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

Percentage Accurate: 92.7% → 99.0%

Time: 8.0s

Alternatives: 9

Speedup: 1.0×

• 25.3% 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: 92.7% 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: 99.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+108}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+108)))
     (+ x (/ y (/ a (- z t))))
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+108)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 1e+108)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 1e+108):
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x + (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * y)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+108))
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * y;
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 1e+108)))
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x + (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+108]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -inf.0 or 1e108 < (*.f64 y (-.f64 z t))

   1. Initial program 85.6%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 1e108

   1. Initial program 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -\infty \lor \neg \left(\left(z - t\right) \cdot y \leq 10^{+108}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+23} \lor \neg \left(t \leq 6.7 \cdot 10^{-12}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.26e+23) (not (<= t 6.7e-12)))
   (- 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 <= -1.26e+23) || !(t <= 6.7e-12)) {
		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 <= (-1.26d+23)) .or. (.not. (t <= 6.7d-12))) 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 <= -1.26e+23) || !(t <= 6.7e-12)) {
		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 <= -1.26e+23) or not (t <= 6.7e-12):
		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 <= -1.26e+23) || !(t <= 6.7e-12))
		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 <= -1.26e+23) || ~((t <= 6.7e-12)))
		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, -1.26e+23], N[Not[LessEqual[t, 6.7e-12]], $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 < -1.26000000000000004e23 or 6.7000000000000001e-12 < t

   1. Initial program 94.5%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in z around 0 87.0%

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

      1. mul-1-neg 87.0%

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

      2. associate-/l* 89.3%

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

      3. distribute-rgt-neg-in 89.3%

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

      4. distribute-neg-frac2 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in x around 0 87.0%

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

      1. associate-*l/ 81.2%

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

      2. *-commutative 81.2%

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

      3. neg-mul-1 81.2%

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

      4. sub-neg 81.2%

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

      5. associate-*r/ 87.0%

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

      6. associate-*l/ 89.3%

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

      7. *-commutative 89.3%

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

   10. Simplified 89.3%

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

   if -1.26000000000000004e23 < t < 6.7000000000000001e-12

   1. Initial program 95.7%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 89.9%

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

      1. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-/r/ 91.8%

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

   9. Applied egg-rr 91.8%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.26 \cdot 10^{+23} \lor \neg \left(t \leq 6.7 \cdot 10^{-12}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+21}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.1e+21)
   (- x (* t (/ y a)))
   (if (<= t 4.5e-13) (+ x (/ z (/ a y))) (- x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.1e+21) {
		tmp = x - (t * (y / a));
	} else if (t <= 4.5e-13) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t / (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 <= (-4.1d+21)) then
        tmp = x - (t * (y / a))
    else if (t <= 4.5d-13) then
        tmp = x + (z / (a / y))
    else
        tmp = x - (t / (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 <= -4.1e+21) {
		tmp = x - (t * (y / a));
	} else if (t <= 4.5e-13) {
		tmp = x + (z / (a / y));
	} else {
		tmp = x - (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.1e+21:
		tmp = x - (t * (y / a))
	elif t <= 4.5e-13:
		tmp = x + (z / (a / y))
	else:
		tmp = x - (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.1e+21)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (t <= 4.5e-13)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(x - Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.1e+21)
		tmp = x - (t * (y / a));
	elseif (t <= 4.5e-13)
		tmp = x + (z / (a / y));
	else
		tmp = x - (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.1e+21], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e-13], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.1e21

   1. Initial program 94.5%

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

      1. associate-/l* 80.3%

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

   3. Simplified 80.3%

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

   5. Taylor expanded in z around 0 85.2%

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

      1. mul-1-neg 85.2%

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

      2. associate-/l* 87.1%

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

      3. distribute-rgt-neg-in 87.1%

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

      4. distribute-neg-frac2 87.1%

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

   7. Simplified 87.1%

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

   8. Taylor expanded in x around 0 85.2%

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

      1. associate-*l/ 73.0%

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

      2. *-commutative 73.0%

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

      3. neg-mul-1 73.0%

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

      4. sub-neg 73.0%

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

      5. associate-*r/ 85.2%

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

      6. associate-*l/ 87.1%

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

      7. *-commutative 87.1%

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

   10. Simplified 87.1%

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

   if -4.1e21 < t < 4.5e-13

   1. Initial program 95.7%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 89.9%

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

      1. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

      1. *-commutative 90.6%

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

      2. associate-/r/ 91.8%

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

   9. Applied egg-rr 91.8%

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

   if 4.5e-13 < t

   1. Initial program 94.5%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around 0 88.3%

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

      1. mul-1-neg 88.3%

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

      2. associate-/l* 90.9%

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

      3. distribute-rgt-neg-in 90.9%

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

      4. distribute-neg-frac2 90.9%

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

   7. Simplified 90.9%

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

   8. Taylor expanded in x around 0 88.3%

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

      1. associate-*l/ 87.5%

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

      2. *-commutative 87.5%

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

      3. neg-mul-1 87.5%

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

      4. sub-neg 87.5%

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

      5. associate-*r/ 88.3%

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

      6. associate-*l/ 90.9%

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

      7. *-commutative 90.9%

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

   10. Simplified 90.9%

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

       1. clear-num 90.9%

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

       2. un-div-inv 91.0%

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

   12. Applied egg-rr 91.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+21}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-13}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+132}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.16e+132) (- x (* t (/ y a))) (+ x (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.16e+132) {
		tmp = x - (t * (y / 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 (t <= (-1.16d+132)) then
        tmp = x - (t * (y / 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 (t <= -1.16e+132) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.16e+132:
		tmp = x - (t * (y / a))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.16e+132)
		tmp = Float64(x - Float64(t * Float64(y / 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 (t <= -1.16e+132)
		tmp = x - (t * (y / a));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.16e+132], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.16000000000000004e132

   1. Initial program 94.4%

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

      1. associate-/l* 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in z around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. associate-/l* 88.5%

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

      3. distribute-rgt-neg-in 88.5%

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

      4. distribute-neg-frac2 88.5%

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

   7. Simplified 88.5%

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

   8. Taylor expanded in x around 0 85.8%

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

      1. associate-*l/ 69.3%

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

      2. *-commutative 69.3%

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

      3. neg-mul-1 69.3%

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

      4. sub-neg 69.3%

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

      5. associate-*r/ 85.8%

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

      6. associate-*l/ 88.5%

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

      7. *-commutative 88.5%

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

   10. Simplified 88.5%

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

   if -1.16000000000000004e132 < t

   1. Initial program 95.2%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.16 \cdot 10^{+132}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+132}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.15e+132) (- x (* t (/ y a))) (+ x (/ y (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.15e+132) {
		tmp = x - (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 (t <= (-1.15d+132)) then
        tmp = x - (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 (t <= -1.15e+132) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.15e+132:
		tmp = x - (t * (y / a))
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.15e+132)
		tmp = Float64(x - Float64(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 (t <= -1.15e+132)
		tmp = x - (t * (y / a));
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.15e+132], N[(x - N[(t * 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 t < -1.1500000000000001e132

   1. Initial program 94.4%

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

      1. associate-/l* 74.9%

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

   3. Simplified 74.9%

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

   5. Taylor expanded in z around 0 85.8%

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

      1. mul-1-neg 85.8%

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

      2. associate-/l* 88.5%

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

      3. distribute-rgt-neg-in 88.5%

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

      4. distribute-neg-frac2 88.5%

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

   7. Simplified 88.5%

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

   8. Taylor expanded in x around 0 85.8%

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

      1. associate-*l/ 69.3%

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

      2. *-commutative 69.3%

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

      3. neg-mul-1 69.3%

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

      4. sub-neg 69.3%

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

      5. associate-*r/ 85.8%

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

      6. associate-*l/ 88.5%

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

      7. *-commutative 88.5%

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

   10. Simplified 88.5%

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

   if -1.1500000000000001e132 < t

   1. Initial program 95.2%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

      1. clear-num 95.2%

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

      2. un-div-inv 95.2%

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

   6. Applied egg-rr 95.2%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.15 \cdot 10^{+132}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

   1. associate-/l* 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in y around 0 95.1%

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

   1. *-lft-identity 95.1%

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

   2. associate-*l/ 95.1%

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

   3. associate-*r* 97.9%

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

   4. associate-/r/ 97.8%

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

   5. associate-*l/ 98.3%

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

   6. *-lft-identity 98.3%

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

7. Simplified 98.3%

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

8. Final simplification 98.3%

   \[\leadsto x + \frac{z - t}{\frac{a}{y}} \]
9. Add Preprocessing

Alternative 7: 67.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.1%

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

   1. associate-/l* 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in z around inf 69.6%

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

   1. associate-/l* 69.5%

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

7. Simplified 69.5%

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

8. Final simplification 69.5%

   \[\leadsto x + y \cdot \frac{z}{a} \]
9. Add Preprocessing

Alternative 8: 70.4% 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 95.1%

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

   1. associate-/l* 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in z around inf 69.6%

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

   1. associate-/l* 69.5%

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

7. Simplified 69.5%

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

   1. *-commutative 69.5%

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

   2. associate-/r/ 72.0%

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

9. Applied egg-rr 72.0%

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

10. Final simplification 72.0%

    \[\leadsto x + \frac{z}{\frac{a}{y}} \]
11. Add Preprocessing

Alternative 9: 38.9% 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 95.1%

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

   1. associate-/l* 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in z around inf 69.6%

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

   1. associate-/l* 69.5%

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

7. Simplified 69.5%

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

8. Taylor expanded in x around inf 42.9%

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

9. Final simplification 42.9%

   \[\leadsto x \]
10. Add Preprocessing

Developer target: 99.1% accurate, 0.5× 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 2024055 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :alt
  (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)))