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

Percentage Accurate: 92.7% → 96.8%

Time: 11.5s

Alternatives: 12

Speedup: 1.0×

• 24.6% of points produce a very large (infinite) output. You may want to add a precondition.

• Rival profile vector overflowed, profile may not be complete

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: 96.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \left(z - t\right) \cdot \left(\frac{1}{a} \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* (- z t) (* (/ 1.0 a) y))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((z - t) * ((1.0 / 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) * ((1.0d0 / a) * y))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((z - t) * ((1.0 / a) * y));
}

Python

def code(x, y, z, t, a):
	return x + ((z - t) * ((1.0 / a) * y))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(z - t) * Float64(Float64(1.0 / a) * y)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((z - t) * ((1.0 / a) * y));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(z - t), $MachinePrecision] * N[(N[(1.0 / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.6%

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

   1. associate-*r/ 92.7%

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

   2. *-commutative 92.7%

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

   3. div-inv 92.6%

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

   4. associate-*l* 97.7%

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

4. Applied egg-rr 97.7%

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

Alternative 2: 50.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+16}:\\ \;\;\;\;\frac{y}{\frac{a}{-t}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.55e+16)
   (/ y (/ a (- t)))
   (if (<= y 6.2e-38) x (if (<= y 3.8e+135) (* y (/ z a)) (* (- y) (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.55e+16) {
		tmp = y / (a / -t);
	} else if (y <= 6.2e-38) {
		tmp = x;
	} else if (y <= 3.8e+135) {
		tmp = y * (z / a);
	} else {
		tmp = -y * (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 (y <= (-2.55d+16)) then
        tmp = y / (a / -t)
    else if (y <= 6.2d-38) then
        tmp = x
    else if (y <= 3.8d+135) then
        tmp = y * (z / a)
    else
        tmp = -y * (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 (y <= -2.55e+16) {
		tmp = y / (a / -t);
	} else if (y <= 6.2e-38) {
		tmp = x;
	} else if (y <= 3.8e+135) {
		tmp = y * (z / a);
	} else {
		tmp = -y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.55e+16:
		tmp = y / (a / -t)
	elif y <= 6.2e-38:
		tmp = x
	elif y <= 3.8e+135:
		tmp = y * (z / a)
	else:
		tmp = -y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.55e+16)
		tmp = Float64(y / Float64(a / Float64(-t)));
	elseif (y <= 6.2e-38)
		tmp = x;
	elseif (y <= 3.8e+135)
		tmp = Float64(y * Float64(z / a));
	else
		tmp = Float64(Float64(-y) * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.55e+16)
		tmp = y / (a / -t);
	elseif (y <= 6.2e-38)
		tmp = x;
	elseif (y <= 3.8e+135)
		tmp = y * (z / a);
	else
		tmp = -y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.55e+16], N[(y / N[(a / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-38], x, If[LessEqual[y, 3.8e+135], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[((-y) * N[(t / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.55e16

   1. Initial program 81.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around 0 81.0%

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

      1. associate-*l/ 99.7%

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

      2. associate-/r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 81.0%

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

      1. +-commutative 81.0%

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

   10. Simplified 81.0%

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

   11. Taylor expanded in t around inf 49.3%

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

       1. mul-1-neg 49.3%

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

       2. associate-*r/ 62.6%

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

       3. *-commutative 62.6%

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

       4. associate-/r/ 59.2%

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

       5. distribute-frac-neg 59.2%

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

   13. Simplified 59.2%

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

   if -2.55e16 < y < 6.19999999999999966e-38

   1. Initial program 99.2%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around inf 58.8%

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

   if 6.19999999999999966e-38 < y < 3.8000000000000001e135

   1. Initial program 94.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around 0 94.4%

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

      1. associate-*l/ 99.8%

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

      2. associate-/r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 94.4%

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

      1. +-commutative 94.4%

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

   10. Simplified 94.4%

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

   11. Taylor expanded in z around inf 42.5%

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

       1. associate-*r/ 48.0%

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

   13. Simplified 48.0%

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

   if 3.8000000000000001e135 < y

   1. Initial program 88.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 88.7%

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

      1. associate-*l/ 96.2%

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

      2. associate-/r/ 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 88.7%

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

      1. +-commutative 88.7%

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

   10. Simplified 88.7%

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

   11. Taylor expanded in t around inf 61.8%

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

       1. mul-1-neg 61.8%

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

       2. associate-*r/ 72.8%

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

       3. *-commutative 72.8%

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

       4. associate-/r/ 72.9%

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

       5. distribute-frac-neg 72.9%

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

   13. Simplified 72.9%

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

       1. distribute-frac-neg 72.9%

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

       2. div-inv 72.9%

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

       3. clear-num 73.0%

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

   15. Applied egg-rr 73.0%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{+16}:\\ \;\;\;\;\frac{y}{\frac{a}{-t}}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-y\right) \cdot \frac{t}{a}\\ \mathbf{if}\;y \leq -2.05 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- y) (/ t a))))
   (if (<= y -2.05e+16)
     t_1
     (if (<= y 5.2e-40) x (if (<= y 3.9e+135) (* y (/ z a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y * (t / a);
	double tmp;
	if (y <= -2.05e+16) {
		tmp = t_1;
	} else if (y <= 5.2e-40) {
		tmp = x;
	} else if (y <= 3.9e+135) {
		tmp = y * (z / a);
	} else {
		tmp = 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 = -y * (t / a)
    if (y <= (-2.05d+16)) then
        tmp = t_1
    else if (y <= 5.2d-40) then
        tmp = x
    else if (y <= 3.9d+135) then
        tmp = y * (z / a)
    else
        tmp = 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 = -y * (t / a);
	double tmp;
	if (y <= -2.05e+16) {
		tmp = t_1;
	} else if (y <= 5.2e-40) {
		tmp = x;
	} else if (y <= 3.9e+135) {
		tmp = y * (z / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y * (t / a)
	tmp = 0
	if y <= -2.05e+16:
		tmp = t_1
	elif y <= 5.2e-40:
		tmp = x
	elif y <= 3.9e+135:
		tmp = y * (z / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) * Float64(t / a))
	tmp = 0.0
	if (y <= -2.05e+16)
		tmp = t_1;
	elseif (y <= 5.2e-40)
		tmp = x;
	elseif (y <= 3.9e+135)
		tmp = Float64(y * Float64(z / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y * (t / a);
	tmp = 0.0;
	if (y <= -2.05e+16)
		tmp = t_1;
	elseif (y <= 5.2e-40)
		tmp = x;
	elseif (y <= 3.9e+135)
		tmp = y * (z / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.05e+16], t$95$1, If[LessEqual[y, 5.2e-40], x, If[LessEqual[y, 3.9e+135], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.05e16 or 3.90000000000000032e135 < y

   1. Initial program 83.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around 0 83.4%

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

      1. associate-*l/ 98.6%

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

      2. associate-/r/ 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 83.4%

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

      1. +-commutative 83.4%

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

   10. Simplified 83.4%

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

   11. Taylor expanded in t around inf 53.2%

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

       1. mul-1-neg 53.2%

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

       2. associate-*r/ 65.8%

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

       3. *-commutative 65.8%

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

       4. associate-/r/ 63.5%

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

       5. distribute-frac-neg 63.5%

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

   13. Simplified 63.5%

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

       1. distribute-frac-neg 63.5%

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

       2. div-inv 63.5%

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

       3. clear-num 63.5%

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

   15. Applied egg-rr 63.5%

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

   if -2.05e16 < y < 5.2000000000000003e-40

   1. Initial program 99.2%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around inf 58.8%

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

   if 5.2000000000000003e-40 < y < 3.90000000000000032e135

   1. Initial program 94.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around 0 94.4%

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

      1. associate-*l/ 99.8%

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

      2. associate-/r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around 0 94.4%

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

      1. +-commutative 94.4%

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

   10. Simplified 94.4%

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

   11. Taylor expanded in z around inf 42.5%

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

       1. associate-*r/ 48.0%

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

   13. Simplified 48.0%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{+16}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+135}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-121} \lor \neg \left(a \leq 7.8 \cdot 10^{-283}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.8e-121) (not (<= a 7.8e-283)))
   (+ x (* y (/ (- z t) a)))
   (/ (* (- z t) y) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.8e-121) || !(a <= 7.8e-283)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = ((z - t) * y) / 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 <= (-1.8d-121)) .or. (.not. (a <= 7.8d-283))) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = ((z - t) * y) / 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 <= -1.8e-121) || !(a <= 7.8e-283)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = ((z - t) * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.8e-121) or not (a <= 7.8e-283):
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = ((z - t) * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.8e-121) || !(a <= 7.8e-283))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(Float64(Float64(z - t) * y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.8e-121) || ~((a <= 7.8e-283)))
		tmp = x + (y * ((z - t) / a));
	else
		tmp = ((z - t) * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.8e-121], N[Not[LessEqual[a, 7.8e-283]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.79999999999999992e-121 or 7.8000000000000004e-283 < a

   1. Initial program 92.1%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   if -1.79999999999999992e-121 < a < 7.8000000000000004e-283

   1. Initial program 99.9%

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

      1. associate-/l* 71.8%

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

   3. Simplified 71.8%

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

   5. Taylor expanded in y around 0 99.9%

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

      1. associate-*l/ 99.9%

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

      2. associate-/r/ 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in x around 0 99.9%

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

      1. +-commutative 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in y around -inf 93.7%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{-121} \lor \neg \left(a \leq 7.8 \cdot 10^{-283}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+63} \lor \neg \left(z \leq 1.5 \cdot 10^{+109}\right):\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.8e+63) (not (<= z 1.5e+109)))
   (+ x (/ (* z y) a))
   (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.8e+63) || !(z <= 1.5e+109)) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = x - (t * (y / 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 ((z <= (-2.8d+63)) .or. (.not. (z <= 1.5d+109))) then
        tmp = x + ((z * y) / a)
    else
        tmp = x - (t * (y / 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 ((z <= -2.8e+63) || !(z <= 1.5e+109)) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.8e+63) or not (z <= 1.5e+109):
		tmp = x + ((z * y) / a)
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.8e+63) || !(z <= 1.5e+109))
		tmp = Float64(x + Float64(Float64(z * y) / a));
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.8e+63) || ~((z <= 1.5e+109)))
		tmp = x + ((z * y) / a);
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.8e+63], N[Not[LessEqual[z, 1.5e+109]], $MachinePrecision]], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.79999999999999987e63 or 1.50000000000000008e109 < z

   1. Initial program 94.7%

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

      1. associate-/l* 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in z around inf 86.4%

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

   if -2.79999999999999987e63 < z < 1.50000000000000008e109

   1. Initial program 93.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 86.0%

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

      1. +-commutative 86.0%

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

      2. associate-*r/ 86.0%

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

      3. mul-1-neg 86.0%

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

      4. distribute-lft-neg-out 86.0%

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

      5. *-commutative 86.0%

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

   7. Simplified 86.0%

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

   8. Taylor expanded in y around 0 86.0%

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

      1. associate-*l/ 88.2%

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

      2. *-commutative 88.2%

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

      3. neg-mul-1 88.2%

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

      4. sub-neg 88.2%

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

      5. associate-*r/ 86.0%

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

      6. associate-*l/ 91.6%

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

      7. *-commutative 91.6%

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

   10. Simplified 91.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+63} \lor \neg \left(z \leq 1.5 \cdot 10^{+109}\right):\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+16} \lor \neg \left(y \leq 2.6 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3e+16) (not (<= y 2.6e-32)))
   (* y (/ (- z t) a))
   (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e+16) || !(y <= 2.6e-32)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + ((z * y) / 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 ((y <= (-3d+16)) .or. (.not. (y <= 2.6d-32))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x + ((z * y) / 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 ((y <= -3e+16) || !(y <= 2.6e-32)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3e+16) or not (y <= 2.6e-32):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3e+16) || !(y <= 2.6e-32))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3e+16) || ~((y <= 2.6e-32)))
		tmp = y * ((z - t) / a);
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3e+16], N[Not[LessEqual[y, 2.6e-32]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e16 or 2.5999999999999997e-32 < y

   1. Initial program 86.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around 0 86.7%

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

      1. associate-*l/ 99.0%

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

      2. associate-/r/ 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 86.7%

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

      1. +-commutative 86.7%

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

   10. Simplified 86.7%

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

   11. Taylor expanded in y around inf 81.0%

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

       1. div-sub 83.7%

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

   13. Simplified 83.7%

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

   if -3e16 < y < 2.5999999999999997e-32

   1. Initial program 99.2%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in z around inf 78.1%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+16} \lor \neg \left(y \leq 2.6 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-16} \lor \neg \left(y \leq 1.52 \cdot 10^{-80}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.9e-16) (not (<= y 1.52e-80))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e-16) || !(y <= 1.52e-80)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = 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 ((y <= (-2.9d-16)) .or. (.not. (y <= 1.52d-80))) then
        tmp = y * ((z - t) / a)
    else
        tmp = 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 ((y <= -2.9e-16) || !(y <= 1.52e-80)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.9e-16) or not (y <= 1.52e-80):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.9e-16) || !(y <= 1.52e-80))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.9e-16) || ~((y <= 1.52e-80)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.9e-16], N[Not[LessEqual[y, 1.52e-80]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.8999999999999998e-16 or 1.5199999999999999e-80 < y

   1. Initial program 88.4%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 88.4%

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

      1. associate-*l/ 99.1%

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

      2. associate-/r/ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in x around 0 88.4%

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

      1. +-commutative 88.4%

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

   10. Simplified 88.4%

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

   11. Taylor expanded in y around inf 77.7%

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

       1. div-sub 79.9%

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

   13. Simplified 79.9%

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

   if -2.8999999999999998e-16 < y < 1.5199999999999999e-80

   1. Initial program 99.2%

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

      1. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around inf 61.5%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-16} \lor \neg \left(y \leq 1.52 \cdot 10^{-80}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-151}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.2e-7) x (if (<= a 1.25e-151) (/ (* z y) a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.2e-7) {
		tmp = x;
	} else if (a <= 1.25e-151) {
		tmp = (z * y) / a;
	} else {
		tmp = 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 (a <= (-5.2d-7)) then
        tmp = x
    else if (a <= 1.25d-151) then
        tmp = (z * y) / a
    else
        tmp = 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 (a <= -5.2e-7) {
		tmp = x;
	} else if (a <= 1.25e-151) {
		tmp = (z * y) / a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.2e-7:
		tmp = x
	elif a <= 1.25e-151:
		tmp = (z * y) / a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.2e-7)
		tmp = x;
	elseif (a <= 1.25e-151)
		tmp = Float64(Float64(z * y) / a);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.2e-7)
		tmp = x;
	elseif (a <= 1.25e-151)
		tmp = (z * y) / a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.2e-7], x, If[LessEqual[a, 1.25e-151], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.19999999999999998e-7 or 1.25000000000000001e-151 < a

   1. Initial program 89.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 56.5%

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

   if -5.19999999999999998e-7 < a < 1.25000000000000001e-151

   1. Initial program 99.8%

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

      1. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in y around 0 99.8%

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

      1. associate-*l/ 99.9%

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

      2. associate-/r/ 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in x around 0 99.8%

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

      1. +-commutative 99.8%

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

   10. Simplified 99.8%

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

   11. Taylor expanded in z around inf 49.3%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-151}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-87}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.5e-23) x (if (<= x 2.9e-87) (/ y (/ a z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.5e-23) {
		tmp = x;
	} else if (x <= 2.9e-87) {
		tmp = y / (a / z);
	} else {
		tmp = 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 (x <= (-4.5d-23)) then
        tmp = x
    else if (x <= 2.9d-87) then
        tmp = y / (a / z)
    else
        tmp = 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 (x <= -4.5e-23) {
		tmp = x;
	} else if (x <= 2.9e-87) {
		tmp = y / (a / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.5e-23:
		tmp = x
	elif x <= 2.9e-87:
		tmp = y / (a / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.5e-23)
		tmp = x;
	elseif (x <= 2.9e-87)
		tmp = Float64(y / Float64(a / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.5e-23)
		tmp = x;
	elseif (x <= 2.9e-87)
		tmp = y / (a / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.5e-23], x, If[LessEqual[x, 2.9e-87], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.49999999999999975e-23 or 2.8999999999999999e-87 < x

   1. Initial program 95.1%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in x around inf 57.9%

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

   if -4.49999999999999975e-23 < x < 2.8999999999999999e-87

   1. Initial program 91.3%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 91.3%

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

      1. associate-*l/ 94.2%

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

      2. associate-/r/ 92.6%

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

   7. Simplified 92.6%

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

   8. Taylor expanded in x around 0 91.3%

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

      1. +-commutative 91.3%

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

   10. Simplified 91.3%

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

   11. Taylor expanded in z around inf 43.1%

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

       1. associate-*r/ 41.9%

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

   13. Simplified 41.9%

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

       1. clear-num 41.8%

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

       2. un-div-inv 42.7%

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

   15. Applied egg-rr 42.7%

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

Alternative 10: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{-151}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8e-7) x (if (<= a 1.25e-151) (* y (/ z a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8e-7) {
		tmp = x;
	} else if (a <= 1.25e-151) {
		tmp = y * (z / a);
	} else {
		tmp = 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 (a <= (-8d-7)) then
        tmp = x
    else if (a <= 1.25d-151) then
        tmp = y * (z / a)
    else
        tmp = 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 (a <= -8e-7) {
		tmp = x;
	} else if (a <= 1.25e-151) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8e-7:
		tmp = x
	elif a <= 1.25e-151:
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8e-7)
		tmp = x;
	elseif (a <= 1.25e-151)
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -8e-7)
		tmp = x;
	elseif (a <= 1.25e-151)
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8e-7], x, If[LessEqual[a, 1.25e-151], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -7.9999999999999996e-7 or 1.25000000000000001e-151 < a

   1. Initial program 89.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 56.5%

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

   if -7.9999999999999996e-7 < a < 1.25000000000000001e-151

   1. Initial program 99.8%

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

      1. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in y around 0 99.8%

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

      1. associate-*l/ 99.9%

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

      2. associate-/r/ 82.9%

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

   7. Simplified 82.9%

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

   8. Taylor expanded in x around 0 99.8%

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

      1. +-commutative 99.8%

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

   10. Simplified 99.8%

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

   11. Taylor expanded in z around inf 49.3%

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

       1. associate-*r/ 44.0%

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

   13. Simplified 44.0%

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

Alternative 11: 96.8% 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 93.6%

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

   1. *-commutative 93.6%

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

   2. associate-/l* 97.7%

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

4. Applied egg-rr 97.7%

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

Alternative 12: 38.8% 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 93.6%

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

   1. associate-/l* 92.7%

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

3. Simplified 92.7%

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

5. Taylor expanded in x around inf 40.5%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.2% 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 2024156 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t)))))))

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