Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E

Percentage Accurate: 92.4% → 99.1%

Time: 8.4s

Alternatives: 11

Speedup: 1.0×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.1e+40)
   (+ x (/ y (/ a (- z t))))
   (if (<= a 1.75e-38) (+ x (/ (* y (- z t)) a)) (fma y (/ (- z t) a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.1e+40) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 1.75e-38) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = fma(y, ((z - t) / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.1e+40)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= 1.75e-38)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.1e+40], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.75e-38], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.1000000000000002e40

   1. Initial program 87.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -4.1000000000000002e40 < a < 1.7500000000000001e-38

   1. Initial program 99.9%

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

   if 1.7500000000000001e-38 < a

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+40}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \end{array} \]

Alternative 2: 97.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+41} \lor \neg \left(z \leq 10^{-71}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2e+41) (not (<= z 1e-71)))
   (+ x (* (- z t) (/ y a)))
   (+ x (/ y (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2e+41) || !(z <= 1e-71)) {
		tmp = x + ((z - t) * (y / a));
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	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+41)) .or. (.not. (z <= 1d-71))) then
        tmp = x + ((z - t) * (y / a))
    else
        tmp = x + (y / (a / (z - t)))
    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+41) || !(z <= 1e-71)) {
		tmp = x + ((z - t) * (y / a));
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2e+41) or not (z <= 1e-71):
		tmp = x + ((z - t) * (y / a))
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2e+41) || !(z <= 1e-71))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2e+41) || ~((z <= 1e-71)))
		tmp = x + ((z - t) * (y / a));
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2e+41], N[Not[LessEqual[z, 1e-71]], $MachinePrecision]], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.00000000000000001e41 or 9.9999999999999992e-72 < z

   1. Initial program 92.0%

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

      1. associate-*l/ 98.4%

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

   3. Simplified 98.4%

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

   if -2.00000000000000001e41 < z < 9.9999999999999992e-72

   1. Initial program 97.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+41} \lor \neg \left(z \leq 10^{-71}\right):\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 3: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+39} \lor \neg \left(a \leq 8.5 \cdot 10^{-25}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.2e+39) (not (<= a 8.5e-25)))
   (+ x (/ y (/ a (- z t))))
   (+ x (/ (* y (- z t)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e+39) || !(a <= 8.5e-25)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + ((y * (z - t)) / a);
	}
	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 ((a <= (-2.2d+39)) .or. (.not. (a <= 8.5d-25))) then
        tmp = x + (y / (a / (z - t)))
    else
        tmp = x + ((y * (z - t)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.2e+39) || !(a <= 8.5e-25)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + ((y * (z - t)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.2e+39) or not (a <= 8.5e-25):
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x + ((y * (z - t)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.2e+39) || !(a <= 8.5e-25))
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.2e+39) || ~((a <= 8.5e-25)))
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x + ((y * (z - t)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.2e+39], N[Not[LessEqual[a, 8.5e-25]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2000000000000001e39 or 8.49999999999999981e-25 < a

   1. Initial program 88.7%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -2.2000000000000001e39 < a < 8.49999999999999981e-25

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+39} \lor \neg \left(a \leq 8.5 \cdot 10^{-25}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]

Alternative 4: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.1e+39)
   (+ x (/ y (/ a (- z t))))
   (if (<= a 8e-38) (+ x (/ (* y (- z t)) a)) (+ x (* y (/ (- z t) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.1e+39) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 8e-38) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	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 (a <= (-4.1d+39)) then
        tmp = x + (y / (a / (z - t)))
    else if (a <= 8d-38) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y * ((z - t) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.1e+39) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 8e-38) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.1e+39:
		tmp = x + (y / (a / (z - t)))
	elif a <= 8e-38:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.1e+39)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= 8e-38)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.1e+39)
		tmp = x + (y / (a / (z - t)));
	elseif (a <= 8e-38)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.1e+39], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8e-38], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.10000000000000004e39

   1. Initial program 87.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -4.10000000000000004e39 < a < 7.9999999999999997e-38

   1. Initial program 99.9%

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

   if 7.9999999999999997e-38 < a

   1. Initial program 90.0%

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

      1. +-commutative 90.0%

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

      2. associate-*r/ 99.9%

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

      3. fma-def 99.9%

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

   3. Simplified 99.9%

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

      1. fma-udef 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.1 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 5: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+135} \lor \neg \left(t \leq 2.45 \cdot 10^{-42}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.2e+135) (not (<= t 2.45e-42)))
   (- x (* t (/ y a)))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.2e+135) || !(t <= 2.45e-42)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / 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 ((t <= (-4.2d+135)) .or. (.not. (t <= 2.45d-42))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (z / (a / 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 ((t <= -4.2e+135) || !(t <= 2.45e-42)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.2e+135) or not (t <= 2.45e-42):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.2e+135) || !(t <= 2.45e-42))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.2e+135) || ~((t <= 2.45e-42)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.2e+135], N[Not[LessEqual[t, 2.45e-42]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.20000000000000019e135 or 2.45e-42 < t

   1. Initial program 95.7%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in z around 0 84.7%

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

      1. mul-1-neg 84.7%

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

      2. associate-*l/ 87.0%

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

      3. distribute-rgt-neg-out 87.0%

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

      4. +-commutative 87.0%

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

      5. *-commutative 87.0%

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

      6. distribute-lft-neg-out 87.0%

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

      7. unsub-neg 87.0%

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

   6. Simplified 87.0%

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

   if -4.20000000000000019e135 < t < 2.45e-42

   1. Initial program 93.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

      1. add-cube-cbrt 92.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{a}{z - t}} \]

      2. div-inv 92.9%

         \[\leadsto x + \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{a \cdot \frac{1}{z - t}}} \]

      3. times-frac 95.9%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{a} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}}} \]

      4. pow2 95.9%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{a} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}} \]

   5. Applied egg-rr 95.9%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{a} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}}} \]

   6. Taylor expanded in z around inf 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+135} \lor \neg \left(t \leq 2.45 \cdot 10^{-42}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+135} \lor \neg \left(t \leq 1.6 \cdot 10^{-42}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.1e+135) (not (<= t 1.6e-42)))
   (- x (/ t (/ a y)))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.1e+135) || !(t <= 1.6e-42)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (z / (a / 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 ((t <= (-2.1d+135)) .or. (.not. (t <= 1.6d-42))) then
        tmp = x - (t / (a / y))
    else
        tmp = x + (z / (a / 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 ((t <= -2.1e+135) || !(t <= 1.6e-42)) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.1e+135) or not (t <= 1.6e-42):
		tmp = x - (t / (a / y))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.1e+135) || !(t <= 1.6e-42))
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.1e+135) || ~((t <= 1.6e-42)))
		tmp = x - (t / (a / y));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.1e+135], N[Not[LessEqual[t, 1.6e-42]], $MachinePrecision]], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.1000000000000001e135 or 1.60000000000000012e-42 < t

   1. Initial program 95.7%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in z around 0 83.4%

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

      1. associate-*r/ 83.4%

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

      2. neg-mul-1 83.4%

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

   6. Simplified 83.4%

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

   7. Taylor expanded in x around 0 84.7%

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

      1. +-commutative 84.7%

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

      2. mul-1-neg 84.7%

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

      3. associate-*l/ 87.0%

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

      4. sub-neg 87.0%

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

      5. associate-*l/ 84.7%

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

      6. *-commutative 84.7%

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

      7. associate-/l* 87.1%

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

   9. Simplified 87.1%

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

   if -2.1000000000000001e135 < t < 1.60000000000000012e-42

   1. Initial program 93.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

      1. add-cube-cbrt 92.9%

         \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{a}{z - t}} \]

      2. div-inv 92.9%

         \[\leadsto x + \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{a \cdot \frac{1}{z - t}}} \]

      3. times-frac 95.9%

         \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{a} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}}} \]

      4. pow2 95.9%

         \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{a} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}} \]

   5. Applied egg-rr 95.9%

      \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{a} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}}} \]

   6. Taylor expanded in z around inf 84.3%

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

      1. *-commutative 84.3%

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

      2. associate-/l* 89.4%

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

   8. Simplified 89.4%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+135} \lor \neg \left(t \leq 1.6 \cdot 10^{-42}\right):\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]

Alternative 7: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. associate-*l/ 95.6%

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

3. Simplified 95.6%

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

4. Final simplification 95.6%

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

Alternative 8: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a}{z}} \end{array} \]

FPCore

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

C

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

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 / (a / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. associate-/l* 92.6%

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

3. Simplified 92.6%

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

4. Taylor expanded in z around inf 70.1%

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

5. Final simplification 70.1%

   \[\leadsto x + \frac{y}{\frac{a}{z}} \]

Alternative 9: 71.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x + \frac{z}{\frac{a}{y}} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x + (z / (a / 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 + (z / (a / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. associate-/l* 92.6%

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

3. Simplified 92.6%

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

   1. add-cube-cbrt 92.2%

      \[\leadsto x + \frac{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}{\frac{a}{z - t}} \]

   2. div-inv 92.2%

      \[\leadsto x + \frac{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}{\color{blue}{a \cdot \frac{1}{z - t}}} \]

   3. times-frac 95.7%

      \[\leadsto x + \color{blue}{\frac{\sqrt[3]{y} \cdot \sqrt[3]{y}}{a} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}}} \]

   4. pow2 95.7%

      \[\leadsto x + \frac{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}{a} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}} \]

5. Applied egg-rr 95.7%

   \[\leadsto x + \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2}}{a} \cdot \frac{\sqrt[3]{y}}{\frac{1}{z - t}}} \]

6. Taylor expanded in z around inf 70.7%

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

   1. *-commutative 70.7%

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

   2. associate-/l* 74.5%

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

8. Simplified 74.5%

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

9. Final simplification 74.5%

   \[\leadsto x + \frac{z}{\frac{a}{y}} \]

Alternative 10: 71.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.5%

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

   1. associate-*l/ 95.6%

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

3. Simplified 95.6%

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

4. Taylor expanded in t around 0 70.7%

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

   1. associate-*l/ 74.7%

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

   2. *-commutative 74.7%

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

6. Simplified 74.7%

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

7. Final simplification 74.7%

   \[\leadsto x + z \cdot \frac{y}{a} \]

Alternative 11: 39.0% accurate, 9.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return 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 = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 94.5%

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

   1. associate-*l/ 95.6%

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

3. Simplified 95.6%

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

4. Taylor expanded in x around inf 42.1%

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

5. Final simplification 42.1%

   \[\leadsto x \]

Developer target: 99.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (+ x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (+ x (/ (* y (- z t)) a))
       (+ x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x + (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x + (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x + Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x + (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x + N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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