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

Percentage Accurate: 93.0% → 97.1%

Time: 10.1s

Alternatives: 14

Speedup: 1.0×

• 24.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.0% 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: 97.1% 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 91.8%

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

   1. associate-/l* 95.8%

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

3. Simplified 95.8%

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

5. Taylor expanded in y around 0 91.8%

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

   1. associate-*l/ 97.3%

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

   2. *-commutative 97.3%

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

7. Simplified 97.3%

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

Alternative 2: 49.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{-a}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-195}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a)))))
   (if (<= z -3.1e+79)
     (* z (/ y a))
     (if (<= z -1.7e-67)
       t_1
       (if (<= z -1.7e-183)
         x
         (if (<= z -1.55e-195)
           (* (- y) (/ t a))
           (if (<= z 4.9e-108) x (if (<= z 6e-39) t_1 (/ z (/ a y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -a);
	double tmp;
	if (z <= -3.1e+79) {
		tmp = z * (y / a);
	} else if (z <= -1.7e-67) {
		tmp = t_1;
	} else if (z <= -1.7e-183) {
		tmp = x;
	} else if (z <= -1.55e-195) {
		tmp = -y * (t / a);
	} else if (z <= 4.9e-108) {
		tmp = x;
	} else if (z <= 6e-39) {
		tmp = t_1;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / -a)
    if (z <= (-3.1d+79)) then
        tmp = z * (y / a)
    else if (z <= (-1.7d-67)) then
        tmp = t_1
    else if (z <= (-1.7d-183)) then
        tmp = x
    else if (z <= (-1.55d-195)) then
        tmp = -y * (t / a)
    else if (z <= 4.9d-108) then
        tmp = x
    else if (z <= 6d-39) then
        tmp = t_1
    else
        tmp = z / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -a);
	double tmp;
	if (z <= -3.1e+79) {
		tmp = z * (y / a);
	} else if (z <= -1.7e-67) {
		tmp = t_1;
	} else if (z <= -1.7e-183) {
		tmp = x;
	} else if (z <= -1.55e-195) {
		tmp = -y * (t / a);
	} else if (z <= 4.9e-108) {
		tmp = x;
	} else if (z <= 6e-39) {
		tmp = t_1;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / -a)
	tmp = 0
	if z <= -3.1e+79:
		tmp = z * (y / a)
	elif z <= -1.7e-67:
		tmp = t_1
	elif z <= -1.7e-183:
		tmp = x
	elif z <= -1.55e-195:
		tmp = -y * (t / a)
	elif z <= 4.9e-108:
		tmp = x
	elif z <= 6e-39:
		tmp = t_1
	else:
		tmp = z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(-a)))
	tmp = 0.0
	if (z <= -3.1e+79)
		tmp = Float64(z * Float64(y / a));
	elseif (z <= -1.7e-67)
		tmp = t_1;
	elseif (z <= -1.7e-183)
		tmp = x;
	elseif (z <= -1.55e-195)
		tmp = Float64(Float64(-y) * Float64(t / a));
	elseif (z <= 4.9e-108)
		tmp = x;
	elseif (z <= 6e-39)
		tmp = t_1;
	else
		tmp = Float64(z / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / -a);
	tmp = 0.0;
	if (z <= -3.1e+79)
		tmp = z * (y / a);
	elseif (z <= -1.7e-67)
		tmp = t_1;
	elseif (z <= -1.7e-183)
		tmp = x;
	elseif (z <= -1.55e-195)
		tmp = -y * (t / a);
	elseif (z <= 4.9e-108)
		tmp = x;
	elseif (z <= 6e-39)
		tmp = t_1;
	else
		tmp = z / (a / y);
	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[z, -3.1e+79], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.7e-67], t$95$1, If[LessEqual[z, -1.7e-183], x, If[LessEqual[z, -1.55e-195], N[((-y) * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.9e-108], x, If[LessEqual[z, 6e-39], t$95$1, N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.0999999999999999e79

   1. Initial program 89.0%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 84.5%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in z around inf 84.1%

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

      1. +-commutative 84.1%

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

   10. Simplified 84.1%

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

   11. Taylor expanded in y around inf 73.6%

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

   if -3.0999999999999999e79 < z < -1.70000000000000005e-67 or 4.8999999999999998e-108 < z < 6.00000000000000055e-39

   1. Initial program 87.5%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around 0 69.5%

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

      1. mul-1-neg 69.5%

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

      2. unsub-neg 69.5%

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

      3. *-commutative 69.5%

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

      4. associate-/l* 77.7%

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

   7. Simplified 77.7%

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

   8. Taylor expanded in x around 0 41.5%

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

      1. mul-1-neg 41.5%

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

      2. associate-*r/ 54.4%

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

      3. distribute-rgt-neg-out 54.4%

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

      4. distribute-neg-frac2 54.4%

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

   10. Simplified 54.4%

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

   if -1.70000000000000005e-67 < z < -1.70000000000000007e-183 or -1.55000000000000001e-195 < z < 4.8999999999999998e-108

   1. Initial program 95.8%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 59.7%

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

   if -1.70000000000000007e-183 < z < -1.55000000000000001e-195

   1. Initial program 84.2%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. unsub-neg 84.2%

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

      3. *-commutative 84.2%

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

      4. associate-/l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 52.0%

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

      1. mul-1-neg 52.0%

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

      2. associate-*l/ 67.8%

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

      3. *-commutative 67.8%

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

      4. distribute-rgt-neg-in 67.8%

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

      5. distribute-frac-neg2 67.8%

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

   10. Simplified 67.8%

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

   if 6.00000000000000055e-39 < z

   1. Initial program 91.9%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-/l* 87.1%

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

   7. Simplified 87.1%

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

   8. Taylor expanded in z around inf 91.6%

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

      1. +-commutative 91.6%

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

   10. Simplified 91.6%

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

   11. Taylor expanded in y around inf 63.2%

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

       1. clear-num 63.2%

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

       2. un-div-inv 63.3%

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

   13. Applied egg-rr 63.3%

       \[\leadsto \color{blue}{\frac{z}{\frac{a}{y}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-67}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-195}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{-a}\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-67}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-183}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{-108}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a)))))
   (if (<= z -3.4e+79)
     (* z (/ y a))
     (if (<= z -1.45e-67)
       t_1
       (if (<= z -1.2e-183)
         x
         (if (<= z -2.5e-201)
           t_1
           (if (<= z 2.95e-108) x (if (<= z 6e-40) t_1 (/ z (/ a y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -a);
	double tmp;
	if (z <= -3.4e+79) {
		tmp = z * (y / a);
	} else if (z <= -1.45e-67) {
		tmp = t_1;
	} else if (z <= -1.2e-183) {
		tmp = x;
	} else if (z <= -2.5e-201) {
		tmp = t_1;
	} else if (z <= 2.95e-108) {
		tmp = x;
	} else if (z <= 6e-40) {
		tmp = t_1;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / -a)
    if (z <= (-3.4d+79)) then
        tmp = z * (y / a)
    else if (z <= (-1.45d-67)) then
        tmp = t_1
    else if (z <= (-1.2d-183)) then
        tmp = x
    else if (z <= (-2.5d-201)) then
        tmp = t_1
    else if (z <= 2.95d-108) then
        tmp = x
    else if (z <= 6d-40) then
        tmp = t_1
    else
        tmp = z / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -a);
	double tmp;
	if (z <= -3.4e+79) {
		tmp = z * (y / a);
	} else if (z <= -1.45e-67) {
		tmp = t_1;
	} else if (z <= -1.2e-183) {
		tmp = x;
	} else if (z <= -2.5e-201) {
		tmp = t_1;
	} else if (z <= 2.95e-108) {
		tmp = x;
	} else if (z <= 6e-40) {
		tmp = t_1;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / -a)
	tmp = 0
	if z <= -3.4e+79:
		tmp = z * (y / a)
	elif z <= -1.45e-67:
		tmp = t_1
	elif z <= -1.2e-183:
		tmp = x
	elif z <= -2.5e-201:
		tmp = t_1
	elif z <= 2.95e-108:
		tmp = x
	elif z <= 6e-40:
		tmp = t_1
	else:
		tmp = z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(-a)))
	tmp = 0.0
	if (z <= -3.4e+79)
		tmp = Float64(z * Float64(y / a));
	elseif (z <= -1.45e-67)
		tmp = t_1;
	elseif (z <= -1.2e-183)
		tmp = x;
	elseif (z <= -2.5e-201)
		tmp = t_1;
	elseif (z <= 2.95e-108)
		tmp = x;
	elseif (z <= 6e-40)
		tmp = t_1;
	else
		tmp = Float64(z / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / -a);
	tmp = 0.0;
	if (z <= -3.4e+79)
		tmp = z * (y / a);
	elseif (z <= -1.45e-67)
		tmp = t_1;
	elseif (z <= -1.2e-183)
		tmp = x;
	elseif (z <= -2.5e-201)
		tmp = t_1;
	elseif (z <= 2.95e-108)
		tmp = x;
	elseif (z <= 6e-40)
		tmp = t_1;
	else
		tmp = z / (a / y);
	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[z, -3.4e+79], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.45e-67], t$95$1, If[LessEqual[z, -1.2e-183], x, If[LessEqual[z, -2.5e-201], t$95$1, If[LessEqual[z, 2.95e-108], x, If[LessEqual[z, 6e-40], t$95$1, N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.40000000000000032e79

   1. Initial program 89.0%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 84.5%

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

   7. Simplified 84.5%

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

   8. Taylor expanded in z around inf 84.1%

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

      1. +-commutative 84.1%

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

   10. Simplified 84.1%

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

   11. Taylor expanded in y around inf 73.6%

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

   if -3.40000000000000032e79 < z < -1.45000000000000002e-67 or -1.19999999999999996e-183 < z < -2.5e-201 or 2.94999999999999982e-108 < z < 6.00000000000000039e-40

   1. Initial program 87.1%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in z around 0 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

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

      3. *-commutative 71.2%

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

      4. associate-/l* 80.4%

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

   7. Simplified 80.4%

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

   8. Taylor expanded in x around 0 42.7%

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

      1. mul-1-neg 42.7%

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

      2. associate-*r/ 56.0%

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

      3. distribute-rgt-neg-out 56.0%

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

      4. distribute-neg-frac2 56.0%

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

   10. Simplified 56.0%

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

   if -1.45000000000000002e-67 < z < -1.19999999999999996e-183 or -2.5e-201 < z < 2.94999999999999982e-108

   1. Initial program 95.8%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 59.7%

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

   if 6.00000000000000039e-40 < z

   1. Initial program 91.9%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-/l* 87.1%

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

   7. Simplified 87.1%

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

   8. Taylor expanded in z around inf 91.6%

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

      1. +-commutative 91.6%

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

   10. Simplified 91.6%

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

   11. Taylor expanded in y around inf 63.2%

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

       1. clear-num 63.2%

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

       2. un-div-inv 63.3%

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

   13. Applied egg-rr 63.3%

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

Alternative 4: 73.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot y}{a}\\ t_2 := t \cdot \frac{y}{-a}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+47}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z y) a))) (t_2 (* t (/ y (- a)))))
   (if (<= t -3.7e+221)
     t_2
     (if (<= t -5e+147)
       t_1
       (if (<= t -1.2e+123) (/ (* y (- t)) a) (if (<= t 2.8e+47) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z * y) / a);
	double t_2 = t * (y / -a);
	double tmp;
	if (t <= -3.7e+221) {
		tmp = t_2;
	} else if (t <= -5e+147) {
		tmp = t_1;
	} else if (t <= -1.2e+123) {
		tmp = (y * -t) / a;
	} else if (t <= 2.8e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x + ((z * y) / a)
    t_2 = t * (y / -a)
    if (t <= (-3.7d+221)) then
        tmp = t_2
    else if (t <= (-5d+147)) then
        tmp = t_1
    else if (t <= (-1.2d+123)) then
        tmp = (y * -t) / a
    else if (t <= 2.8d+47) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z * y) / a);
	double t_2 = t * (y / -a);
	double tmp;
	if (t <= -3.7e+221) {
		tmp = t_2;
	} else if (t <= -5e+147) {
		tmp = t_1;
	} else if (t <= -1.2e+123) {
		tmp = (y * -t) / a;
	} else if (t <= 2.8e+47) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z * y) / a)
	t_2 = t * (y / -a)
	tmp = 0
	if t <= -3.7e+221:
		tmp = t_2
	elif t <= -5e+147:
		tmp = t_1
	elif t <= -1.2e+123:
		tmp = (y * -t) / a
	elif t <= 2.8e+47:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z * y) / a))
	t_2 = Float64(t * Float64(y / Float64(-a)))
	tmp = 0.0
	if (t <= -3.7e+221)
		tmp = t_2;
	elseif (t <= -5e+147)
		tmp = t_1;
	elseif (t <= -1.2e+123)
		tmp = Float64(Float64(y * Float64(-t)) / a);
	elseif (t <= 2.8e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z * y) / a);
	t_2 = t * (y / -a);
	tmp = 0.0;
	if (t <= -3.7e+221)
		tmp = t_2;
	elseif (t <= -5e+147)
		tmp = t_1;
	elseif (t <= -1.2e+123)
		tmp = (y * -t) / a;
	elseif (t <= 2.8e+47)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+221], t$95$2, If[LessEqual[t, -5e+147], t$95$1, If[LessEqual[t, -1.2e+123], N[(N[(y * (-t)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 2.8e+47], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.70000000000000001e221 or 2.79999999999999988e47 < t

   1. Initial program 83.7%

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

      1. associate-/l* 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in z around 0 80.5%

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

      1. mul-1-neg 80.5%

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

      2. unsub-neg 80.5%

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

      3. *-commutative 80.5%

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

      4. associate-/l* 88.8%

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

   7. Simplified 88.8%

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

   8. Taylor expanded in x around 0 59.3%

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

      1. mul-1-neg 59.3%

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

      2. associate-*r/ 67.4%

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

      3. distribute-rgt-neg-out 67.4%

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

      4. distribute-neg-frac2 67.4%

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

   10. Simplified 67.4%

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

   if -3.70000000000000001e221 < t < -5.0000000000000002e147 or -1.19999999999999994e123 < t < 2.79999999999999988e47

   1. Initial program 94.8%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 83.1%

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

   if -5.0000000000000002e147 < t < -1.19999999999999994e123

   1. Initial program 99.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. unsub-neg 75.3%

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

      3. *-commutative 75.3%

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

      4. associate-/l* 75.3%

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

   7. Simplified 75.3%

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

   8. Taylor expanded in x around 0 75.3%

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

      1. mul-1-neg 75.3%

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

      2. associate-*r/ 75.3%

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

      3. distribute-rgt-neg-out 75.3%

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

      4. distribute-neg-frac2 75.3%

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

   10. Simplified 75.3%

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

       1. *-commutative 75.3%

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

       2. distribute-frac-neg2 75.3%

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

       3. distribute-frac-neg 75.3%

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

       4. associate-*l/ 75.3%

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

   12. Applied egg-rr 75.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+221}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+147}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+123}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+162} \lor \neg \left(z \leq 6.8 \cdot 10^{-53} \lor \neg \left(z \leq 720\right) \land z \leq 2.6 \cdot 10^{+37}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.4e+162)
         (not (or (<= z 6.8e-53) (and (not (<= z 720.0)) (<= z 2.6e+37)))))
   (* z (/ y a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.4e+162) || !((z <= 6.8e-53) || (!(z <= 720.0) && (z <= 2.6e+37)))) {
		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 ((z <= (-9.4d+162)) .or. (.not. (z <= 6.8d-53) .or. (.not. (z <= 720.0d0)) .and. (z <= 2.6d+37))) 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 ((z <= -9.4e+162) || !((z <= 6.8e-53) || (!(z <= 720.0) && (z <= 2.6e+37)))) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.4e+162) or not ((z <= 6.8e-53) or (not (z <= 720.0) and (z <= 2.6e+37))):
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.4e+162) || !((z <= 6.8e-53) || (!(z <= 720.0) && (z <= 2.6e+37))))
		tmp = Float64(z * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.4e+162) || ~(((z <= 6.8e-53) || (~((z <= 720.0)) && (z <= 2.6e+37)))))
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.4e+162], N[Not[Or[LessEqual[z, 6.8e-53], And[N[Not[LessEqual[z, 720.0]], $MachinePrecision], LessEqual[z, 2.6e+37]]]], $MachinePrecision]], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -9.40000000000000006e162 or 6.8e-53 < z < 720 or 2.5999999999999999e37 < z

   1. Initial program 88.0%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in t around 0 80.9%

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

      1. +-commutative 80.9%

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

      2. associate-/l* 85.8%

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

   7. Simplified 85.8%

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

   8. Taylor expanded in z around inf 89.7%

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

      1. +-commutative 89.7%

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

   10. Simplified 89.7%

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

   11. Taylor expanded in y around inf 73.7%

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

   if -9.40000000000000006e162 < z < 6.8e-53 or 720 < z < 2.5999999999999999e37

   1. Initial program 94.0%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in x around inf 50.2%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+162} \lor \neg \left(z \leq 6.8 \cdot 10^{-53} \lor \neg \left(z \leq 720\right) \land z \leq 2.6 \cdot 10^{+37}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 48.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.4e+162)
   (* z (/ y a))
   (if (<= z 2.4e-113)
     x
     (if (<= z 1.6e-5) (/ (* z y) a) (if (<= z 8.8e+36) x (/ z (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.4e+162) {
		tmp = z * (y / a);
	} else if (z <= 2.4e-113) {
		tmp = x;
	} else if (z <= 1.6e-5) {
		tmp = (z * y) / a;
	} else if (z <= 8.8e+36) {
		tmp = x;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.4d+162)) then
        tmp = z * (y / a)
    else if (z <= 2.4d-113) then
        tmp = x
    else if (z <= 1.6d-5) then
        tmp = (z * y) / a
    else if (z <= 8.8d+36) then
        tmp = x
    else
        tmp = z / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.4e+162) {
		tmp = z * (y / a);
	} else if (z <= 2.4e-113) {
		tmp = x;
	} else if (z <= 1.6e-5) {
		tmp = (z * y) / a;
	} else if (z <= 8.8e+36) {
		tmp = x;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.4e+162:
		tmp = z * (y / a)
	elif z <= 2.4e-113:
		tmp = x
	elif z <= 1.6e-5:
		tmp = (z * y) / a
	elif z <= 8.8e+36:
		tmp = x
	else:
		tmp = z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.4e+162)
		tmp = Float64(z * Float64(y / a));
	elseif (z <= 2.4e-113)
		tmp = x;
	elseif (z <= 1.6e-5)
		tmp = Float64(Float64(z * y) / a);
	elseif (z <= 8.8e+36)
		tmp = x;
	else
		tmp = Float64(z / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.4e+162)
		tmp = z * (y / a);
	elseif (z <= 2.4e-113)
		tmp = x;
	elseif (z <= 1.6e-5)
		tmp = (z * y) / a;
	elseif (z <= 8.8e+36)
		tmp = x;
	else
		tmp = z / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.4e+162], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-113], x, If[LessEqual[z, 1.6e-5], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[z, 8.8e+36], x, N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.40000000000000006e162

   1. Initial program 84.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. associate-/l* 89.1%

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

   7. Simplified 89.1%

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

   8. Taylor expanded in z around inf 91.9%

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

      1. +-commutative 91.9%

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

   10. Simplified 91.9%

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

   11. Taylor expanded in y around inf 89.1%

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

   if -9.40000000000000006e162 < z < 2.40000000000000012e-113 or 1.59999999999999993e-5 < z < 8.80000000000000002e36

   1. Initial program 95.3%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around inf 53.8%

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

   if 2.40000000000000012e-113 < z < 1.59999999999999993e-5

   1. Initial program 87.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in z around inf 39.8%

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

      1. +-commutative 39.8%

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

   10. Simplified 39.8%

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

   11. Taylor expanded in y around inf 26.4%

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

       1. associate-*r/ 32.9%

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

   13. Applied egg-rr 32.9%

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

   if 8.80000000000000002e36 < z

   1. Initial program 89.9%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-/l* 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in z around inf 93.6%

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

      1. +-commutative 93.6%

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

   10. Simplified 93.6%

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

   11. Taylor expanded in y around inf 68.1%

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

       1. clear-num 68.1%

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

       2. un-div-inv 68.2%

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

   13. Applied egg-rr 68.2%

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

Alternative 7: 48.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.4e+162)
   (* z (/ y a))
   (if (<= z 2.4e-113)
     x
     (if (<= z 1.8e-6) (* y (/ z a)) (if (<= z 9.6e+27) x (/ z (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.4e+162) {
		tmp = z * (y / a);
	} else if (z <= 2.4e-113) {
		tmp = x;
	} else if (z <= 1.8e-6) {
		tmp = y * (z / a);
	} else if (z <= 9.6e+27) {
		tmp = x;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.4d+162)) then
        tmp = z * (y / a)
    else if (z <= 2.4d-113) then
        tmp = x
    else if (z <= 1.8d-6) then
        tmp = y * (z / a)
    else if (z <= 9.6d+27) then
        tmp = x
    else
        tmp = z / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.4e+162) {
		tmp = z * (y / a);
	} else if (z <= 2.4e-113) {
		tmp = x;
	} else if (z <= 1.8e-6) {
		tmp = y * (z / a);
	} else if (z <= 9.6e+27) {
		tmp = x;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.4e+162:
		tmp = z * (y / a)
	elif z <= 2.4e-113:
		tmp = x
	elif z <= 1.8e-6:
		tmp = y * (z / a)
	elif z <= 9.6e+27:
		tmp = x
	else:
		tmp = z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.4e+162)
		tmp = Float64(z * Float64(y / a));
	elseif (z <= 2.4e-113)
		tmp = x;
	elseif (z <= 1.8e-6)
		tmp = Float64(y * Float64(z / a));
	elseif (z <= 9.6e+27)
		tmp = x;
	else
		tmp = Float64(z / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.4e+162)
		tmp = z * (y / a);
	elseif (z <= 2.4e-113)
		tmp = x;
	elseif (z <= 1.8e-6)
		tmp = y * (z / a);
	elseif (z <= 9.6e+27)
		tmp = x;
	else
		tmp = z / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.4e+162], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-113], x, If[LessEqual[z, 1.8e-6], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e+27], x, N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.40000000000000006e162

   1. Initial program 84.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around 0 81.4%

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

      1. +-commutative 81.4%

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

      2. associate-/l* 89.1%

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

   7. Simplified 89.1%

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

   8. Taylor expanded in z around inf 91.9%

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

      1. +-commutative 91.9%

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

   10. Simplified 91.9%

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

   11. Taylor expanded in y around inf 89.1%

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

   if -9.40000000000000006e162 < z < 2.40000000000000012e-113 or 1.79999999999999992e-6 < z < 9.59999999999999991e27

   1. Initial program 95.3%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around inf 53.8%

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

   if 2.40000000000000012e-113 < z < 1.79999999999999992e-6

   1. Initial program 87.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in z around inf 39.8%

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

      1. +-commutative 39.8%

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

   10. Simplified 39.8%

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

   11. Taylor expanded in y around inf 26.4%

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

       1. clear-num 26.3%

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

       2. un-div-inv 26.4%

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

   13. Applied egg-rr 26.4%

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

       1. associate-/r/ 32.8%

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

   15. Applied egg-rr 32.8%

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

   if 9.59999999999999991e27 < z

   1. Initial program 89.9%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in t around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-/l* 87.9%

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

   7. Simplified 87.9%

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

   8. Taylor expanded in z around inf 93.6%

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

      1. +-commutative 93.6%

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

   10. Simplified 93.6%

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

   11. Taylor expanded in y around inf 68.1%

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

       1. clear-num 68.1%

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

       2. un-div-inv 68.2%

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

   13. Applied egg-rr 68.2%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-6}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -9.4 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y a))))
   (if (<= z -9.4e+162)
     t_1
     (if (<= z 2.4e-113)
       x
       (if (<= z 4.2e-7) (* y (/ z a)) (if (<= z 4e+34) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / a);
	double tmp;
	if (z <= -9.4e+162) {
		tmp = t_1;
	} else if (z <= 2.4e-113) {
		tmp = x;
	} else if (z <= 4.2e-7) {
		tmp = y * (z / a);
	} else if (z <= 4e+34) {
		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 = z * (y / a)
    if (z <= (-9.4d+162)) then
        tmp = t_1
    else if (z <= 2.4d-113) then
        tmp = x
    else if (z <= 4.2d-7) then
        tmp = y * (z / a)
    else if (z <= 4d+34) 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 = z * (y / a);
	double tmp;
	if (z <= -9.4e+162) {
		tmp = t_1;
	} else if (z <= 2.4e-113) {
		tmp = x;
	} else if (z <= 4.2e-7) {
		tmp = y * (z / a);
	} else if (z <= 4e+34) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / a)
	tmp = 0
	if z <= -9.4e+162:
		tmp = t_1
	elif z <= 2.4e-113:
		tmp = x
	elif z <= 4.2e-7:
		tmp = y * (z / a)
	elif z <= 4e+34:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / a))
	tmp = 0.0
	if (z <= -9.4e+162)
		tmp = t_1;
	elseif (z <= 2.4e-113)
		tmp = x;
	elseif (z <= 4.2e-7)
		tmp = Float64(y * Float64(z / a));
	elseif (z <= 4e+34)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / a);
	tmp = 0.0;
	if (z <= -9.4e+162)
		tmp = t_1;
	elseif (z <= 2.4e-113)
		tmp = x;
	elseif (z <= 4.2e-7)
		tmp = y * (z / a);
	elseif (z <= 4e+34)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.4e+162], t$95$1, If[LessEqual[z, 2.4e-113], x, If[LessEqual[z, 4.2e-7], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e+34], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.40000000000000006e162 or 3.99999999999999978e34 < z

   1. Initial program 87.4%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in t around 0 82.8%

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

      1. +-commutative 82.8%

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

      2. associate-/l* 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in z around inf 92.9%

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

      1. +-commutative 92.9%

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

   10. Simplified 92.9%

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

   11. Taylor expanded in y around inf 76.9%

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

   if -9.40000000000000006e162 < z < 2.40000000000000012e-113 or 4.2e-7 < z < 3.99999999999999978e34

   1. Initial program 95.3%

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

      1. associate-/l* 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in x around inf 53.8%

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

   if 2.40000000000000012e-113 < z < 4.2e-7

   1. Initial program 87.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around 0 49.6%

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

      1. +-commutative 49.6%

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

      2. associate-/l* 49.6%

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

   7. Simplified 49.6%

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

   8. Taylor expanded in z around inf 39.8%

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

      1. +-commutative 39.8%

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

   10. Simplified 39.8%

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

   11. Taylor expanded in y around inf 26.4%

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

       1. clear-num 26.3%

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

       2. un-div-inv 26.4%

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

   13. Applied egg-rr 26.4%

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

       1. associate-/r/ 32.8%

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

   15. Applied egg-rr 32.8%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+162}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-113}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-7}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-39}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{y}{a} + \frac{x}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2.65e+81)
   (+ x (/ y (/ a z)))
   (if (<= z 2e-39) (- x (/ t (/ a y))) (* z (+ (/ y a) (/ x z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.65e+81) {
		tmp = x + (y / (a / z));
	} else if (z <= 2e-39) {
		tmp = x - (t / (a / y));
	} else {
		tmp = z * ((y / a) + (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2.65d+81)) then
        tmp = x + (y / (a / z))
    else if (z <= 2d-39) then
        tmp = x - (t / (a / y))
    else
        tmp = z * ((y / a) + (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2.65e+81) {
		tmp = x + (y / (a / z));
	} else if (z <= 2e-39) {
		tmp = x - (t / (a / y));
	} else {
		tmp = z * ((y / a) + (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2.65e+81:
		tmp = x + (y / (a / z))
	elif z <= 2e-39:
		tmp = x - (t / (a / y))
	else:
		tmp = z * ((y / a) + (x / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2.65e+81)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (z <= 2e-39)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = Float64(z * Float64(Float64(y / a) + Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2.65e+81)
		tmp = x + (y / (a / z));
	elseif (z <= 2e-39)
		tmp = x - (t / (a / y));
	else
		tmp = z * ((y / a) + (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2.65e+81], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2e-39], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y / a), $MachinePrecision] + N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.65000000000000014e81

   1. Initial program 88.8%

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

      1. associate-/l* 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in t around 0 78.9%

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

      1. +-commutative 78.9%

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

      2. associate-/l* 84.3%

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

   7. Simplified 84.3%

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

      1. clear-num 84.2%

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

      2. un-div-inv 85.8%

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

   9. Applied egg-rr 85.8%

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

   if -2.65000000000000014e81 < z < 1.99999999999999986e-39

   1. Initial program 92.8%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around 0 92.8%

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

      1. associate-*l/ 96.7%

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

      2. *-commutative 96.7%

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

   7. Simplified 96.7%

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

   8. Taylor expanded in z around 0 82.5%

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

      1. associate-*l/ 87.1%

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

      2. *-commutative 87.1%

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

      3. neg-mul-1 87.1%

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

      4. sub-neg 87.1%

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

      5. *-commutative 87.1%

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

      6. associate-*l/ 82.5%

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

      7. associate-*r/ 89.8%

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

   10. Simplified 89.8%

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

       1. associate-*r/ 82.5%

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

       2. clear-num 82.5%

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

       3. associate-/l/ 89.9%

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

       4. clear-num 89.9%

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

   12. Applied egg-rr 89.9%

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

   if 1.99999999999999986e-39 < z

   1. Initial program 91.9%

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

      1. associate-/l* 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in t around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-/l* 87.1%

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

   7. Simplified 87.1%

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

   8. Taylor expanded in z around inf 91.6%

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

      1. +-commutative 91.6%

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

   10. Simplified 91.6%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+81}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-39}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\frac{y}{a} + \frac{x}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 72.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+263} \lor \neg \left(t \leq 2 \cdot 10^{+85}\right):\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.2e+263) (not (<= t 2e+85)))
   (* t (/ y (- a)))
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e+263) || !(t <= 2e+85)) {
		tmp = t * (y / -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+263)) .or. (.not. (t <= 2d+85))) then
        tmp = t * (y / -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+263) || !(t <= 2e+85)) {
		tmp = t * (y / -a);
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.2e+263) or not (t <= 2e+85):
		tmp = t * (y / -a)
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.2e+263) || !(t <= 2e+85))
		tmp = Float64(t * Float64(y / Float64(-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+263) || ~((t <= 2e+85)))
		tmp = t * (y / -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+263], N[Not[LessEqual[t, 2e+85]], $MachinePrecision]], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.2000000000000004e263 or 2e85 < t

   1. Initial program 81.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. unsub-neg 77.5%

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

      3. *-commutative 77.5%

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

      4. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

   8. Taylor expanded in x around 0 59.6%

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

      1. mul-1-neg 59.6%

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

      2. associate-*r/ 71.3%

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

      3. distribute-rgt-neg-out 71.3%

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

      4. distribute-neg-frac2 71.3%

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

   10. Simplified 71.3%

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

   if -5.2000000000000004e263 < t < 2e85

   1. Initial program 94.7%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in t around 0 79.3%

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

      1. +-commutative 79.3%

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

      2. associate-/l* 81.1%

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

   7. Simplified 81.1%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+263} \lor \neg \left(t \leq 2 \cdot 10^{+85}\right):\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 82.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-56}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.4e+79)
   (+ x (/ y (/ a z)))
   (if (<= z 3.2e-56) (- x (/ t (/ a y))) (+ x (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.4e+79) {
		tmp = x + (y / (a / z));
	} else if (z <= 3.2e-56) {
		tmp = x - (t / (a / y));
	} 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 (z <= (-3.4d+79)) then
        tmp = x + (y / (a / z))
    else if (z <= 3.2d-56) then
        tmp = x - (t / (a / y))
    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 (z <= -3.4e+79) {
		tmp = x + (y / (a / z));
	} else if (z <= 3.2e-56) {
		tmp = x - (t / (a / y));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.4e+79:
		tmp = x + (y / (a / z))
	elif z <= 3.2e-56:
		tmp = x - (t / (a / y))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.4e+79)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (z <= 3.2e-56)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	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 (z <= -3.4e+79)
		tmp = x + (y / (a / z));
	elseif (z <= 3.2e-56)
		tmp = x - (t / (a / y));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.4e+79], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e-56], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.40000000000000032e79

   1. Initial program 89.0%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 84.5%

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

   7. Simplified 84.5%

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

      1. clear-num 84.4%

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

      2. un-div-inv 86.1%

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

   9. Applied egg-rr 86.1%

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

   if -3.40000000000000032e79 < z < 3.19999999999999986e-56

   1. Initial program 93.0%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around 0 93.0%

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

      1. associate-*l/ 97.2%

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

      2. *-commutative 97.2%

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

   7. Simplified 97.2%

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

   8. Taylor expanded in z around 0 83.8%

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

      1. associate-*l/ 87.9%

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

      2. *-commutative 87.9%

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

      3. neg-mul-1 87.9%

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

      4. sub-neg 87.9%

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

      5. *-commutative 87.9%

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

      6. associate-*l/ 83.8%

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

      7. associate-*r/ 91.2%

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

   10. Simplified 91.2%

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

       1. associate-*r/ 83.8%

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

       2. clear-num 83.8%

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

       3. associate-/l/ 91.2%

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

       4. clear-num 91.2%

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

   12. Applied egg-rr 91.2%

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

   if 3.19999999999999986e-56 < z

   1. Initial program 91.4%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in t around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. associate-/l* 82.6%

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

   7. Simplified 82.6%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-56}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 82.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-55}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e+79)
   (+ x (/ y (/ a z)))
   (if (<= z 5e-55) (- x (* t (/ y a))) (+ x (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e+79) {
		tmp = x + (y / (a / z));
	} else if (z <= 5e-55) {
		tmp = x - (t * (y / 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 (z <= (-3.5d+79)) then
        tmp = x + (y / (a / z))
    else if (z <= 5d-55) then
        tmp = x - (t * (y / 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 (z <= -3.5e+79) {
		tmp = x + (y / (a / z));
	} else if (z <= 5e-55) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e+79:
		tmp = x + (y / (a / z))
	elif z <= 5e-55:
		tmp = x - (t * (y / a))
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e+79)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (z <= 5e-55)
		tmp = Float64(x - Float64(t * Float64(y / 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 (z <= -3.5e+79)
		tmp = x + (y / (a / z));
	elseif (z <= 5e-55)
		tmp = x - (t * (y / a));
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e+79], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-55], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.4999999999999998e79

   1. Initial program 89.0%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 84.5%

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

   7. Simplified 84.5%

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

      1. clear-num 84.4%

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

      2. un-div-inv 86.1%

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

   9. Applied egg-rr 86.1%

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

   if -3.4999999999999998e79 < z < 5.0000000000000002e-55

   1. Initial program 93.0%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in y around 0 93.0%

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

      1. associate-*l/ 97.2%

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

      2. *-commutative 97.2%

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

   7. Simplified 97.2%

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

   8. Taylor expanded in z around 0 83.8%

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

      1. associate-*l/ 87.9%

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

      2. *-commutative 87.9%

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

      3. neg-mul-1 87.9%

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

      4. sub-neg 87.9%

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

      5. *-commutative 87.9%

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

      6. associate-*l/ 83.8%

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

      7. associate-*r/ 91.2%

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

   10. Simplified 91.2%

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

   if 5.0000000000000002e-55 < z

   1. Initial program 91.4%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in t around 0 79.6%

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

      1. +-commutative 79.6%

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

      2. associate-/l* 82.6%

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

   7. Simplified 82.6%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+79}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-55}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 93.4% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.8%

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

   1. associate-/l* 95.8%

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

3. Simplified 95.8%

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

Alternative 14: 39.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-/l* 95.8%

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

3. Simplified 95.8%

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

5. Taylor expanded in x around inf 38.7%

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

Developer target: 99.3% 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 2024107 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

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

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