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

Percentage Accurate: 61.2% → 89.2%

Time: 27.3s

Alternatives: 12

Speedup: 18.6×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 61.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 0.00036:\\ \;\;\;\;z \cdot \frac{y \cdot x}{\sqrt{z \cdot z - t \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+31)
   (* y (- x))
   (if (<= z 0.00036)
     (* z (/ (* y x) (sqrt (- (* z z) (* t a)))))
     (* (* y x) (/ z (+ z (* -0.5 (* a (/ t z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+31) {
		tmp = y * -x;
	} else if (z <= 0.00036) {
		tmp = z * ((y * x) / sqrt(((z * z) - (t * a))));
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	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 <= (-1d+31)) then
        tmp = y * -x
    else if (z <= 0.00036d0) then
        tmp = z * ((y * x) / sqrt(((z * z) - (t * a))))
    else
        tmp = (y * x) * (z / (z + ((-0.5d0) * (a * (t / z)))))
    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 <= -1e+31) {
		tmp = y * -x;
	} else if (z <= 0.00036) {
		tmp = z * ((y * x) / Math.sqrt(((z * z) - (t * a))));
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+31:
		tmp = y * -x
	elif z <= 0.00036:
		tmp = z * ((y * x) / math.sqrt(((z * z) - (t * a))))
	else:
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+31)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 0.00036)
		tmp = Float64(z * Float64(Float64(y * x) / sqrt(Float64(Float64(z * z) - Float64(t * a)))));
	else
		tmp = Float64(Float64(y * x) * Float64(z / Float64(z + Float64(-0.5 * Float64(a * Float64(t / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+31)
		tmp = y * -x;
	elseif (z <= 0.00036)
		tmp = z * ((y * x) / sqrt(((z * z) - (t * a))));
	else
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+31], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 0.00036], N[(z * N[(N[(y * x), $MachinePrecision] / N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * N[(z / N[(z + N[(-0.5 * N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.9999999999999996e30

   1. Initial program 37.0%

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

      1. associate-*l* 30.8%

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

      2. associate-*r/ 35.2%

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

      3. *-commutative 35.2%

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

      4. associate-/l* 40.4%

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

   3. Simplified 40.4%

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

   4. Taylor expanded in z around -inf 94.4%

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

      1. mul-1-neg 94.4%

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

      2. distribute-rgt-neg-in 94.4%

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

   6. Simplified 94.4%

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

   if -9.9999999999999996e30 < z < 3.60000000000000023e-4

   1. Initial program 89.3%

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

      1. associate-*l/ 91.0%

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

   3. Simplified 91.0%

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

   if 3.60000000000000023e-4 < z

   1. Initial program 32.4%

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

      1. *-commutative 32.4%

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

      2. associate-/l* 33.9%

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

   3. Simplified 33.9%

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

   4. Taylor expanded in z around inf 68.5%

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

      1. associate-/r/ 83.7%

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

      2. +-commutative 83.7%

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

      3. fma-def 83.7%

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

      4. associate-/l* 91.9%

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

   6. Applied egg-rr 91.9%

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

      1. fma-udef 91.9%

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

      2. div-inv 91.9%

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

      3. clear-num 91.9%

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

   8. Applied egg-rr 91.9%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 0.00036:\\ \;\;\;\;z \cdot \frac{y \cdot x}{\sqrt{z \cdot z - t \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \]

Alternative 2: 89.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{\frac{\sqrt{z \cdot z - t \cdot a}}{y}}\\ \mathbf{if}\;z \leq -6 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-168}:\\ \;\;\;\;\frac{z}{\frac{\sqrt{t \cdot \left(-a\right)}}{y \cdot x}}\\ \mathbf{elif}\;z \leq 0.00036:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z (/ (sqrt (- (* z z) (* t a))) y)))))
   (if (<= z -6e+51)
     (* y (- x))
     (if (<= z -3.4e-151)
       t_1
       (if (<= z 7.2e-168)
         (/ z (/ (sqrt (* t (- a))) (* y x)))
         (if (<= z 0.00036)
           t_1
           (* (* y x) (/ z (+ z (* -0.5 (* a (/ t z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / (sqrt(((z * z) - (t * a))) / y));
	double tmp;
	if (z <= -6e+51) {
		tmp = y * -x;
	} else if (z <= -3.4e-151) {
		tmp = t_1;
	} else if (z <= 7.2e-168) {
		tmp = z / (sqrt((t * -a)) / (y * x));
	} else if (z <= 0.00036) {
		tmp = t_1;
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (sqrt(((z * z) - (t * a))) / y))
    if (z <= (-6d+51)) then
        tmp = y * -x
    else if (z <= (-3.4d-151)) then
        tmp = t_1
    else if (z <= 7.2d-168) then
        tmp = z / (sqrt((t * -a)) / (y * x))
    else if (z <= 0.00036d0) then
        tmp = t_1
    else
        tmp = (y * x) * (z / (z + ((-0.5d0) * (a * (t / z)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / (Math.sqrt(((z * z) - (t * a))) / y));
	double tmp;
	if (z <= -6e+51) {
		tmp = y * -x;
	} else if (z <= -3.4e-151) {
		tmp = t_1;
	} else if (z <= 7.2e-168) {
		tmp = z / (Math.sqrt((t * -a)) / (y * x));
	} else if (z <= 0.00036) {
		tmp = t_1;
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / (math.sqrt(((z * z) - (t * a))) / y))
	tmp = 0
	if z <= -6e+51:
		tmp = y * -x
	elif z <= -3.4e-151:
		tmp = t_1
	elif z <= 7.2e-168:
		tmp = z / (math.sqrt((t * -a)) / (y * x))
	elif z <= 0.00036:
		tmp = t_1
	else:
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / Float64(sqrt(Float64(Float64(z * z) - Float64(t * a))) / y)))
	tmp = 0.0
	if (z <= -6e+51)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -3.4e-151)
		tmp = t_1;
	elseif (z <= 7.2e-168)
		tmp = Float64(z / Float64(sqrt(Float64(t * Float64(-a))) / Float64(y * x)));
	elseif (z <= 0.00036)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * x) * Float64(z / Float64(z + Float64(-0.5 * Float64(a * Float64(t / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / (sqrt(((z * z) - (t * a))) / y));
	tmp = 0.0;
	if (z <= -6e+51)
		tmp = y * -x;
	elseif (z <= -3.4e-151)
		tmp = t_1;
	elseif (z <= 7.2e-168)
		tmp = z / (sqrt((t * -a)) / (y * x));
	elseif (z <= 0.00036)
		tmp = t_1;
	else
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+51], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -3.4e-151], t$95$1, If[LessEqual[z, 7.2e-168], N[(z / N[(N[Sqrt[N[(t * (-a)), $MachinePrecision]], $MachinePrecision] / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00036], t$95$1, N[(N[(y * x), $MachinePrecision] * N[(z / N[(z + N[(-0.5 * N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6e51

   1. Initial program 33.0%

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

      1. associate-*l* 26.4%

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

      2. associate-*r/ 31.1%

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

      3. *-commutative 31.1%

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

      4. associate-/l* 36.6%

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

   3. Simplified 36.6%

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

   4. Taylor expanded in z around -inf 94.0%

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

      1. mul-1-neg 94.0%

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

      2. distribute-rgt-neg-in 94.0%

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

   6. Simplified 94.0%

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

   if -6e51 < z < -3.4000000000000003e-151 or 7.1999999999999998e-168 < z < 3.60000000000000023e-4

   1. Initial program 92.3%

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

      1. associate-*l* 89.1%

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

      2. associate-*r/ 90.3%

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

      3. *-commutative 90.3%

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

      4. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   if -3.4000000000000003e-151 < z < 7.1999999999999998e-168

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in z around 0 87.6%

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

      1. mul-1-neg 76.8%

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

      2. distribute-rgt-neg-out 76.8%

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

   6. Simplified 87.6%

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

   if 3.60000000000000023e-4 < z

   1. Initial program 32.4%

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

      1. *-commutative 32.4%

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

      2. associate-/l* 33.9%

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

   3. Simplified 33.9%

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

   4. Taylor expanded in z around inf 68.5%

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

      1. associate-/r/ 83.7%

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

      2. +-commutative 83.7%

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

      3. fma-def 83.7%

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

      4. associate-/l* 91.9%

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

   6. Applied egg-rr 91.9%

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

      1. fma-udef 91.9%

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

      2. div-inv 91.9%

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

      3. clear-num 91.9%

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

   8. Applied egg-rr 91.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \frac{z}{\frac{\sqrt{z \cdot z - t \cdot a}}{y}}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-168}:\\ \;\;\;\;\frac{z}{\frac{\sqrt{t \cdot \left(-a\right)}}{y \cdot x}}\\ \mathbf{elif}\;z \leq 0.00036:\\ \;\;\;\;x \cdot \frac{z}{\frac{\sqrt{z \cdot z - t \cdot a}}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \]

Alternative 3: 82.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{z}{\frac{\sqrt{t \cdot \left(-a\right)}}{y}}\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-199}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{0.5 \cdot \frac{t \cdot a}{z} - z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* x (/ z (/ (sqrt (* t (- a))) y)))))
   (if (<= z -3.6e-44)
     (* y (- x))
     (if (<= z -2.55e-69)
       t_1
       (if (<= z -5.2e-199)
         (/ (* z (* y x)) (- (* 0.5 (/ (* t a) z)) z))
         (if (<= z 2.1e-88)
           t_1
           (* (* y x) (/ z (+ z (* -0.5 (* a (/ t z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / (sqrt((t * -a)) / y));
	double tmp;
	if (z <= -3.6e-44) {
		tmp = y * -x;
	} else if (z <= -2.55e-69) {
		tmp = t_1;
	} else if (z <= -5.2e-199) {
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z);
	} else if (z <= 2.1e-88) {
		tmp = t_1;
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (z / (sqrt((t * -a)) / y))
    if (z <= (-3.6d-44)) then
        tmp = y * -x
    else if (z <= (-2.55d-69)) then
        tmp = t_1
    else if (z <= (-5.2d-199)) then
        tmp = (z * (y * x)) / ((0.5d0 * ((t * a) / z)) - z)
    else if (z <= 2.1d-88) then
        tmp = t_1
    else
        tmp = (y * x) * (z / (z + ((-0.5d0) * (a * (t / z)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x * (z / (Math.sqrt((t * -a)) / y));
	double tmp;
	if (z <= -3.6e-44) {
		tmp = y * -x;
	} else if (z <= -2.55e-69) {
		tmp = t_1;
	} else if (z <= -5.2e-199) {
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z);
	} else if (z <= 2.1e-88) {
		tmp = t_1;
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x * (z / (math.sqrt((t * -a)) / y))
	tmp = 0
	if z <= -3.6e-44:
		tmp = y * -x
	elif z <= -2.55e-69:
		tmp = t_1
	elif z <= -5.2e-199:
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z)
	elif z <= 2.1e-88:
		tmp = t_1
	else:
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x * Float64(z / Float64(sqrt(Float64(t * Float64(-a))) / y)))
	tmp = 0.0
	if (z <= -3.6e-44)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -2.55e-69)
		tmp = t_1;
	elseif (z <= -5.2e-199)
		tmp = Float64(Float64(z * Float64(y * x)) / Float64(Float64(0.5 * Float64(Float64(t * a) / z)) - z));
	elseif (z <= 2.1e-88)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * x) * Float64(z / Float64(z + Float64(-0.5 * Float64(a * Float64(t / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x * (z / (sqrt((t * -a)) / y));
	tmp = 0.0;
	if (z <= -3.6e-44)
		tmp = y * -x;
	elseif (z <= -2.55e-69)
		tmp = t_1;
	elseif (z <= -5.2e-199)
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z);
	elseif (z <= 2.1e-88)
		tmp = t_1;
	else
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x * N[(z / N[(N[Sqrt[N[(t * (-a)), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.6e-44], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -2.55e-69], t$95$1, If[LessEqual[z, -5.2e-199], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(N[(0.5 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-88], t$95$1, N[(N[(y * x), $MachinePrecision] * N[(z / N[(z + N[(-0.5 * N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5999999999999999e-44

   1. Initial program 46.1%

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

      1. associate-*l* 40.9%

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

      2. associate-*r/ 45.8%

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

      3. *-commutative 45.8%

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

      4. associate-/l* 50.2%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in z around -inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-rgt-neg-in 91.8%

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

   6. Simplified 91.8%

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

   if -3.5999999999999999e-44 < z < -2.54999999999999993e-69 or -5.2000000000000001e-199 < z < 2.1e-88

   1. Initial program 82.1%

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

      1. associate-*l* 74.8%

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

      2. associate-*r/ 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-/l* 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in z around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. distribute-rgt-neg-out 75.1%

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

   6. Simplified 75.1%

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

   if -2.54999999999999993e-69 < z < -5.2000000000000001e-199

   1. Initial program 99.7%

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

   2. Taylor expanded in z around -inf 73.2%

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

      1. neg-mul-1 73.2%

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

      2. unsub-neg 73.2%

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

   4. Simplified 73.2%

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

   if 2.1e-88 < z

   1. Initial program 44.6%

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

      1. *-commutative 44.6%

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

      2. associate-/l* 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in z around inf 71.2%

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

      1. associate-/r/ 84.6%

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

      2. +-commutative 84.6%

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

      3. fma-def 84.6%

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

      4. associate-/l* 91.3%

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

   6. Applied egg-rr 91.3%

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

      1. fma-udef 91.3%

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

      2. div-inv 91.3%

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

      3. clear-num 91.3%

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

   8. Applied egg-rr 91.3%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \frac{z}{\frac{\sqrt{t \cdot \left(-a\right)}}{y}}\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-199}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{0.5 \cdot \frac{t \cdot a}{z} - z}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \frac{z}{\frac{\sqrt{t \cdot \left(-a\right)}}{y}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \]

Alternative 4: 83.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y \cdot x}{\sqrt{t \cdot \left(-a\right)}}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-65}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-105}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{0.5 \cdot \frac{t \cdot a}{z} - z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-87}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ (* y x) (sqrt (* t (- a)))))))
   (if (<= z -3.2e-44)
     (* y (- x))
     (if (<= z -1.8e-65)
       t_1
       (if (<= z -1.1e-105)
         (/ (* z (* y x)) (- (* 0.5 (/ (* t a) z)) z))
         (if (<= z 4.1e-87)
           t_1
           (* (* y x) (/ z (+ z (* -0.5 (* a (/ t z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y * x) / sqrt((t * -a)));
	double tmp;
	if (z <= -3.2e-44) {
		tmp = y * -x;
	} else if (z <= -1.8e-65) {
		tmp = t_1;
	} else if (z <= -1.1e-105) {
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z);
	} else if (z <= 4.1e-87) {
		tmp = t_1;
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * ((y * x) / sqrt((t * -a)))
    if (z <= (-3.2d-44)) then
        tmp = y * -x
    else if (z <= (-1.8d-65)) then
        tmp = t_1
    else if (z <= (-1.1d-105)) then
        tmp = (z * (y * x)) / ((0.5d0 * ((t * a) / z)) - z)
    else if (z <= 4.1d-87) then
        tmp = t_1
    else
        tmp = (y * x) * (z / (z + ((-0.5d0) * (a * (t / z)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * ((y * x) / Math.sqrt((t * -a)));
	double tmp;
	if (z <= -3.2e-44) {
		tmp = y * -x;
	} else if (z <= -1.8e-65) {
		tmp = t_1;
	} else if (z <= -1.1e-105) {
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z);
	} else if (z <= 4.1e-87) {
		tmp = t_1;
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * ((y * x) / math.sqrt((t * -a)))
	tmp = 0
	if z <= -3.2e-44:
		tmp = y * -x
	elif z <= -1.8e-65:
		tmp = t_1
	elif z <= -1.1e-105:
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z)
	elif z <= 4.1e-87:
		tmp = t_1
	else:
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(Float64(y * x) / sqrt(Float64(t * Float64(-a)))))
	tmp = 0.0
	if (z <= -3.2e-44)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -1.8e-65)
		tmp = t_1;
	elseif (z <= -1.1e-105)
		tmp = Float64(Float64(z * Float64(y * x)) / Float64(Float64(0.5 * Float64(Float64(t * a) / z)) - z));
	elseif (z <= 4.1e-87)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * x) * Float64(z / Float64(z + Float64(-0.5 * Float64(a * Float64(t / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * ((y * x) / sqrt((t * -a)));
	tmp = 0.0;
	if (z <= -3.2e-44)
		tmp = y * -x;
	elseif (z <= -1.8e-65)
		tmp = t_1;
	elseif (z <= -1.1e-105)
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z);
	elseif (z <= 4.1e-87)
		tmp = t_1;
	else
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(N[(y * x), $MachinePrecision] / N[Sqrt[N[(t * (-a)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e-44], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -1.8e-65], t$95$1, If[LessEqual[z, -1.1e-105], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(N[(0.5 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-87], t$95$1, N[(N[(y * x), $MachinePrecision] * N[(z / N[(z + N[(-0.5 * N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.19999999999999995e-44

   1. Initial program 46.1%

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

      1. associate-*l* 40.9%

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

      2. associate-*r/ 45.8%

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

      3. *-commutative 45.8%

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

      4. associate-/l* 50.2%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in z around -inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-rgt-neg-in 91.8%

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

   6. Simplified 91.8%

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

   if -3.19999999999999995e-44 < z < -1.7999999999999999e-65 or -1.10000000000000002e-105 < z < 4.10000000000000033e-87

   1. Initial program 85.2%

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

      1. associate-*l/ 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in z around 0 82.2%

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

      1. mul-1-neg 73.3%

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

      2. distribute-rgt-neg-out 73.3%

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

   6. Simplified 82.2%

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

   if -1.7999999999999999e-65 < z < -1.10000000000000002e-105

   1. Initial program 99.7%

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

   2. Taylor expanded in z around -inf 81.6%

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

      1. neg-mul-1 81.6%

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

      2. unsub-neg 81.6%

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

   4. Simplified 81.6%

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

   if 4.10000000000000033e-87 < z

   1. Initial program 44.6%

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

      1. *-commutative 44.6%

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

      2. associate-/l* 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in z around inf 71.2%

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

      1. associate-/r/ 84.6%

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

      2. +-commutative 84.6%

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

      3. fma-def 84.6%

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

      4. associate-/l* 91.3%

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

   6. Applied egg-rr 91.3%

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

      1. fma-udef 91.3%

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

      2. div-inv 91.3%

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

      3. clear-num 91.3%

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

   8. Applied egg-rr 91.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-44}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-65}:\\ \;\;\;\;z \cdot \frac{y \cdot x}{\sqrt{t \cdot \left(-a\right)}}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-105}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{0.5 \cdot \frac{t \cdot a}{z} - z}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-87}:\\ \;\;\;\;z \cdot \frac{y \cdot x}{\sqrt{t \cdot \left(-a\right)}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \]

Alternative 5: 83.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{\sqrt{t \cdot \left(-a\right)}}{y \cdot x}}\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-106}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{0.5 \cdot \frac{t \cdot a}{z} - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ (sqrt (* t (- a))) (* y x)))))
   (if (<= z -2.9e-43)
     (* y (- x))
     (if (<= z -2.2e-66)
       t_1
       (if (<= z -1.04e-106)
         (/ (* z (* y x)) (- (* 0.5 (/ (* t a) z)) z))
         (if (<= z 6.5e-88)
           t_1
           (* (* y x) (/ z (+ z (* -0.5 (* a (/ t z))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (sqrt((t * -a)) / (y * x));
	double tmp;
	if (z <= -2.9e-43) {
		tmp = y * -x;
	} else if (z <= -2.2e-66) {
		tmp = t_1;
	} else if (z <= -1.04e-106) {
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z);
	} else if (z <= 6.5e-88) {
		tmp = t_1;
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (sqrt((t * -a)) / (y * x))
    if (z <= (-2.9d-43)) then
        tmp = y * -x
    else if (z <= (-2.2d-66)) then
        tmp = t_1
    else if (z <= (-1.04d-106)) then
        tmp = (z * (y * x)) / ((0.5d0 * ((t * a) / z)) - z)
    else if (z <= 6.5d-88) then
        tmp = t_1
    else
        tmp = (y * x) * (z / (z + ((-0.5d0) * (a * (t / z)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (Math.sqrt((t * -a)) / (y * x));
	double tmp;
	if (z <= -2.9e-43) {
		tmp = y * -x;
	} else if (z <= -2.2e-66) {
		tmp = t_1;
	} else if (z <= -1.04e-106) {
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z);
	} else if (z <= 6.5e-88) {
		tmp = t_1;
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (math.sqrt((t * -a)) / (y * x))
	tmp = 0
	if z <= -2.9e-43:
		tmp = y * -x
	elif z <= -2.2e-66:
		tmp = t_1
	elif z <= -1.04e-106:
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z)
	elif z <= 6.5e-88:
		tmp = t_1
	else:
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(sqrt(Float64(t * Float64(-a))) / Float64(y * x)))
	tmp = 0.0
	if (z <= -2.9e-43)
		tmp = Float64(y * Float64(-x));
	elseif (z <= -2.2e-66)
		tmp = t_1;
	elseif (z <= -1.04e-106)
		tmp = Float64(Float64(z * Float64(y * x)) / Float64(Float64(0.5 * Float64(Float64(t * a) / z)) - z));
	elseif (z <= 6.5e-88)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * x) * Float64(z / Float64(z + Float64(-0.5 * Float64(a * Float64(t / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (sqrt((t * -a)) / (y * x));
	tmp = 0.0;
	if (z <= -2.9e-43)
		tmp = y * -x;
	elseif (z <= -2.2e-66)
		tmp = t_1;
	elseif (z <= -1.04e-106)
		tmp = (z * (y * x)) / ((0.5 * ((t * a) / z)) - z);
	elseif (z <= 6.5e-88)
		tmp = t_1;
	else
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(N[Sqrt[N[(t * (-a)), $MachinePrecision]], $MachinePrecision] / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e-43], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, -2.2e-66], t$95$1, If[LessEqual[z, -1.04e-106], N[(N[(z * N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(N[(0.5 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.5e-88], t$95$1, N[(N[(y * x), $MachinePrecision] * N[(z / N[(z + N[(-0.5 * N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9000000000000001e-43

   1. Initial program 46.1%

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

      1. associate-*l* 40.9%

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

      2. associate-*r/ 45.8%

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

      3. *-commutative 45.8%

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

      4. associate-/l* 50.2%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in z around -inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-rgt-neg-in 91.8%

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

   6. Simplified 91.8%

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

   if -2.9000000000000001e-43 < z < -2.2000000000000001e-66 or -1.04e-106 < z < 6.50000000000000006e-88

   1. Initial program 85.2%

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

      1. *-commutative 85.2%

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

      2. associate-/l* 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in z around 0 82.2%

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

      1. mul-1-neg 73.3%

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

      2. distribute-rgt-neg-out 73.3%

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

   6. Simplified 82.2%

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

   if -2.2000000000000001e-66 < z < -1.04e-106

   1. Initial program 99.7%

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

   2. Taylor expanded in z around -inf 81.6%

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

      1. neg-mul-1 81.6%

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

      2. unsub-neg 81.6%

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

   4. Simplified 81.6%

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

   if 6.50000000000000006e-88 < z

   1. Initial program 44.6%

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

      1. *-commutative 44.6%

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

      2. associate-/l* 45.0%

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

   3. Simplified 45.0%

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

   4. Taylor expanded in z around inf 71.2%

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

      1. associate-/r/ 84.6%

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

      2. +-commutative 84.6%

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

      3. fma-def 84.6%

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

      4. associate-/l* 91.3%

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

   6. Applied egg-rr 91.3%

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

      1. fma-udef 91.3%

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

      2. div-inv 91.3%

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

      3. clear-num 91.3%

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

   8. Applied egg-rr 91.3%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-43}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{z}{\frac{\sqrt{t \cdot \left(-a\right)}}{y \cdot x}}\\ \mathbf{elif}\;z \leq -1.04 \cdot 10^{-106}:\\ \;\;\;\;\frac{z \cdot \left(y \cdot x\right)}{0.5 \cdot \frac{t \cdot a}{z} - z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{z}{\frac{\sqrt{t \cdot \left(-a\right)}}{y \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \]

Alternative 6: 76.6% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \frac{z}{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.9e-199)
   (* y (- x))
   (if (<= z 1.32e-33)
     (* x (/ z (/ (+ z (* -0.5 (/ (* t a) z))) y)))
     (* y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.9e-199) {
		tmp = y * -x;
	} else if (z <= 1.32e-33) {
		tmp = x * (z / ((z + (-0.5 * ((t * a) / z))) / 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 <= (-2.9d-199)) then
        tmp = y * -x
    else if (z <= 1.32d-33) then
        tmp = x * (z / ((z + ((-0.5d0) * ((t * a) / z))) / 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 <= -2.9e-199) {
		tmp = y * -x;
	} else if (z <= 1.32e-33) {
		tmp = x * (z / ((z + (-0.5 * ((t * a) / z))) / y));
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.9e-199:
		tmp = y * -x
	elif z <= 1.32e-33:
		tmp = x * (z / ((z + (-0.5 * ((t * a) / z))) / y))
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.9e-199)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 1.32e-33)
		tmp = Float64(x * Float64(z / Float64(Float64(z + Float64(-0.5 * Float64(Float64(t * a) / z))) / 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 <= -2.9e-199)
		tmp = y * -x;
	elseif (z <= 1.32e-33)
		tmp = x * (z / ((z + (-0.5 * ((t * a) / z))) / y));
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.9e-199], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 1.32e-33], N[(x * N[(z / N[(N[(z + N[(-0.5 * N[(N[(t * a), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.9e-199

   1. Initial program 61.4%

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

      1. associate-*l* 56.0%

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

      2. associate-*r/ 57.1%

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

      3. *-commutative 57.1%

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

      4. associate-/l* 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in z around -inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. distribute-rgt-neg-in 80.3%

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

   6. Simplified 80.3%

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

   if -2.9e-199 < z < 1.31999999999999993e-33

   1. Initial program 83.6%

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

      1. associate-*l* 77.0%

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

      2. associate-*r/ 81.9%

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

      3. *-commutative 81.9%

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

      4. associate-/l* 82.5%

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

   3. Simplified 82.5%

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

   4. Taylor expanded in z around inf 64.5%

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

   if 1.31999999999999993e-33 < z

   1. Initial program 39.0%

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

      1. associate-*l* 37.6%

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

      2. associate-*r/ 40.3%

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

      3. *-commutative 40.3%

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

      4. associate-/l* 38.3%

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

   3. Simplified 38.3%

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

   4. Taylor expanded in z around inf 91.0%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 1.32 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \frac{z}{\frac{z + -0.5 \cdot \frac{t \cdot a}{z}}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 7: 76.0% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-154}:\\ \;\;\;\;-2 \cdot \frac{\frac{\left(z \cdot y\right) \cdot \left(z \cdot x\right)}{a}}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.6e-199)
   (* y (- x))
   (if (<= z 2.9e-154) (* -2.0 (/ (/ (* (* z y) (* z x)) a) t)) (* y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.6e-199) {
		tmp = y * -x;
	} else if (z <= 2.9e-154) {
		tmp = -2.0 * ((((z * y) * (z * x)) / a) / t);
	} 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 <= (-2.6d-199)) then
        tmp = y * -x
    else if (z <= 2.9d-154) then
        tmp = (-2.0d0) * ((((z * y) * (z * x)) / a) / t)
    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 <= -2.6e-199) {
		tmp = y * -x;
	} else if (z <= 2.9e-154) {
		tmp = -2.0 * ((((z * y) * (z * x)) / a) / t);
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.6e-199:
		tmp = y * -x
	elif z <= 2.9e-154:
		tmp = -2.0 * ((((z * y) * (z * x)) / a) / t)
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.6e-199)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 2.9e-154)
		tmp = Float64(-2.0 * Float64(Float64(Float64(Float64(z * y) * Float64(z * x)) / a) / t));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.6e-199)
		tmp = y * -x;
	elseif (z <= 2.9e-154)
		tmp = -2.0 * ((((z * y) * (z * x)) / a) / t);
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.6e-199], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 2.9e-154], N[(-2.0 * N[(N[(N[(N[(z * y), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6000000000000001e-199

   1. Initial program 61.4%

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

      1. associate-*l* 56.0%

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

      2. associate-*r/ 57.1%

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

      3. *-commutative 57.1%

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

      4. associate-/l* 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in z around -inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. distribute-rgt-neg-in 80.3%

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

   6. Simplified 80.3%

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

   if -2.6000000000000001e-199 < z < 2.9e-154

   1. Initial program 84.5%

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

      1. *-commutative 84.5%

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

      2. associate-/l* 87.3%

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

   3. Simplified 87.3%

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

   4. Taylor expanded in z around inf 64.7%

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

      1. associate-/r/ 66.1%

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

      2. +-commutative 66.1%

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

      3. fma-def 66.1%

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

      4. associate-/l* 66.9%

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

   6. Applied egg-rr 66.9%

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

   7. Taylor expanded in z around 0 64.3%

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

      1. times-frac 64.3%

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

      2. unpow2 64.3%

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

      3. associate-*r* 64.6%

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

      4. associate-*r/ 64.6%

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

      5. associate-*l/ 64.8%

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

      6. associate-*r* 64.9%

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

      7. *-commutative 64.9%

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

   9. Simplified 64.9%

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

   if 2.9e-154 < z

   1. Initial program 48.0%

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

      1. associate-*l* 46.4%

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

      2. associate-*r/ 51.0%

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

      3. *-commutative 51.0%

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

      4. associate-/l* 50.2%

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

   3. Simplified 50.2%

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

   4. Taylor expanded in z around inf 82.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-154}:\\ \;\;\;\;-2 \cdot \frac{\frac{\left(z \cdot y\right) \cdot \left(z \cdot x\right)}{a}}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 8: 77.5% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -7.2e-199)
   (* y (- x))
   (* (* y x) (/ z (+ z (* -0.5 (* a (/ t z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -7.2e-199) {
		tmp = y * -x;
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	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 <= (-7.2d-199)) then
        tmp = y * -x
    else
        tmp = (y * x) * (z / (z + ((-0.5d0) * (a * (t / z)))))
    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 <= -7.2e-199) {
		tmp = y * -x;
	} else {
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -7.2e-199:
		tmp = y * -x
	else:
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -7.2e-199)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(Float64(y * x) * Float64(z / Float64(z + Float64(-0.5 * Float64(a * Float64(t / z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -7.2e-199)
		tmp = y * -x;
	else
		tmp = (y * x) * (z / (z + (-0.5 * (a * (t / z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -7.2e-199], N[(y * (-x)), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * N[(z / N[(z + N[(-0.5 * N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.2000000000000003e-199

   1. Initial program 61.4%

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

      1. associate-*l* 56.0%

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

      2. associate-*r/ 57.1%

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

      3. *-commutative 57.1%

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

      4. associate-/l* 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in z around -inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. distribute-rgt-neg-in 80.3%

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

   6. Simplified 80.3%

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

   if -7.2000000000000003e-199 < z

   1. Initial program 59.0%

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

      1. *-commutative 59.0%

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

      2. associate-/l* 61.4%

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

   3. Simplified 61.4%

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

   4. Taylor expanded in z around inf 67.2%

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

      1. associate-/r/ 75.8%

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

      2. +-commutative 75.8%

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

      3. fma-def 75.8%

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

      4. associate-/l* 80.1%

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

   6. Applied egg-rr 80.1%

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

      1. fma-udef 80.1%

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

      2. div-inv 80.1%

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

      3. clear-num 80.1%

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

   8. Applied egg-rr 80.1%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\\ \end{array} \]

Alternative 9: 75.6% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-83}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.55e-199)
   (* y (- x))
   (if (<= z 4.4e-83) (/ (* y (* z x)) z) (* y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.55e-199) {
		tmp = y * -x;
	} else if (z <= 4.4e-83) {
		tmp = (y * (z * x)) / z;
	} 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 <= (-1.55d-199)) then
        tmp = y * -x
    else if (z <= 4.4d-83) then
        tmp = (y * (z * x)) / z
    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 <= -1.55e-199) {
		tmp = y * -x;
	} else if (z <= 4.4e-83) {
		tmp = (y * (z * x)) / z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.55e-199:
		tmp = y * -x
	elif z <= 4.4e-83:
		tmp = (y * (z * x)) / z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.55e-199)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 4.4e-83)
		tmp = Float64(Float64(y * Float64(z * x)) / z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.55e-199)
		tmp = y * -x;
	elseif (z <= 4.4e-83)
		tmp = (y * (z * x)) / z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.55e-199], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 4.4e-83], N[(N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.55000000000000006e-199

   1. Initial program 61.4%

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

      1. associate-*l* 56.0%

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

      2. associate-*r/ 57.1%

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

      3. *-commutative 57.1%

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

      4. associate-/l* 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in z around -inf 80.3%

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

      1. mul-1-neg 80.3%

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

      2. distribute-rgt-neg-in 80.3%

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

   6. Simplified 80.3%

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

   if -1.55000000000000006e-199 < z < 4.40000000000000015e-83

   1. Initial program 81.7%

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

   2. Taylor expanded in z around inf 48.8%

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

   3. Taylor expanded in x around 0 54.1%

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

   if 4.40000000000000015e-83 < z

   1. Initial program 43.9%

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

      1. associate-*l* 42.1%

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

      2. associate-*r/ 44.6%

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

      3. *-commutative 44.6%

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

      4. associate-/l* 42.6%

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

   3. Simplified 42.6%

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

   4. Taylor expanded in z around inf 89.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-199}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-83}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 10: 75.2% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{x \cdot \left(z \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.45e-257)
   (* y (- x))
   (if (<= z 8.5e-86) (/ (* x (* z y)) z) (* y x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.45e-257) {
		tmp = y * -x;
	} else if (z <= 8.5e-86) {
		tmp = (x * (z * y)) / z;
	} 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 <= (-2.45d-257)) then
        tmp = y * -x
    else if (z <= 8.5d-86) then
        tmp = (x * (z * y)) / z
    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 <= -2.45e-257) {
		tmp = y * -x;
	} else if (z <= 8.5e-86) {
		tmp = (x * (z * y)) / z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.45e-257:
		tmp = y * -x
	elif z <= 8.5e-86:
		tmp = (x * (z * y)) / z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.45e-257)
		tmp = Float64(y * Float64(-x));
	elseif (z <= 8.5e-86)
		tmp = Float64(Float64(x * Float64(z * y)) / z);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.45e-257)
		tmp = y * -x;
	elseif (z <= 8.5e-86)
		tmp = (x * (z * y)) / z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.45e-257], N[(y * (-x)), $MachinePrecision], If[LessEqual[z, 8.5e-86], N[(N[(x * N[(z * y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.45000000000000006e-257

   1. Initial program 62.8%

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

      1. associate-*l* 56.2%

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

      2. associate-*r/ 57.2%

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

      3. *-commutative 57.2%

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

      4. associate-/l* 58.5%

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

   3. Simplified 58.5%

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

   4. Taylor expanded in z around -inf 77.5%

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

      1. mul-1-neg 77.5%

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

      2. distribute-rgt-neg-in 77.5%

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

   6. Simplified 77.5%

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

   if -2.45000000000000006e-257 < z < 8.499999999999999e-86

   1. Initial program 81.1%

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

   2. Taylor expanded in z around inf 51.3%

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

   3. Taylor expanded in x around 0 55.4%

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

      1. associate-*r* 57.3%

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

      2. *-commutative 57.3%

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

   5. Simplified 57.3%

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

   if 8.499999999999999e-86 < z

   1. Initial program 43.9%

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

      1. associate-*l* 42.1%

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

      2. associate-*r/ 44.6%

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

      3. *-commutative 44.6%

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

      4. associate-/l* 42.6%

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

   3. Simplified 42.6%

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

   4. Taylor expanded in z around inf 89.6%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-257}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-86}:\\ \;\;\;\;\frac{x \cdot \left(z \cdot y\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 11: 73.0% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-310}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e-310) (* y (- x)) (* y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e-310) {
		tmp = y * -x;
	} 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 <= (-2d-310)) then
        tmp = y * -x
    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 <= -2e-310) {
		tmp = y * -x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e-310:
		tmp = y * -x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e-310)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e-310)
		tmp = y * -x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e-310], N[(y * (-x)), $MachinePrecision], N[(y * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.999999999999994e-310

   1. Initial program 65.6%

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

      1. associate-*l* 58.7%

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

      2. associate-*r/ 60.2%

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

      3. *-commutative 60.2%

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

      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. Taylor expanded in z around -inf 68.0%

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

      1. mul-1-neg 68.0%

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

      2. distribute-rgt-neg-in 68.0%

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

   6. Simplified 68.0%

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

   if -1.999999999999994e-310 < z

   1. Initial program 53.5%

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

      1. associate-*l* 51.9%

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

      2. associate-*r/ 55.7%

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

      3. *-commutative 55.7%

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

      4. associate-/l* 55.4%

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

   3. Simplified 55.4%

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

   4. Taylor expanded in z around inf 75.2%

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

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-310}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 12: 43.8% accurate, 37.7× speedup

Math

\[\begin{array}{l} \\ y \cdot x \end{array} \]

FPCore

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

C

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

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 = y * x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y * x), $MachinePrecision]

Derivation

1. Initial program 60.0%

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

   1. associate-*l* 55.6%

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

   2. associate-*r/ 58.1%

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

   3. *-commutative 58.1%

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

   4. associate-/l* 58.2%

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

3. Simplified 58.2%

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

4. Taylor expanded in z around inf 41.8%

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

5. Final simplification 41.8%

   \[\leadsto y \cdot x \]

Developer target: 88.9% 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 2023274 
(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)))))