175 < z

   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. associate-*l* 52.8%

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

      2. associate-*r/ 56.2%

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

      3. *-commutative 56.2%

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

      4. associate-/l* 58.7%

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

   3. Simplified 58.7%

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

   4. Taylor expanded in z around inf 82.4%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{-2}{t} \cdot \frac{x \cdot \left(y \cdot \left(z \cdot z\right)\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 15: 74.6% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-184}:\\ \;\;\;\;\frac{y}{\frac{-0.5}{x} \cdot \left(t \cdot \frac{a}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -1.9e-57)
   (* y (- x))
   (if (<= z 8e-184) (/ y (* (/ -0.5 x) (* t (/ a (* z 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 <= -1.9e-57) {
		tmp = y * -x;
	} else if (z <= 8e-184) {
		tmp = y / ((-0.5 / x) * (t * (a / (z * 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 <= (-1.9d-57)) then
        tmp = y * -x
    else if (z <= 8d-184) then
        tmp = y / (((-0.5d0) / x) * (t * (a / (z * 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 <= -1.9e-57) {
		tmp = y * -x;
	} else if (z <= 8e-184) {
		tmp = y / ((-0.5 / x) * (t * (a / (z * 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 <= -1.9e-57:
		tmp = y * -x
	elif z <= 8e-184:
		tmp = y / ((-0.5 / x) * (t * (a / (z * 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 <= -1.9e-57)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 8e-184)
		tmp = Float64(y / Float64(Float64(-0.5 / x) * Float64(t * Float64(a / Float64(z * 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 <= -1.9e-57)
		tmp = y * -x;
	elseif (z <= 8e-184)
		tmp = y / ((-0.5 / x) * (t * (a / (z * 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, -1.9e-57], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 8e-184], N[(y / N[(N[(-0.5 / x), $MachinePrecision] * N[(t * N[(a / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e-57

   1. Initial program 61.0%

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

      1. associate-*l* 59.4%

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

      2. associate-*r/ 60.7%

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

      3. *-commutative 60.7%

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

      4. associate-/l* 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around -inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. distribute-rgt-neg-out 90.1%

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

   6. Simplified 90.1%

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

   if -1.8999999999999999e-57 < z < 8.0000000000000005e-184

   1. Initial program 77.5%

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

      1. associate-*l* 77.8%

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

      2. associate-*r/ 77.8%

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

      3. *-commutative 77.8%

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

      4. associate-/l* 74.5%

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

   3. Simplified 74.5%

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

      1. associate-*r/ 72.8%

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

      2. associate-*l/ 70.9%

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

      3. associate-/l* 74.3%

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

      4. associate-/r/ 77.7%

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

      5. *-commutative 77.7%

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

      6. associate-/l* 73.6%

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

   5. Applied egg-rr 73.6%

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

   6. Taylor expanded in z around inf 48.8%

      \[\leadsto \frac{y}{\color{blue}{-0.5 \cdot \frac{a \cdot t}{{z}^{2} \cdot x} + \frac{1}{x}}} \]
   7. Step-by-step derivation

      1. fma-def 48.8%

         \[\leadsto \frac{y}{\color{blue}{\mathsf{fma}\left(-0.5, \frac{a \cdot t}{{z}^{2} \cdot x}, \frac{1}{x}\right)}} \]

      2. associate-/l* 49.3%

         \[\leadsto \frac{y}{\mathsf{fma}\left(-0.5, \color{blue}{\frac{a}{\frac{{z}^{2} \cdot x}{t}}}, \frac{1}{x}\right)} \]

      3. associate-/l* 47.6%

         \[\leadsto \frac{y}{\mathsf{fma}\left(-0.5, \frac{a}{\color{blue}{\frac{{z}^{2}}{\frac{t}{x}}}}, \frac{1}{x}\right)} \]

      4. unpow2 47.6%

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

   8. Simplified 47.6%

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

   9. Taylor expanded in a around inf 50.5%

      \[\leadsto \frac{y}{\color{blue}{-0.5 \cdot \frac{a \cdot t}{{z}^{2} \cdot x}}} \]
   10. Step-by-step derivation

       1. associate-*r/ 50.5%

          \[\leadsto \frac{y}{\color{blue}{\frac{-0.5 \cdot \left(a \cdot t\right)}{{z}^{2} \cdot x}}} \]

       2. *-commutative 50.5%

          \[\leadsto \frac{y}{\frac{-0.5 \cdot \left(a \cdot t\right)}{\color{blue}{x \cdot {z}^{2}}}} \]

       3. times-frac 50.5%

          \[\leadsto \frac{y}{\color{blue}{\frac{-0.5}{x} \cdot \frac{a \cdot t}{{z}^{2}}}} \]

       4. associate-*l/ 51.0%

          \[\leadsto \frac{y}{\frac{-0.5}{x} \cdot \color{blue}{\left(\frac{a}{{z}^{2}} \cdot t\right)}} \]

       5. unpow2 51.0%

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

   11. Simplified 51.0%

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

   if 8.0000000000000005e-184 < z

   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. associate-*l* 52.8%

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

      2. associate-*r/ 56.2%

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

      3. *-commutative 56.2%

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

      4. associate-/l* 58.7%

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

   3. Simplified 58.7%

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

   4. Taylor expanded in z around inf 82.4%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-184}:\\ \;\;\;\;\frac{y}{\frac{-0.5}{x} \cdot \left(t \cdot \frac{a}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 16: 74.9% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.36 \cdot 10^{-141}:\\ \;\;\;\;\frac{y}{\frac{-0.5 \cdot \left(\frac{a}{z} \cdot \frac{t}{z}\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -1.9e-57)
   (* y (- x))
   (if (<= z 2.36e-141) (/ y (/ (* -0.5 (* (/ a z) (/ t z))) 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 <= -1.9e-57) {
		tmp = y * -x;
	} else if (z <= 2.36e-141) {
		tmp = y / ((-0.5 * ((a / z) * (t / z))) / 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 <= (-1.9d-57)) then
        tmp = y * -x
    else if (z <= 2.36d-141) then
        tmp = y / (((-0.5d0) * ((a / z) * (t / z))) / 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 <= -1.9e-57) {
		tmp = y * -x;
	} else if (z <= 2.36e-141) {
		tmp = y / ((-0.5 * ((a / z) * (t / z))) / 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 <= -1.9e-57:
		tmp = y * -x
	elif z <= 2.36e-141:
		tmp = y / ((-0.5 * ((a / z) * (t / z))) / 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 <= -1.9e-57)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 2.36e-141)
		tmp = Float64(y / Float64(Float64(-0.5 * Float64(Float64(a / z) * Float64(t / z))) / 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 <= -1.9e-57)
		tmp = y * -x;
	elseif (z <= 2.36e-141)
		tmp = y / ((-0.5 * ((a / z) * (t / z))) / 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, -1.9e-57], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 2.36e-141], N[(y / N[(N[(-0.5 * N[(N[(a / z), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.8999999999999999e-57

   1. Initial program 61.0%

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

      1. associate-*l* 59.4%

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

      2. associate-*r/ 60.7%

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

      3. *-commutative 60.7%

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

      4. associate-/l* 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around -inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. distribute-rgt-neg-out 90.1%

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

   6. Simplified 90.1%

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

   if -1.8999999999999999e-57 < z < 2.35999999999999986e-141

   1. Initial program 77.4%

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

      1. associate-*l* 79.1%

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

      2. associate-*r/ 79.0%

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

      3. *-commutative 79.0%

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

      4. associate-/l* 75.9%

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

   3. Simplified 75.9%

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

      1. associate-*r/ 74.3%

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

      2. associate-*l/ 71.3%

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

      3. associate-/l* 74.4%

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

      4. associate-/r/ 77.6%

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

      5. *-commutative 77.6%

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

      6. associate-/l* 73.8%

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

   5. Applied egg-rr 73.8%

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

   6. Taylor expanded in z around inf 53.6%

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

   7. Taylor expanded in z around 0 49.2%

      \[\leadsto \frac{y}{\frac{\color{blue}{-0.5 \cdot \frac{a \cdot t}{{z}^{2}}}}{x}} \]
   8. Step-by-step derivation

      1. unpow2 49.2%

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

      2. times-frac 51.4%

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

   9. Simplified 51.4%

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

   if 2.35999999999999986e-141 < z

   1. Initial program 56.9%

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

      1. associate-*l* 51.0%

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

      2. associate-*r/ 54.5%

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

      3. *-commutative 54.5%

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

      4. associate-/l* 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in z around inf 83.5%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-57}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.36 \cdot 10^{-141}:\\ \;\;\;\;\frac{y}{\frac{-0.5 \cdot \left(\frac{a}{z} \cdot \frac{t}{z}\right)}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 17: 76.2% accurate, 6.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \end{array} \]

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 -5.2e-176)
   (* y (- x))
   (/ y (/ (/ (+ z (* -0.5 (/ (* t a) z))) z) x))))

C

assert(x < y);
assert(t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.2e-176) {
		tmp = y * -x;
	} else {
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= (-5.2d-176)) then
        tmp = y * -x
    else
        tmp = y / (((z + ((-0.5d0) * ((t * a) / z))) / z) / 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 <= -5.2e-176) {
		tmp = y * -x;
	} else {
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= -5.2e-176:
		tmp = y * -x
	else:
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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 <= -5.2e-176)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y / Float64(Float64(Float64(z + Float64(-0.5 * Float64(Float64(t * a) / z))) / z) / 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 <= -5.2e-176)
		tmp = y * -x;
	else
		tmp = y / (((z + (-0.5 * ((t * a) / z))) / z) / 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, -5.2e-176], N[(y * (-x)), $MachinePrecision], N[(y / N[(N[(N[(z + N[(-0.5 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.19999999999999984e-176

   1. Initial program 66.5%

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

      1. associate-*l* 65.2%

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

      2. associate-*r/ 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-/l* 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in z around -inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-out 84.5%

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

   6. Simplified 84.5%

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

   if -5.19999999999999984e-176 < 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. associate-*l* 59.1%

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

      2. associate-*r/ 62.0%

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

      3. *-commutative 62.0%

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

      4. associate-/l* 62.9%

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

   3. Simplified 62.9%

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

      1. associate-*r/ 61.2%

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

      2. associate-*l/ 59.6%

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

      3. associate-/l* 62.2%

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

      4. associate-/r/ 64.2%

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

      5. *-commutative 64.2%

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

      6. associate-/l* 63.1%

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

   5. Applied egg-rr 63.1%

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

   6. Taylor expanded in z around inf 74.9%

      \[\leadsto \frac{y}{\frac{\frac{\color{blue}{z + -0.5 \cdot \frac{a \cdot t}{z}}}{z}}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-176}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{z}}{x}}\\ \end{array} \]

Alternative 18: 76.2% accurate, 9.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-181}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot x\right)}{-z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -1.2e-50)
   (* y (- x))
   (if (<= z 2.9e-181) (/ (* 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 <= -1.2e-50) {
		tmp = y * -x;
	} else if (z <= 2.9e-181) {
		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 <= (-1.2d-50)) then
        tmp = y * -x
    else if (z <= 2.9d-181) 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 <= -1.2e-50) {
		tmp = y * -x;
	} else if (z <= 2.9e-181) {
		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 <= -1.2e-50:
		tmp = y * -x
	elif z <= 2.9e-181:
		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 <= -1.2e-50)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 2.9e-181)
		tmp = Float64(Float64(y * Float64(z * 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 <= -1.2e-50)
		tmp = y * -x;
	elseif (z <= 2.9e-181)
		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, -1.2e-50], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 2.9e-181], N[(N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision] / (-z)), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000001e-50

   1. Initial program 61.0%

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

      1. associate-*l* 59.4%

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

      2. associate-*r/ 60.7%

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

      3. *-commutative 60.7%

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

      4. associate-/l* 59.9%

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

   3. Simplified 59.9%

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

   4. Taylor expanded in z around -inf 90.1%

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

      1. mul-1-neg 90.1%

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

      2. distribute-rgt-neg-out 90.1%

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

   6. Simplified 90.1%

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

   if -1.20000000000000001e-50 < z < 2.8999999999999998e-181

   1. Initial program 77.5%

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

   2. Taylor expanded in z around -inf 44.0%

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

      1. neg-mul-1 44.0%

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

   4. Simplified 44.0%

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

   5. Taylor expanded in x around 0 46.9%

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

   if 2.8999999999999998e-181 < z

   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. associate-*l* 52.8%

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

      2. associate-*r/ 56.2%

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

      3. *-commutative 56.2%

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

      4. associate-/l* 58.7%

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

   3. Simplified 58.7%

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

   4. Taylor expanded in z around inf 82.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-181}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot x\right)}{-z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 19: 74.5% accurate, 10.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-174}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \frac{z \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -4.2e-174)
   (* y (- x))
   (if (<= z 9.2e-208) (* x (/ (* z y) 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 <= -4.2e-174) {
		tmp = y * -x;
	} else if (z <= 9.2e-208) {
		tmp = x * ((z * y) / 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 <= (-4.2d-174)) then
        tmp = y * -x
    else if (z <= 9.2d-208) then
        tmp = x * ((z * y) / 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 <= -4.2e-174) {
		tmp = y * -x;
	} else if (z <= 9.2e-208) {
		tmp = x * ((z * y) / 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 <= -4.2e-174:
		tmp = y * -x
	elif z <= 9.2e-208:
		tmp = x * ((z * y) / 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 <= -4.2e-174)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 9.2e-208)
		tmp = Float64(x * Float64(Float64(z * y) / 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 <= -4.2e-174)
		tmp = y * -x;
	elseif (z <= 9.2e-208)
		tmp = x * ((z * y) / 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, -4.2e-174], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 9.2e-208], N[(x * N[(N[(z * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000021e-174

   1. Initial program 66.5%

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

      1. associate-*l* 65.2%

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

      2. associate-*r/ 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-/l* 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in z around -inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-out 84.5%

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

   6. Simplified 84.5%

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

   if -4.20000000000000021e-174 < z < 9.19999999999999986e-208

   1. Initial program 72.0%

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

      1. associate-*l* 72.4%

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

      2. associate-*r/ 74.4%

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

   3. Simplified 74.4%

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

   4. Taylor expanded in z around inf 35.7%

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

   if 9.19999999999999986e-208 < z

   1. Initial program 58.2%

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

      1. associate-*l* 53.6%

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

      2. associate-*r/ 56.9%

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

      3. *-commutative 56.9%

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

      4. associate-/l* 59.3%

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

   3. Simplified 59.3%

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

   4. Taylor expanded in z around inf 80.4%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-174}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-208}:\\ \;\;\;\;x \cdot \frac{z \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 20: 75.8% accurate, 10.2× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;\frac{x \cdot \left(z \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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-171)
   (* y (- x))
   (if (<= z 2.3e-122) (/ (* x (* z y)) 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-171) {
		tmp = y * -x;
	} else if (z <= 2.3e-122) {
		tmp = (x * (z * y)) / 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-171)) then
        tmp = y * -x
    else if (z <= 2.3d-122) then
        tmp = (x * (z * y)) / 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-171) {
		tmp = y * -x;
	} else if (z <= 2.3e-122) {
		tmp = (x * (z * y)) / 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-171:
		tmp = y * -x
	elif z <= 2.3e-122:
		tmp = (x * (z * y)) / 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-171)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 2.3e-122)
		tmp = Float64(Float64(x * Float64(z * y)) / 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-171)
		tmp = y * -x;
	elseif (z <= 2.3e-122)
		tmp = (x * (z * y)) / 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-171], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 2.3e-122], N[(N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2e-171

   1. Initial program 66.5%

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

      1. associate-*l* 65.2%

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

      2. associate-*r/ 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-/l* 63.7%

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

   3. Simplified 63.7%

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

   4. Taylor expanded in z around -inf 84.5%

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

      1. mul-1-neg 84.5%

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

      2. distribute-rgt-neg-out 84.5%

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

   6. Simplified 84.5%

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

   if -2e-171 < z < 2.30000000000000007e-122

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf 41.9%

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

      1. div-inv 41.9%

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

      2. *-commutative 41.9%

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

   4. Applied egg-rr 41.9%

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

      1. associate-*r/ 41.9%

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

      2. *-rgt-identity 41.9%

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

      3. /-rgt-identity 41.9%

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

      4. *-commutative 41.9%

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

      5. /-rgt-identity 41.9%

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

      6. associate-*l* 43.0%

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

   6. Simplified 43.0%

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

   if 2.30000000000000007e-122 < z

   1. Initial program 56.5%

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

      1. associate-*l* 52.3%

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

      2. associate-*r/ 55.3%

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

      3. *-commutative 55.3%

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

      4. associate-/l* 55.8%

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

   3. Simplified 55.8%

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

   4. Taylor expanded in z around inf 83.9%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-122}:\\ \;\;\;\;\frac{x \cdot \left(z \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 21: 73.6% accurate, 18.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ [t, a] = \mathsf{sort}([t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-293}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

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 -5e-293) (* 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 <= -5e-293) {
		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 <= (-5d-293)) 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 <= -5e-293) {
		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 <= -5e-293:
		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 <= -5e-293)
		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 <= -5e-293)
		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, -5e-293], N[(y * (-x)), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000003e-293

   1. Initial program 68.1%

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

      1. associate-*l* 67.1%

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

      2. associate-*r/ 67.2%

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

      3. *-commutative 67.2%

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

      4. associate-/l* 65.9%

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

   3. Simplified 65.9%

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

   4. Taylor expanded in z around -inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. distribute-rgt-neg-out 72.3%

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

   6. Simplified 72.3%

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

   if -5.0000000000000003e-293 < z

   1. Initial program 60.3%

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

      1. associate-*l* 56.6%

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

      2. associate-*r/ 60.0%

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

      3. *-commutative 60.0%

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

      4. associate-/l* 61.0%

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

   3. Simplified 61.0%

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

   4. Taylor expanded in z around inf 69.9%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-293}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 22: 43.8% 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 63.8%

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

   1. associate-*l* 61.4%

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

   2. associate-*r/ 63.3%

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

   3. *-commutative 63.3%

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

   4. associate-/l* 63.2%

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

3. Simplified 63.2%

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

4. Taylor expanded in z around inf 46.5%

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

5. Final simplification 46.5%

   \[\leadsto y \cdot x \]

Developer target: 89.3% 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 2023279 
(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)))))