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

Percentage Accurate: 61.8% → 89.4%

Time: 24.3s

Alternatives: 14

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: 61.8% 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: 89.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+100}:\\ \;\;\;\;\frac{z \cdot \left(x \cdot y\right)}{\sqrt{z \cdot z - t \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+78)
   (* x (- y))
   (if (<= z 7e+100) (/ (* z (* x y)) (sqrt (- (* z z) (* t a)))) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+78) {
		tmp = x * -y;
	} else if (z <= 7e+100) {
		tmp = (z * (x * y)) / sqrt(((z * z) - (t * a)));
	} else {
		tmp = x * y;
	}
	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 <= (-1.05d+78)) then
        tmp = x * -y
    else if (z <= 7d+100) then
        tmp = (z * (x * y)) / sqrt(((z * z) - (t * a)))
    else
        tmp = x * y
    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 <= -1.05e+78) {
		tmp = x * -y;
	} else if (z <= 7e+100) {
		tmp = (z * (x * y)) / Math.sqrt(((z * z) - (t * a)));
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+78:
		tmp = x * -y
	elif z <= 7e+100:
		tmp = (z * (x * y)) / math.sqrt(((z * z) - (t * a)))
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+78)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 7e+100)
		tmp = Float64(Float64(z * Float64(x * y)) / sqrt(Float64(Float64(z * z) - Float64(t * a))));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+78)
		tmp = x * -y;
	elseif (z <= 7e+100)
		tmp = (z * (x * y)) / sqrt(((z * z) - (t * a)));
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+78], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 7e+100], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05e78

   1. Initial program 32.0%

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

   2. Taylor expanded in z around -inf 98.5%

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

      1. mul-1-neg 98.5%

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

      2. distribute-rgt-neg-out 98.5%

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

   4. Simplified 98.5%

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

   if -1.05e78 < z < 6.99999999999999953e100

   1. Initial program 86.7%

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

   if 6.99999999999999953e100 < z

   1. Initial program 35.7%

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

   2. Taylor expanded in z around inf 98.2%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+78}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+100}:\\ \;\;\;\;\frac{z \cdot \left(x \cdot y\right)}{\sqrt{z \cdot z - t \cdot a}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 2: 89.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.06 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \frac{z}{\frac{\sqrt{z \cdot z - t \cdot a}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.06e+80)
   (* x (- y))
   (if (<= z 1.1e+100) (* x (/ z (/ (sqrt (- (* z z) (* t a))) y))) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.06e+80) {
		tmp = x * -y;
	} else if (z <= 1.1e+100) {
		tmp = x * (z / (sqrt(((z * z) - (t * a))) / y));
	} else {
		tmp = x * y;
	}
	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 <= (-2.06d+80)) then
        tmp = x * -y
    else if (z <= 1.1d+100) then
        tmp = x * (z / (sqrt(((z * z) - (t * a))) / y))
    else
        tmp = x * y
    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 <= -2.06e+80) {
		tmp = x * -y;
	} else if (z <= 1.1e+100) {
		tmp = x * (z / (Math.sqrt(((z * z) - (t * a))) / y));
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.06e+80:
		tmp = x * -y
	elif z <= 1.1e+100:
		tmp = x * (z / (math.sqrt(((z * z) - (t * a))) / y))
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.06e+80)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 1.1e+100)
		tmp = Float64(x * Float64(z / Float64(sqrt(Float64(Float64(z * z) - Float64(t * a))) / y)));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.06e+80)
		tmp = x * -y;
	elseif (z <= 1.1e+100)
		tmp = x * (z / (sqrt(((z * z) - (t * a))) / y));
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.06e+80], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 1.1e+100], N[(x * N[(z / N[(N[Sqrt[N[(N[(z * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.06e80

   1. Initial program 31.0%

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

   2. Taylor expanded in z around -inf 98.5%

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

      1. mul-1-neg 98.5%

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

      2. distribute-rgt-neg-out 98.5%

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

   4. Simplified 98.5%

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

   if -2.06e80 < z < 1.1e100

   1. Initial program 86.8%

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

      1. associate-*l* 81.3%

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

      2. associate-*r/ 80.9%

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

      3. *-commutative 80.9%

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

      4. associate-/l* 82.1%

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

   3. Simplified 82.1%

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

   if 1.1e100 < z

   1. Initial program 35.7%

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

   2. Taylor expanded in z around inf 98.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.06 \cdot 10^{+80}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+100}:\\ \;\;\;\;x \cdot \frac{z}{\frac{\sqrt{z \cdot z - t \cdot a}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 3: 81.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{z}{\frac{\sqrt{a \cdot \left(-t\right)}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.8e-91)
   (* x (- y))
   (if (<= z 5.2e-70) (* x (/ z (/ (sqrt (* a (- t))) y))) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.8e-91) {
		tmp = x * -y;
	} else if (z <= 5.2e-70) {
		tmp = x * (z / (sqrt((a * -t)) / y));
	} else {
		tmp = x * y;
	}
	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 <= (-2.8d-91)) then
        tmp = x * -y
    else if (z <= 5.2d-70) then
        tmp = x * (z / (sqrt((a * -t)) / y))
    else
        tmp = x * y
    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 <= -2.8e-91) {
		tmp = x * -y;
	} else if (z <= 5.2e-70) {
		tmp = x * (z / (Math.sqrt((a * -t)) / y));
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.8e-91:
		tmp = x * -y
	elif z <= 5.2e-70:
		tmp = x * (z / (math.sqrt((a * -t)) / y))
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.8e-91)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 5.2e-70)
		tmp = Float64(x * Float64(z / Float64(sqrt(Float64(a * Float64(-t))) / y)));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.8e-91)
		tmp = x * -y;
	elseif (z <= 5.2e-70)
		tmp = x * (z / (sqrt((a * -t)) / y));
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.8e-91], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 5.2e-70], N[(x * N[(z / N[(N[Sqrt[N[(a * (-t)), $MachinePrecision]], $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.8e-91

   1. Initial program 56.8%

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

   2. Taylor expanded in z around -inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-rgt-neg-out 91.8%

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

   4. Simplified 91.8%

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

   if -2.8e-91 < z < 5.20000000000000004e-70

   1. Initial program 81.3%

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

      1. associate-*l* 76.8%

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

      2. associate-*r/ 75.8%

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

      3. *-commutative 75.8%

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

      4. associate-/l* 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in z around 0 67.9%

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

      1. associate-*r* 67.9%

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

      2. neg-mul-1 67.9%

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

      3. *-commutative 67.9%

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

   6. Simplified 67.9%

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

   if 5.20000000000000004e-70 < z

   1. Initial program 55.9%

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

   2. Taylor expanded in z around inf 87.1%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \frac{z}{\frac{\sqrt{a \cdot \left(-t\right)}}{y}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 82.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\sqrt{a \cdot \left(-t\right)}} \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.4e-91)
   (* x (- y))
   (if (<= z 9.2e-70) (* (/ y (sqrt (* a (- t)))) (* z x)) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.4e-91) {
		tmp = x * -y;
	} else if (z <= 9.2e-70) {
		tmp = (y / sqrt((a * -t))) * (z * x);
	} else {
		tmp = x * y;
	}
	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 <= (-1.4d-91)) then
        tmp = x * -y
    else if (z <= 9.2d-70) then
        tmp = (y / sqrt((a * -t))) * (z * x)
    else
        tmp = x * y
    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 <= -1.4e-91) {
		tmp = x * -y;
	} else if (z <= 9.2e-70) {
		tmp = (y / Math.sqrt((a * -t))) * (z * x);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.4e-91:
		tmp = x * -y
	elif z <= 9.2e-70:
		tmp = (y / math.sqrt((a * -t))) * (z * x)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.4e-91)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 9.2e-70)
		tmp = Float64(Float64(y / sqrt(Float64(a * Float64(-t)))) * Float64(z * x));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.4e-91)
		tmp = x * -y;
	elseif (z <= 9.2e-70)
		tmp = (y / sqrt((a * -t))) * (z * x);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.4e-91], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 9.2e-70], N[(N[(y / N[Sqrt[N[(a * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(z * x), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.4e-91

   1. Initial program 56.8%

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

   2. Taylor expanded in z around -inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-rgt-neg-out 91.8%

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

   4. Simplified 91.8%

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

   if -1.4e-91 < z < 9.20000000000000002e-70

   1. Initial program 81.3%

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

      1. associate-*l* 76.8%

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

      2. *-commutative 76.8%

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

      3. associate-*l* 79.0%

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

      4. associate-*r/ 79.1%

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

      5. *-commutative 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in z around 0 72.9%

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

      1. associate-*r* 67.9%

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

      2. neg-mul-1 67.9%

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

      3. *-commutative 67.9%

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

   6. Simplified 72.9%

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

   if 9.20000000000000002e-70 < z

   1. Initial program 55.9%

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

   2. Taylor expanded in z around inf 87.1%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-91}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\sqrt{a \cdot \left(-t\right)}} \cdot \left(z \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 5: 81.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-69}:\\ \;\;\;\;\frac{z \cdot \left(x \cdot y\right)}{\sqrt{a \cdot \left(-t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -6e-103)
   (* x (- y))
   (if (<= z 1.1e-69) (/ (* z (* x y)) (sqrt (* a (- t)))) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -6e-103) {
		tmp = x * -y;
	} else if (z <= 1.1e-69) {
		tmp = (z * (x * y)) / sqrt((a * -t));
	} else {
		tmp = x * y;
	}
	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 <= (-6d-103)) then
        tmp = x * -y
    else if (z <= 1.1d-69) then
        tmp = (z * (x * y)) / sqrt((a * -t))
    else
        tmp = x * y
    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 <= -6e-103) {
		tmp = x * -y;
	} else if (z <= 1.1e-69) {
		tmp = (z * (x * y)) / Math.sqrt((a * -t));
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -6e-103:
		tmp = x * -y
	elif z <= 1.1e-69:
		tmp = (z * (x * y)) / math.sqrt((a * -t))
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -6e-103)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 1.1e-69)
		tmp = Float64(Float64(z * Float64(x * y)) / sqrt(Float64(a * Float64(-t))));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -6e-103)
		tmp = x * -y;
	elseif (z <= 1.1e-69)
		tmp = (z * (x * y)) / sqrt((a * -t));
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -6e-103], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 1.1e-69], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] / N[Sqrt[N[(a * (-t)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6e-103

   1. Initial program 56.8%

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

   2. Taylor expanded in z around -inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-rgt-neg-out 91.8%

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

   4. Simplified 91.8%

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

   if -6e-103 < z < 1.1e-69

   1. Initial program 81.3%

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

   2. Taylor expanded in z around 0 73.7%

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

      1. associate-*r* 67.9%

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

      2. neg-mul-1 67.9%

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

      3. *-commutative 67.9%

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

   4. Simplified 73.7%

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

   if 1.1e-69 < z

   1. Initial program 55.9%

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

   2. Taylor expanded in z around inf 87.1%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-69}:\\ \;\;\;\;\frac{z \cdot \left(x \cdot y\right)}{\sqrt{a \cdot \left(-t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 6: 75.3% accurate, 6.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-162}:\\ \;\;\;\;\frac{\left(z \cdot y\right) \cdot \left(-x\right)}{-0.5 \cdot \left(t \cdot \frac{a}{z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.6e-103)
   (* x (- y))
   (if (<= z 2.8e-162) (/ (* (* z y) (- x)) (* -0.5 (* t (/ a z)))) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.6e-103) {
		tmp = x * -y;
	} else if (z <= 2.8e-162) {
		tmp = ((z * y) * -x) / (-0.5 * (t * (a / z)));
	} else {
		tmp = x * y;
	}
	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 <= (-1.6d-103)) then
        tmp = x * -y
    else if (z <= 2.8d-162) then
        tmp = ((z * y) * -x) / ((-0.5d0) * (t * (a / z)))
    else
        tmp = x * y
    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 <= -1.6e-103) {
		tmp = x * -y;
	} else if (z <= 2.8e-162) {
		tmp = ((z * y) * -x) / (-0.5 * (t * (a / z)));
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.6e-103:
		tmp = x * -y
	elif z <= 2.8e-162:
		tmp = ((z * y) * -x) / (-0.5 * (t * (a / z)))
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.6e-103)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 2.8e-162)
		tmp = Float64(Float64(Float64(z * y) * Float64(-x)) / Float64(-0.5 * Float64(t * Float64(a / z))));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.6e-103)
		tmp = x * -y;
	elseif (z <= 2.8e-162)
		tmp = ((z * y) * -x) / (-0.5 * (t * (a / z)));
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.6e-103], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 2.8e-162], N[(N[(N[(z * y), $MachinePrecision] * (-x)), $MachinePrecision] / N[(-0.5 * N[(t * N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.59999999999999988e-103

   1. Initial program 56.8%

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

   2. Taylor expanded in z around -inf 91.8%

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

      1. mul-1-neg 91.8%

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

      2. distribute-rgt-neg-out 91.8%

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

   4. Simplified 91.8%

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

   if -1.59999999999999988e-103 < z < 2.80000000000000022e-162

   1. Initial program 77.6%

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

      1. associate-*l* 76.1%

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

      2. *-commutative 76.1%

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

      3. associate-*l* 76.4%

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

      4. associate-*r/ 76.6%

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

      5. *-commutative 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in z around -inf 45.2%

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

      1. associate-*l/ 47.2%

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

      2. frac-2neg 47.2%

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

      3. *-commutative 47.2%

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

      4. +-commutative 47.2%

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

      5. fma-def 47.2%

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

      6. *-commutative 47.2%

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

      7. add-sqr-sqrt 30.7%

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

      8. sqrt-unprod 47.1%

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

      9. mul-1-neg 47.1%

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

      10. mul-1-neg 47.1%

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

      11. sqr-neg 47.1%

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

      12. sqrt-prod 16.6%

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

      13. add-sqr-sqrt 45.3%

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

   6. Applied egg-rr 45.3%

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

      1. associate-*r* 45.2%

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

      2. distribute-rgt-neg-in 45.2%

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

      3. *-commutative 45.2%

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

      4. neg-sub0 45.2%

         \[\leadsto \frac{\left(z \cdot y\right) \cdot \left(-x\right)}{\color{blue}{0 - \mathsf{fma}\left(0.5, \frac{t \cdot a}{z}, z\right)}} \]

      5. fma-udef 45.2%

         \[\leadsto \frac{\left(z \cdot y\right) \cdot \left(-x\right)}{0 - \color{blue}{\left(0.5 \cdot \frac{t \cdot a}{z} + z\right)}} \]

      6. associate--r+ 45.2%

         \[\leadsto \frac{\left(z \cdot y\right) \cdot \left(-x\right)}{\color{blue}{\left(0 - 0.5 \cdot \frac{t \cdot a}{z}\right) - z}} \]

      7. neg-sub0 45.2%

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

      8. distribute-lft-neg-in 45.2%

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

      9. metadata-eval 45.2%

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

      10. *-commutative 45.2%

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

   8. Simplified 45.2%

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

   9. Taylor expanded in a around inf 41.3%

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

       1. associate-/l* 45.4%

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

       2. associate-/r/ 45.5%

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

   11. Simplified 45.5%

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

   if 2.80000000000000022e-162 < z

   1. Initial program 62.4%

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

   2. Taylor expanded in z around inf 78.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-103}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-162}:\\ \;\;\;\;\frac{\left(z \cdot y\right) \cdot \left(-x\right)}{-0.5 \cdot \left(t \cdot \frac{a}{z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 7: 77.1% accurate, 6.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e-148)
   (* x (- y))
   (* 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 <= -3.5e-148) {
		tmp = x * -y;
	} 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 <= (-3.5d-148)) then
        tmp = x * -y
    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 <= -3.5e-148) {
		tmp = x * -y;
	} 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 <= -3.5e-148:
		tmp = x * -y
	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 <= -3.5e-148)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(y * Float64(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 <= -3.5e-148)
		tmp = x * -y;
	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, -3.5e-148], N[(x * (-y)), $MachinePrecision], N[(y * N[(x * N[(z / N[(z + N[(-0.5 * N[(a * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.5e-148

   1. Initial program 58.1%

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

   2. Taylor expanded in z around -inf 85.8%

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

      1. mul-1-neg 85.8%

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

      2. distribute-rgt-neg-out 85.8%

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

   4. Simplified 85.8%

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

   if -3.5e-148 < z

   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/ 64.3%

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

      2. associate-/l* 61.8%

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

      3. associate-*l/ 63.4%

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

      4. associate-*r/ 61.9%

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

      5. associate-/r/ 64.0%

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

      6. associate-*r* 66.7%

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

      7. pow2 66.7%

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

   3. Applied egg-rr 66.7%

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

   4. Taylor expanded in z around inf 68.1%

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

      1. associate-*r/ 70.2%

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

   6. Simplified 70.2%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-148}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{z}{z + -0.5 \cdot \left(a \cdot \frac{t}{z}\right)}\right)\\ \end{array} \]

Alternative 8: 75.3% accurate, 7.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-112}:\\ \;\;\;\;\frac{1}{z \cdot \frac{\frac{1}{y}}{z \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.4e-175)
   (* x (- y))
   (if (<= z 1.85e-112) (/ 1.0 (* z (/ (/ 1.0 y) (* z x)))) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.4e-175) {
		tmp = x * -y;
	} else if (z <= 1.85e-112) {
		tmp = 1.0 / (z * ((1.0 / y) / (z * x)));
	} else {
		tmp = x * y;
	}
	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 <= (-2.4d-175)) then
        tmp = x * -y
    else if (z <= 1.85d-112) then
        tmp = 1.0d0 / (z * ((1.0d0 / y) / (z * x)))
    else
        tmp = x * y
    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 <= -2.4e-175) {
		tmp = x * -y;
	} else if (z <= 1.85e-112) {
		tmp = 1.0 / (z * ((1.0 / y) / (z * x)));
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.4e-175:
		tmp = x * -y
	elif z <= 1.85e-112:
		tmp = 1.0 / (z * ((1.0 / y) / (z * x)))
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.4e-175)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 1.85e-112)
		tmp = Float64(1.0 / Float64(z * Float64(Float64(1.0 / y) / Float64(z * x))));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.4e-175)
		tmp = x * -y;
	elseif (z <= 1.85e-112)
		tmp = 1.0 / (z * ((1.0 / y) / (z * x)));
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.4e-175], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 1.85e-112], N[(1.0 / N[(z * N[(N[(1.0 / y), $MachinePrecision] / N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.4e-175

   1. Initial program 60.1%

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

   2. Taylor expanded in z around -inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-out 83.4%

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

   4. Simplified 83.4%

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

   if -2.4e-175 < z < 1.8499999999999999e-112

   1. Initial program 79.4%

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

      1. associate-*l* 78.7%

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

      2. *-commutative 78.7%

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

      3. associate-*l* 77.0%

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

      4. associate-*r/ 76.2%

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

      5. *-commutative 76.2%

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

   3. Simplified 76.2%

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

   4. Taylor expanded in z around -inf 31.3%

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

      1. associate-*r/ 31.3%

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

      2. neg-mul-1 31.3%

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

   6. Simplified 31.3%

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

      1. associate-*l/ 41.1%

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

      2. clear-num 41.1%

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

      3. add-sqr-sqrt 24.3%

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

      4. sqrt-unprod 45.5%

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

      5. sqr-neg 45.5%

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

      6. sqrt-unprod 17.1%

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

      7. add-sqr-sqrt 44.0%

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

      8. *-commutative 44.0%

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

   8. Applied egg-rr 44.0%

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

      1. associate-/r* 34.4%

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

   10. Simplified 34.4%

       \[\leadsto \color{blue}{\frac{1}{\frac{\frac{z}{y}}{z \cdot x}}} \]
   11. Step-by-step derivation

       1. div-inv 34.4%

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

       2. *-un-lft-identity 34.4%

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

       3. times-frac 44.1%

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

   12. Applied egg-rr 44.1%

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

   if 1.8499999999999999e-112 < z

   1. Initial program 59.2%

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

   2. Taylor expanded in z around inf 83.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-112}:\\ \;\;\;\;\frac{1}{z \cdot \frac{\frac{1}{y}}{z \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 9: 74.9% accurate, 9.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-141}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot x\right)}{-z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -4.2e-42)
   (* x (- y))
   (if (<= z 3e-141) (/ (* y (* z x)) (- z)) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e-42) {
		tmp = x * -y;
	} else if (z <= 3e-141) {
		tmp = (y * (z * x)) / -z;
	} else {
		tmp = x * y;
	}
	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 <= (-4.2d-42)) then
        tmp = x * -y
    else if (z <= 3d-141) then
        tmp = (y * (z * x)) / -z
    else
        tmp = x * y
    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 <= -4.2e-42) {
		tmp = x * -y;
	} else if (z <= 3e-141) {
		tmp = (y * (z * x)) / -z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e-42:
		tmp = x * -y
	elif z <= 3e-141:
		tmp = (y * (z * x)) / -z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e-42)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 3e-141)
		tmp = Float64(Float64(y * Float64(z * x)) / Float64(-z));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e-42)
		tmp = x * -y;
	elseif (z <= 3e-141)
		tmp = (y * (z * x)) / -z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4.2e-42], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 3e-141], N[(N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision] / (-z)), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000013e-42

   1. Initial program 52.3%

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

   2. Taylor expanded in z around -inf 93.8%

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

      1. mul-1-neg 93.8%

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

      2. distribute-rgt-neg-out 93.8%

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

   4. Simplified 93.8%

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

   if -4.20000000000000013e-42 < z < 2.99999999999999983e-141

   1. Initial program 81.6%

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

      1. associate-/l* 79.4%

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

      2. *-commutative 79.4%

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

      3. associate-/l* 81.6%

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

      4. associate-*l* 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in z around -inf 46.5%

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

      1. neg-mul-1 46.5%

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

   6. Simplified 46.5%

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

   if 2.99999999999999983e-141 < z

   1. Initial program 60.4%

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

   2. Taylor expanded in z around inf 80.9%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-141}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot x\right)}{-z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 10: 73.2% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-141}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.1e-194)
   (* x (- y))
   (if (<= z 3e-141) (* (* z x) (/ y z)) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.1e-194) {
		tmp = x * -y;
	} else if (z <= 3e-141) {
		tmp = (z * x) * (y / z);
	} else {
		tmp = x * y;
	}
	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 <= (-2.1d-194)) then
        tmp = x * -y
    else if (z <= 3d-141) then
        tmp = (z * x) * (y / z)
    else
        tmp = x * y
    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 <= -2.1e-194) {
		tmp = x * -y;
	} else if (z <= 3e-141) {
		tmp = (z * x) * (y / z);
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.1e-194:
		tmp = x * -y
	elif z <= 3e-141:
		tmp = (z * x) * (y / z)
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.1e-194)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 3e-141)
		tmp = Float64(Float64(z * x) * Float64(y / z));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.1e-194)
		tmp = x * -y;
	elseif (z <= 3e-141)
		tmp = (z * x) * (y / z);
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.1e-194], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 3e-141], N[(N[(z * x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e-194

   1. Initial program 60.3%

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

   2. Taylor expanded in z around -inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. distribute-rgt-neg-out 82.4%

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

   4. Simplified 82.4%

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

   if -2.1e-194 < z < 2.99999999999999983e-141

   1. Initial program 79.4%

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

      1. associate-*l* 79.8%

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

      2. *-commutative 79.8%

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

      3. associate-*l* 77.9%

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

      4. associate-*r/ 75.7%

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

      5. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in z around inf 34.6%

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

   if 2.99999999999999983e-141 < z

   1. Initial program 60.4%

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

   2. Taylor expanded in z around inf 80.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-141}:\\ \;\;\;\;\left(z \cdot x\right) \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 11: 74.0% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-111}:\\ \;\;\;\;\frac{y}{\frac{z}{z \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e-194)
   (* x (- y))
   (if (<= z 2e-111) (/ y (/ z (* z x))) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e-194) {
		tmp = x * -y;
	} else if (z <= 2e-111) {
		tmp = y / (z / (z * x));
	} else {
		tmp = x * y;
	}
	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 <= (-9.2d-194)) then
        tmp = x * -y
    else if (z <= 2d-111) then
        tmp = y / (z / (z * x))
    else
        tmp = x * y
    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 <= -9.2e-194) {
		tmp = x * -y;
	} else if (z <= 2e-111) {
		tmp = y / (z / (z * x));
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e-194:
		tmp = x * -y
	elif z <= 2e-111:
		tmp = y / (z / (z * x))
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e-194)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 2e-111)
		tmp = Float64(y / Float64(z / Float64(z * x)));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.2e-194)
		tmp = x * -y;
	elseif (z <= 2e-111)
		tmp = y / (z / (z * x));
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e-194], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 2e-111], N[(y / N[(z / N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.2000000000000001e-194

   1. Initial program 60.3%

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

   2. Taylor expanded in z around -inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. distribute-rgt-neg-out 82.4%

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

   4. Simplified 82.4%

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

   if -9.2000000000000001e-194 < z < 2.00000000000000018e-111

   1. Initial program 80.3%

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

      1. associate-*l* 79.5%

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

      2. associate-*r/ 77.3%

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

      3. *-commutative 77.3%

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

      4. associate-/l* 75.3%

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

   3. Simplified 75.3%

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

      1. associate-*r/ 78.7%

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

      2. associate-/l* 77.7%

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

      3. *-commutative 77.7%

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

      4. associate-/l* 79.3%

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

      5. pow2 79.3%

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

      6. *-commutative 79.3%

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

   5. Applied egg-rr 79.3%

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

   6. Taylor expanded in z around inf 37.9%

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

   if 2.00000000000000018e-111 < z

   1. Initial program 59.2%

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

   2. Taylor expanded in z around inf 83.2%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-111}:\\ \;\;\;\;\frac{y}{\frac{z}{z \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 12: 75.2% accurate, 10.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.5e-175)
   (* x (- y))
   (if (<= z 5.2e-113) (/ (* y (* z x)) z) (* x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.5e-175) {
		tmp = x * -y;
	} else if (z <= 5.2e-113) {
		tmp = (y * (z * x)) / z;
	} else {
		tmp = x * y;
	}
	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 <= (-9.5d-175)) then
        tmp = x * -y
    else if (z <= 5.2d-113) then
        tmp = (y * (z * x)) / z
    else
        tmp = x * y
    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 <= -9.5e-175) {
		tmp = x * -y;
	} else if (z <= 5.2e-113) {
		tmp = (y * (z * x)) / z;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.5e-175:
		tmp = x * -y
	elif z <= 5.2e-113:
		tmp = (y * (z * x)) / z
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.5e-175)
		tmp = Float64(x * Float64(-y));
	elseif (z <= 5.2e-113)
		tmp = Float64(Float64(y * Float64(z * x)) / z);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.5e-175)
		tmp = x * -y;
	elseif (z <= 5.2e-113)
		tmp = (y * (z * x)) / z;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.5e-175], N[(x * (-y)), $MachinePrecision], If[LessEqual[z, 5.2e-113], N[(N[(y * N[(z * x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.50000000000000052e-175

   1. Initial program 60.1%

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

   2. Taylor expanded in z around -inf 83.4%

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

      1. mul-1-neg 83.4%

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

      2. distribute-rgt-neg-out 83.4%

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

   4. Simplified 83.4%

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

   if -9.50000000000000052e-175 < z < 5.1999999999999998e-113

   1. Initial program 79.4%

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

      1. associate-/l* 75.0%

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

      2. *-commutative 75.0%

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

      3. associate-/l* 79.4%

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

      4. associate-*l* 77.0%

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

   3. Simplified 77.0%

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

   4. Taylor expanded in z around inf 44.0%

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

   if 5.1999999999999998e-113 < z

   1. Initial program 59.2%

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

   2. Taylor expanded in z around inf 83.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{-175}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-113}:\\ \;\;\;\;\frac{y \cdot \left(z \cdot x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 13: 72.5% accurate, 18.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.05e-303) (* x (- y)) (* x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.05e-303) {
		tmp = x * -y;
	} else {
		tmp = x * y;
	}
	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 <= (-2.05d-303)) then
        tmp = x * -y
    else
        tmp = x * y
    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 <= -2.05e-303) {
		tmp = x * -y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.05e-303:
		tmp = x * -y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.05e-303)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.05e-303)
		tmp = x * -y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.05e-303], N[(x * (-y)), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.05000000000000009e-303

   1. Initial program 61.9%

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

   2. Taylor expanded in z around -inf 76.4%

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

      1. mul-1-neg 76.4%

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

      2. distribute-rgt-neg-out 76.4%

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

   4. Simplified 76.4%

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

   if -2.05000000000000009e-303 < z

   1. Initial program 64.5%

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

   2. Taylor expanded in z around inf 68.2%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.05 \cdot 10^{-303}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 14: 43.3% accurate, 37.7× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.1%

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

2. Taylor expanded in z around inf 41.1%

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

3. Final simplification 41.1%

   \[\leadsto x \cdot y \]

Developer target: 88.5% 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 2023310 
(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)))))