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

Percentage Accurate: 93.2% → 97.0%

Time: 14.4s

Alternatives: 12

Speedup: 0.8×

• 24.7% 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: 93.2% 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: 97.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

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 + ((-1.0d0) / ((a / y) * (1.0d0 / (z - t))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. associate-/l* 91.4%

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

3. Simplified 91.4%

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

   1. associate-*r/ 96.2%

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

   2. clear-num 96.1%

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

6. Applied egg-rr 96.1%

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

   1. associate-/r* 99.0%

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

   2. div-inv 99.0%

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

8. Applied egg-rr 99.0%

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

9. Final simplification 99.0%

   \[\leadsto x + \frac{-1}{\frac{a}{y} \cdot \frac{1}{z - t}} \]
10. Add Preprocessing

Alternative 2: 49.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{a}\\ \mathbf{if}\;a \leq -1 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t a))))
   (if (<= a -1e-32)
     x
     (if (<= a -1.25e-121)
       t_1
       (if (<= a 2.1e-62)
         (* z (/ (- y) a))
         (if (<= a 5.8e-22) t_1 (if (<= a 2.8e+49) (* y (/ z (- a))) x)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / a);
	double tmp;
	if (a <= -1e-32) {
		tmp = x;
	} else if (a <= -1.25e-121) {
		tmp = t_1;
	} else if (a <= 2.1e-62) {
		tmp = z * (-y / a);
	} else if (a <= 5.8e-22) {
		tmp = t_1;
	} else if (a <= 2.8e+49) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * (t / a)
    if (a <= (-1d-32)) then
        tmp = x
    else if (a <= (-1.25d-121)) then
        tmp = t_1
    else if (a <= 2.1d-62) then
        tmp = z * (-y / a)
    else if (a <= 5.8d-22) then
        tmp = t_1
    else if (a <= 2.8d+49) 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 t_1 = y * (t / a);
	double tmp;
	if (a <= -1e-32) {
		tmp = x;
	} else if (a <= -1.25e-121) {
		tmp = t_1;
	} else if (a <= 2.1e-62) {
		tmp = z * (-y / a);
	} else if (a <= 5.8e-22) {
		tmp = t_1;
	} else if (a <= 2.8e+49) {
		tmp = y * (z / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / a)
	tmp = 0
	if a <= -1e-32:
		tmp = x
	elif a <= -1.25e-121:
		tmp = t_1
	elif a <= 2.1e-62:
		tmp = z * (-y / a)
	elif a <= 5.8e-22:
		tmp = t_1
	elif a <= 2.8e+49:
		tmp = y * (z / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / a))
	tmp = 0.0
	if (a <= -1e-32)
		tmp = x;
	elseif (a <= -1.25e-121)
		tmp = t_1;
	elseif (a <= 2.1e-62)
		tmp = Float64(z * Float64(Float64(-y) / a));
	elseif (a <= 5.8e-22)
		tmp = t_1;
	elseif (a <= 2.8e+49)
		tmp = Float64(y * Float64(z / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / a);
	tmp = 0.0;
	if (a <= -1e-32)
		tmp = x;
	elseif (a <= -1.25e-121)
		tmp = t_1;
	elseif (a <= 2.1e-62)
		tmp = z * (-y / a);
	elseif (a <= 5.8e-22)
		tmp = t_1;
	elseif (a <= 2.8e+49)
		tmp = y * (z / -a);
	else
		tmp = x;
	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[a, -1e-32], x, If[LessEqual[a, -1.25e-121], t$95$1, If[LessEqual[a, 2.1e-62], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-22], t$95$1, If[LessEqual[a, 2.8e+49], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], x]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.00000000000000006e-32 or 2.7999999999999998e49 < a

   1. Initial program 93.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 62.3%

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

   if -1.00000000000000006e-32 < a < -1.24999999999999997e-121 or 2.0999999999999999e-62 < a < 5.8000000000000003e-22

   1. Initial program 99.8%

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

      1. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in t around inf 64.0%

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

      1. *-commutative 64.0%

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

      2. associate-/l* 64.0%

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

   7. Simplified 64.0%

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

   if -1.24999999999999997e-121 < a < 2.0999999999999999e-62

   1. Initial program 98.8%

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

      1. associate-/l* 80.5%

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

   3. Simplified 80.5%

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

   5. Taylor expanded in x around 0 87.7%

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

      1. mul-1-neg 87.7%

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

      2. distribute-frac-neg 87.7%

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

      3. *-commutative 87.7%

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

      4. distribute-lft-neg-in 87.7%

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

      5. associate-*r/ 87.7%

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

      6. *-commutative 87.7%

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

      7. neg-sub0 87.7%

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

      8. sub-neg 87.7%

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

      9. +-commutative 87.7%

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

      10. associate--r+ 87.7%

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

      11. neg-sub0 87.7%

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

      12. remove-double-neg 87.7%

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

   7. Simplified 87.7%

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

   8. Taylor expanded in t around 0 65.9%

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

      1. neg-mul-1 65.9%

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

   10. Simplified 65.9%

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

   if 5.8000000000000003e-22 < a < 2.7999999999999998e49

   1. Initial program 93.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 55.6%

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

      1. mul-1-neg 55.6%

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

      2. associate-/l* 62.4%

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

      3. distribute-rgt-neg-in 62.4%

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

      4. distribute-frac-neg2 62.4%

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

   7. Simplified 62.4%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-121}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-62}:\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-22}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;a \leq 2.8 \cdot 10^{+49}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -1 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= y -1e+40)
     t_1
     (if (<= y -7.4e-110) (* y (/ (- z) a)) (if (<= y 6.6e-21) x t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -1e+40) {
		tmp = t_1;
	} else if (y <= -7.4e-110) {
		tmp = y * (-z / a);
	} else if (y <= 6.6e-21) {
		tmp = x;
	} 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 = t * (y / a)
    if (y <= (-1d+40)) then
        tmp = t_1
    else if (y <= (-7.4d-110)) then
        tmp = y * (-z / a)
    else if (y <= 6.6d-21) then
        tmp = x
    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 = t * (y / a);
	double tmp;
	if (y <= -1e+40) {
		tmp = t_1;
	} else if (y <= -7.4e-110) {
		tmp = y * (-z / a);
	} else if (y <= 6.6e-21) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if y <= -1e+40:
		tmp = t_1
	elif y <= -7.4e-110:
		tmp = y * (-z / a)
	elif y <= 6.6e-21:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (y <= -1e+40)
		tmp = t_1;
	elseif (y <= -7.4e-110)
		tmp = Float64(y * Float64(Float64(-z) / a));
	elseif (y <= 6.6e-21)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (y <= -1e+40)
		tmp = t_1;
	elseif (y <= -7.4e-110)
		tmp = y * (-z / a);
	elseif (y <= 6.6e-21)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1e+40], t$95$1, If[LessEqual[y, -7.4e-110], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e-21], x, t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.00000000000000003e40 or 6.60000000000000018e-21 < y

   1. Initial program 93.3%

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

      1. clear-num 93.2%

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

      2. associate-/r/ 93.3%

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

   4. Applied egg-rr 93.3%

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

   5. Taylor expanded in t around inf 47.4%

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

      1. associate-/l* 55.3%

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

   7. Simplified 55.3%

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

   if -1.00000000000000003e40 < y < -7.40000000000000032e-110

   1. Initial program 99.9%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. associate-/l* 49.8%

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

      3. distribute-rgt-neg-in 49.8%

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

      4. distribute-frac-neg2 49.8%

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

   7. Simplified 49.8%

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

   if -7.40000000000000032e-110 < y < 6.60000000000000018e-21

   1. Initial program 99.0%

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

      1. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in x around inf 63.3%

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

4. Final simplification 57.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-110}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 92.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-161} \lor \neg \left(a \leq 4.4 \cdot 10^{-107}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.25e-161) (not (<= a 4.4e-107)))
   (+ x (* y (/ (- t z) a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.25e-161) || !(a <= 4.4e-107)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.25d-161)) .or. (.not. (a <= 4.4d-107))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.25e-161) || !(a <= 4.4e-107)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.25e-161) or not (a <= 4.4e-107):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.25e-161) || !(a <= 4.4e-107))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.25e-161) || ~((a <= 4.4e-107)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.25e-161], N[Not[LessEqual[a, 4.4e-107]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.2499999999999998e-161 or 4.40000000000000025e-107 < a

   1. Initial program 95.2%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   if -2.2499999999999998e-161 < a < 4.40000000000000025e-107

   1. Initial program 98.7%

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

      1. associate-/l* 77.4%

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

   3. Simplified 77.4%

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

   5. Taylor expanded in x around 0 91.0%

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

      1. mul-1-neg 91.0%

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

      2. distribute-frac-neg 91.0%

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

      3. *-commutative 91.0%

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

      4. distribute-lft-neg-in 91.0%

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

      5. associate-*r/ 92.3%

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

      6. *-commutative 92.3%

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

      7. neg-sub0 92.3%

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

      8. sub-neg 92.3%

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

      9. +-commutative 92.3%

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

      10. associate--r+ 92.3%

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

      11. neg-sub0 92.3%

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

      12. remove-double-neg 92.3%

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

   7. Simplified 92.3%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.25 \cdot 10^{-161} \lor \neg \left(a \leq 4.4 \cdot 10^{-107}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y * (z - t)) <= -math.inf:
		tmp = x - (y / (a / (z - t)))
	else:
		tmp = x + ((y * (t - z)) / a)
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 78.5%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

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

   1. Initial program 97.9%

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

4. Final simplification 98.1%

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

Alternative 6: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+43} \lor \neg \left(t \leq 5.8 \cdot 10^{+47}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.4e+43) (not (<= t 5.8e+47)))
   (+ x (* y (/ t a)))
   (- x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.4e+43) || !(t <= 5.8e+47)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - ((y * z) / 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 <= (-1.4d+43)) .or. (.not. (t <= 5.8d+47))) then
        tmp = x + (y * (t / a))
    else
        tmp = x - ((y * z) / 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 <= -1.4e+43) || !(t <= 5.8e+47)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.4e+43) or not (t <= 5.8e+47):
		tmp = x + (y * (t / a))
	else:
		tmp = x - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.4e+43) || !(t <= 5.8e+47))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.4e+43) || ~((t <= 5.8e+47)))
		tmp = x + (y * (t / a));
	else
		tmp = x - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.4e+43], N[Not[LessEqual[t, 5.8e+47]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.40000000000000009e43 or 5.79999999999999961e47 < t

   1. Initial program 96.2%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

      1. associate-*r/ 96.2%

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

      2. clear-num 96.1%

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

   6. Applied egg-rr 96.1%

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

      1. associate-/r* 99.8%

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

      2. div-inv 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in z around 0 89.2%

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

       1. cancel-sign-sub-inv 89.2%

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

       2. metadata-eval 89.2%

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

       3. *-commutative 89.2%

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

       4. *-lft-identity 89.2%

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

       5. associate-*r/ 86.6%

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

   11. Simplified 86.6%

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

   if -1.40000000000000009e43 < t < 5.79999999999999961e47

   1. Initial program 96.2%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in z around inf 88.1%

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

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{+43} \lor \neg \left(t \leq 5.8 \cdot 10^{+47}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+40} \lor \neg \left(t \leq 2.3 \cdot 10^{+50}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.2e+40) (not (<= t 2.3e+50)))
   (+ x (* y (/ t a)))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e+40) || !(t <= 2.3e+50)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y * (z / 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 <= (-5.2d+40)) .or. (.not. (t <= 2.3d+50))) then
        tmp = x + (y * (t / a))
    else
        tmp = x - (y * (z / 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 <= -5.2e+40) || !(t <= 2.3e+50)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.2e+40) or not (t <= 2.3e+50):
		tmp = x + (y * (t / a))
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.2e+40) || !(t <= 2.3e+50))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.2e+40) || ~((t <= 2.3e+50)))
		tmp = x + (y * (t / a));
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.2e+40], N[Not[LessEqual[t, 2.3e+50]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2000000000000001e40 or 2.29999999999999997e50 < t

   1. Initial program 96.2%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

      1. associate-*r/ 96.2%

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

      2. clear-num 96.1%

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

   6. Applied egg-rr 96.1%

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

      1. associate-/r* 99.8%

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

      2. div-inv 99.8%

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

   8. Applied egg-rr 99.8%

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

   9. Taylor expanded in z around 0 89.2%

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

       1. cancel-sign-sub-inv 89.2%

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

       2. metadata-eval 89.2%

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

       3. *-commutative 89.2%

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

       4. *-lft-identity 89.2%

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

       5. associate-*r/ 86.6%

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

   11. Simplified 86.6%

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

   if -5.2000000000000001e40 < t < 2.29999999999999997e50

   1. Initial program 96.2%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in z around inf 88.1%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+40} \lor \neg \left(t \leq 2.3 \cdot 10^{+50}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-117} \lor \neg \left(a \leq 5.8 \cdot 10^{+47}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -6.5e-117) (not (<= a 5.8e+47)))
   (+ x (* y (/ t a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.5e-117) || !(a <= 5.8e+47)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-6.5d-117)) .or. (.not. (a <= 5.8d+47))) then
        tmp = x + (y * (t / a))
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -6.5e-117) || !(a <= 5.8e+47)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -6.5e-117) or not (a <= 5.8e+47):
		tmp = x + (y * (t / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -6.5e-117) || !(a <= 5.8e+47))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -6.5e-117) || ~((a <= 5.8e+47)))
		tmp = x + (y * (t / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -6.5e-117], N[Not[LessEqual[a, 5.8e+47]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5000000000000001e-117 or 5.79999999999999961e47 < a

   1. Initial program 94.6%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

      1. associate-*r/ 94.6%

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

      2. clear-num 94.5%

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

   6. Applied egg-rr 94.5%

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

      1. associate-/r* 99.1%

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

      2. div-inv 99.1%

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

   8. Applied egg-rr 99.1%

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

   9. Taylor expanded in z around 0 79.8%

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

       1. cancel-sign-sub-inv 79.8%

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

       2. metadata-eval 79.8%

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

       3. *-commutative 79.8%

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

       4. *-lft-identity 79.8%

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

       5. associate-*r/ 81.5%

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

   11. Simplified 81.5%

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

   if -6.5000000000000001e-117 < a < 5.79999999999999961e47

   1. Initial program 98.3%

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

      1. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in x around 0 85.3%

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

      1. mul-1-neg 85.3%

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

      2. distribute-frac-neg 85.3%

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

      3. *-commutative 85.3%

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

      4. distribute-lft-neg-in 85.3%

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

      5. associate-*r/ 86.1%

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

      6. *-commutative 86.1%

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

      7. neg-sub0 86.1%

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

      8. sub-neg 86.1%

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

      9. +-commutative 86.1%

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

      10. associate--r+ 86.1%

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

      11. neg-sub0 86.1%

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

      12. remove-double-neg 86.1%

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

   7. Simplified 86.1%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-117} \lor \neg \left(a \leq 5.8 \cdot 10^{+47}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+91}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{+184}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.8e+91) x (if (<= a 1.26e+184) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.8e+91) {
		tmp = x;
	} else if (a <= 1.26e+184) {
		tmp = (y / a) * (t - 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 (a <= (-5.8d+91)) then
        tmp = x
    else if (a <= 1.26d+184) then
        tmp = (y / a) * (t - 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 (a <= -5.8e+91) {
		tmp = x;
	} else if (a <= 1.26e+184) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -5.8e+91:
		tmp = x
	elif a <= 1.26e+184:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.8e+91)
		tmp = x;
	elseif (a <= 1.26e+184)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -5.8e+91)
		tmp = x;
	elseif (a <= 1.26e+184)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.8e+91], x, If[LessEqual[a, 1.26e+184], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -5.80000000000000028e91 or 1.26e184 < a

   1. Initial program 91.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 75.1%

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

   if -5.80000000000000028e91 < a < 1.26e184

   1. Initial program 98.3%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

   5. Taylor expanded in x around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. distribute-frac-neg 77.5%

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

      3. *-commutative 77.5%

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

      4. distribute-lft-neg-in 77.5%

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

      5. associate-*r/ 78.5%

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

      6. *-commutative 78.5%

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

      7. neg-sub0 78.5%

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

      8. sub-neg 78.5%

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

      9. +-commutative 78.5%

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

      10. associate--r+ 78.5%

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

      11. neg-sub0 78.5%

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

      12. remove-double-neg 78.5%

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

   7. Simplified 78.5%

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

Alternative 10: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -360 \lor \neg \left(y \leq 7.5 \cdot 10^{-20}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -360.0) (not (<= y 7.5e-20))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -360.0) || !(y <= 7.5e-20)) {
		tmp = t * (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 ((y <= (-360.0d0)) .or. (.not. (y <= 7.5d-20))) then
        tmp = t * (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 ((y <= -360.0) || !(y <= 7.5e-20)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -360.0) or not (y <= 7.5e-20):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -360.0) || !(y <= 7.5e-20))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -360.0) || ~((y <= 7.5e-20)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -360.0], N[Not[LessEqual[y, 7.5e-20]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -360 or 7.49999999999999981e-20 < y

   1. Initial program 93.5%

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

      1. clear-num 93.4%

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

      2. associate-/r/ 93.5%

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

   4. Applied egg-rr 93.5%

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

   5. Taylor expanded in t around inf 46.9%

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

      1. associate-/l* 54.5%

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

   7. Simplified 54.5%

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

   if -360 < y < 7.49999999999999981e-20

   1. Initial program 99.2%

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

      1. associate-/l* 83.0%

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

   3. Simplified 83.0%

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

   5. Taylor expanded in x around inf 57.8%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -360 \lor \neg \left(y \leq 7.5 \cdot 10^{-20}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ x + \frac{1}{\frac{\frac{a}{y}}{t - z}} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (1.0d0 / ((a / y) / (t - z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. clear-num 96.1%

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

   2. associate-/r/ 96.2%

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

4. Applied egg-rr 96.2%

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

   1. associate-/r/ 96.1%

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

   2. associate-/r* 99.0%

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

6. Applied egg-rr 99.0%

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

7. Final simplification 99.0%

   \[\leadsto x + \frac{1}{\frac{\frac{a}{y}}{t - z}} \]
8. Add Preprocessing

Alternative 12: 39.4% 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 96.2%

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

   1. associate-/l* 91.4%

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

3. Simplified 91.4%

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

5. Taylor expanded in x around inf 38.6%

   \[\leadsto \color{blue}{x} \]
6. 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 2024110 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :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)))