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

Percentage Accurate: 93.1% → 97.0%

Time: 9.7s

Alternatives: 12

Speedup: 1.0×

• 25.8% 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: 93.1% 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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

   1. associate-/l* 94.3%

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

3. Simplified 94.3%

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

5. Taylor expanded in y around 0 93.3%

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

   1. associate-*l/ 98.0%

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

   2. *-commutative 98.0%

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

7. Simplified 98.0%

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

8. Final simplification 98.0%

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

Alternative 2: 47.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{t}{-a}\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+162}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{+65} \lor \neg \left(y \leq 1.55 \cdot 10^{+130}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ t (- a)))))
   (if (<= y -4.5e+162)
     (/ (* z y) a)
     (if (<= y -2.1e+53)
       t_1
       (if (<= y -2.6e-36)
         (* y (/ z a))
         (if (<= y 2.7e-45)
           x
           (if (or (<= y 7.1e+65) (not (<= y 1.55e+130)))
             t_1
             (/ y (/ a z)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / -a);
	double tmp;
	if (y <= -4.5e+162) {
		tmp = (z * y) / a;
	} else if (y <= -2.1e+53) {
		tmp = t_1;
	} else if (y <= -2.6e-36) {
		tmp = y * (z / a);
	} else if (y <= 2.7e-45) {
		tmp = x;
	} else if ((y <= 7.1e+65) || !(y <= 1.55e+130)) {
		tmp = t_1;
	} else {
		tmp = y / (a / 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) :: t_1
    real(8) :: tmp
    t_1 = y * (t / -a)
    if (y <= (-4.5d+162)) then
        tmp = (z * y) / a
    else if (y <= (-2.1d+53)) then
        tmp = t_1
    else if (y <= (-2.6d-36)) then
        tmp = y * (z / a)
    else if (y <= 2.7d-45) then
        tmp = x
    else if ((y <= 7.1d+65) .or. (.not. (y <= 1.55d+130))) then
        tmp = t_1
    else
        tmp = y / (a / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (t / -a);
	double tmp;
	if (y <= -4.5e+162) {
		tmp = (z * y) / a;
	} else if (y <= -2.1e+53) {
		tmp = t_1;
	} else if (y <= -2.6e-36) {
		tmp = y * (z / a);
	} else if (y <= 2.7e-45) {
		tmp = x;
	} else if ((y <= 7.1e+65) || !(y <= 1.55e+130)) {
		tmp = t_1;
	} else {
		tmp = y / (a / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (t / -a)
	tmp = 0
	if y <= -4.5e+162:
		tmp = (z * y) / a
	elif y <= -2.1e+53:
		tmp = t_1
	elif y <= -2.6e-36:
		tmp = y * (z / a)
	elif y <= 2.7e-45:
		tmp = x
	elif (y <= 7.1e+65) or not (y <= 1.55e+130):
		tmp = t_1
	else:
		tmp = y / (a / z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(t / Float64(-a)))
	tmp = 0.0
	if (y <= -4.5e+162)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= -2.1e+53)
		tmp = t_1;
	elseif (y <= -2.6e-36)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= 2.7e-45)
		tmp = x;
	elseif ((y <= 7.1e+65) || !(y <= 1.55e+130))
		tmp = t_1;
	else
		tmp = Float64(y / Float64(a / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (t / -a);
	tmp = 0.0;
	if (y <= -4.5e+162)
		tmp = (z * y) / a;
	elseif (y <= -2.1e+53)
		tmp = t_1;
	elseif (y <= -2.6e-36)
		tmp = y * (z / a);
	elseif (y <= 2.7e-45)
		tmp = x;
	elseif ((y <= 7.1e+65) || ~((y <= 1.55e+130)))
		tmp = t_1;
	else
		tmp = y / (a / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.5e+162], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -2.1e+53], t$95$1, If[LessEqual[y, -2.6e-36], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-45], x, If[Or[LessEqual[y, 7.1e+65], N[Not[LessEqual[y, 1.55e+130]], $MachinePrecision]], t$95$1, N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.49999999999999972e162

   1. Initial program 88.3%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 79.0%

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

   9. Taylor expanded in z around inf 64.2%

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

       1. *-commutative 64.2%

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

       2. associate-*l/ 72.6%

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

   11. Applied egg-rr 72.6%

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

   if -4.49999999999999972e162 < y < -2.1000000000000002e53 or 2.69999999999999985e-45 < y < 7.1000000000000003e65 or 1.55e130 < y

   1. Initial program 88.9%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 88.9%

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

      1. associate-*l/ 97.6%

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

      2. *-commutative 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in z around 0 66.0%

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

      1. associate-*l/ 72.3%

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

      2. *-commutative 72.3%

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

      3. neg-mul-1 72.3%

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

      4. sub-neg 72.3%

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

      5. associate-*r/ 66.0%

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

      6. associate-*l/ 70.3%

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

      7. *-commutative 70.3%

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

   10. Simplified 70.3%

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

   11. Taylor expanded in x around 0 51.3%

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

       1. associate-*r/ 51.3%

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

       2. neg-mul-1 51.3%

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

       3. distribute-lft-neg-in 51.3%

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

       4. *-commutative 51.3%

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

       5. associate-/l* 57.5%

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

   13. Simplified 57.5%

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

   if -2.1000000000000002e53 < y < -2.6e-36

   1. Initial program 94.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 94.9%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 89.5%

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

   9. Taylor expanded in z around inf 74.5%

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

   if -2.6e-36 < y < 2.69999999999999985e-45

   1. Initial program 99.9%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in x around inf 67.3%

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

   if 7.1000000000000003e65 < y < 1.55e130

   1. Initial program 83.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around 0 83.3%

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

      1. associate-*l/ 94.5%

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

      2. *-commutative 94.5%

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

   7. Simplified 94.5%

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

   8. Taylor expanded in y around inf 76.8%

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

   9. Taylor expanded in z around inf 65.2%

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

       1. clear-num 65.2%

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

       2. un-div-inv 65.3%

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

   11. Applied egg-rr 65.3%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+162}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{+65} \lor \neg \left(y \leq 1.55 \cdot 10^{+130}\right):\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 47.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+157}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+66} \lor \neg \left(y \leq 1.85 \cdot 10^{+130}\right):\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5.4e+157)
   (/ (* z y) a)
   (if (<= y -9.2e+51)
     (* t (/ y (- a)))
     (if (<= y -2.3e-36)
       (* y (/ z a))
       (if (<= y 2.4e-44)
         x
         (if (or (<= y 1e+66) (not (<= y 1.85e+130)))
           (* y (/ t (- a)))
           (/ y (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5.4e+157) {
		tmp = (z * y) / a;
	} else if (y <= -9.2e+51) {
		tmp = t * (y / -a);
	} else if (y <= -2.3e-36) {
		tmp = y * (z / a);
	} else if (y <= 2.4e-44) {
		tmp = x;
	} else if ((y <= 1e+66) || !(y <= 1.85e+130)) {
		tmp = y * (t / -a);
	} else {
		tmp = y / (a / 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 (y <= (-5.4d+157)) then
        tmp = (z * y) / a
    else if (y <= (-9.2d+51)) then
        tmp = t * (y / -a)
    else if (y <= (-2.3d-36)) then
        tmp = y * (z / a)
    else if (y <= 2.4d-44) then
        tmp = x
    else if ((y <= 1d+66) .or. (.not. (y <= 1.85d+130))) then
        tmp = y * (t / -a)
    else
        tmp = y / (a / 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 (y <= -5.4e+157) {
		tmp = (z * y) / a;
	} else if (y <= -9.2e+51) {
		tmp = t * (y / -a);
	} else if (y <= -2.3e-36) {
		tmp = y * (z / a);
	} else if (y <= 2.4e-44) {
		tmp = x;
	} else if ((y <= 1e+66) || !(y <= 1.85e+130)) {
		tmp = y * (t / -a);
	} else {
		tmp = y / (a / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5.4e+157:
		tmp = (z * y) / a
	elif y <= -9.2e+51:
		tmp = t * (y / -a)
	elif y <= -2.3e-36:
		tmp = y * (z / a)
	elif y <= 2.4e-44:
		tmp = x
	elif (y <= 1e+66) or not (y <= 1.85e+130):
		tmp = y * (t / -a)
	else:
		tmp = y / (a / z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5.4e+157)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= -9.2e+51)
		tmp = Float64(t * Float64(y / Float64(-a)));
	elseif (y <= -2.3e-36)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= 2.4e-44)
		tmp = x;
	elseif ((y <= 1e+66) || !(y <= 1.85e+130))
		tmp = Float64(y * Float64(t / Float64(-a)));
	else
		tmp = Float64(y / Float64(a / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5.4e+157)
		tmp = (z * y) / a;
	elseif (y <= -9.2e+51)
		tmp = t * (y / -a);
	elseif (y <= -2.3e-36)
		tmp = y * (z / a);
	elseif (y <= 2.4e-44)
		tmp = x;
	elseif ((y <= 1e+66) || ~((y <= 1.85e+130)))
		tmp = y * (t / -a);
	else
		tmp = y / (a / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5.4e+157], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -9.2e+51], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.3e-36], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-44], x, If[Or[LessEqual[y, 1e+66], N[Not[LessEqual[y, 1.85e+130]], $MachinePrecision]], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -5.4000000000000001e157

   1. Initial program 88.3%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 79.0%

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

   9. Taylor expanded in z around inf 64.2%

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

       1. *-commutative 64.2%

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

       2. associate-*l/ 72.6%

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

   11. Applied egg-rr 72.6%

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

   if -5.4000000000000001e157 < y < -9.2000000000000002e51

   1. Initial program 85.4%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 85.4%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0 70.3%

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

      1. associate-*l/ 83.3%

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

      2. *-commutative 83.3%

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

      3. neg-mul-1 83.3%

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

      4. sub-neg 83.3%

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

      5. associate-*r/ 70.3%

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

      6. associate-*l/ 84.6%

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

      7. *-commutative 84.6%

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

   10. Simplified 84.6%

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

   11. Taylor expanded in x around 0 62.9%

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

       1. mul-1-neg 62.9%

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

       2. associate-/l* 77.2%

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

       3. distribute-lft-neg-in 77.2%

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

       4. *-commutative 77.2%

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

   13. Simplified 77.2%

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

   if -9.2000000000000002e51 < y < -2.29999999999999996e-36

   1. Initial program 94.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 94.9%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 89.5%

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

   9. Taylor expanded in z around inf 74.5%

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

   if -2.29999999999999996e-36 < y < 2.40000000000000009e-44

   1. Initial program 99.9%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in x around inf 67.3%

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

   if 2.40000000000000009e-44 < y < 9.99999999999999945e65 or 1.8500000000000001e130 < y

   1. Initial program 89.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around 0 89.5%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   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 65.2%

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

      1. associate-*l/ 70.3%

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

      2. *-commutative 70.3%

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

      3. neg-mul-1 70.3%

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

      4. sub-neg 70.3%

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

      5. associate-*r/ 65.2%

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

      6. associate-*l/ 67.7%

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

      7. *-commutative 67.7%

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

   10. Simplified 67.7%

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

   11. Taylor expanded in x around 0 49.2%

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

       1. associate-*r/ 49.2%

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

       2. neg-mul-1 49.2%

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

       3. distribute-lft-neg-in 49.2%

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

       4. *-commutative 49.2%

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

       5. associate-/l* 54.2%

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

   13. Simplified 54.2%

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

   if 9.99999999999999945e65 < y < 1.8500000000000001e130

   1. Initial program 83.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around 0 83.3%

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

      1. associate-*l/ 94.5%

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

      2. *-commutative 94.5%

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

   7. Simplified 94.5%

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

   8. Taylor expanded in y around inf 76.8%

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

   9. Taylor expanded in z around inf 65.2%

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

       1. clear-num 65.2%

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

       2. un-div-inv 65.3%

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

   11. Applied egg-rr 65.3%

       \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+157}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+51}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+66} \lor \neg \left(y \leq 1.85 \cdot 10^{+130}\right):\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -4.1 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) (/ y a))))
   (if (<= y -4.1e-44)
     t_1
     (if (<= y 2.75e-170)
       x
       (if (<= y 6.6e-53) t_1 (if (<= y 2.5e-46) x (* y (/ (- z t) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / a);
	double tmp;
	if (y <= -4.1e-44) {
		tmp = t_1;
	} else if (y <= 2.75e-170) {
		tmp = x;
	} else if (y <= 6.6e-53) {
		tmp = t_1;
	} else if (y <= 2.5e-46) {
		tmp = x;
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * (y / a)
    if (y <= (-4.1d-44)) then
        tmp = t_1
    else if (y <= 2.75d-170) then
        tmp = x
    else if (y <= 6.6d-53) then
        tmp = t_1
    else if (y <= 2.5d-46) then
        tmp = x
    else
        tmp = y * ((z - t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * (y / a);
	double tmp;
	if (y <= -4.1e-44) {
		tmp = t_1;
	} else if (y <= 2.75e-170) {
		tmp = x;
	} else if (y <= 6.6e-53) {
		tmp = t_1;
	} else if (y <= 2.5e-46) {
		tmp = x;
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * (y / a)
	tmp = 0
	if y <= -4.1e-44:
		tmp = t_1
	elif y <= 2.75e-170:
		tmp = x
	elif y <= 6.6e-53:
		tmp = t_1
	elif y <= 2.5e-46:
		tmp = x
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * Float64(y / a))
	tmp = 0.0
	if (y <= -4.1e-44)
		tmp = t_1;
	elseif (y <= 2.75e-170)
		tmp = x;
	elseif (y <= 6.6e-53)
		tmp = t_1;
	elseif (y <= 2.5e-46)
		tmp = x;
	else
		tmp = Float64(y * Float64(Float64(z - t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * (y / a);
	tmp = 0.0;
	if (y <= -4.1e-44)
		tmp = t_1;
	elseif (y <= 2.75e-170)
		tmp = x;
	elseif (y <= 6.6e-53)
		tmp = t_1;
	elseif (y <= 2.5e-46)
		tmp = x;
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.1e-44], t$95$1, If[LessEqual[y, 2.75e-170], x, If[LessEqual[y, 6.6e-53], t$95$1, If[LessEqual[y, 2.5e-46], x, N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.09999999999999992e-44 or 2.75000000000000009e-170 < y < 6.60000000000000009e-53

   1. Initial program 92.2%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in y around 0 92.2%

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

      1. associate-*l/ 98.7%

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

      2. *-commutative 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in y around inf 73.1%

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

   9. Taylor expanded in z around 0 67.0%

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

       1. +-commutative 67.0%

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

       2. associate-*l/ 66.6%

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

       3. mul-1-neg 66.6%

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

       4. associate-/l* 70.9%

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

       5. distribute-lft-neg-in 70.9%

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

       6. *-commutative 70.9%

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

       7. distribute-lft-out 82.6%

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

       8. sub-neg 82.6%

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

       9. *-commutative 82.6%

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

       10. associate-/l* 77.5%

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

       11. associate-*l/ 77.8%

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

       12. *-commutative 77.8%

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

   11. Simplified 77.8%

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

   12. Taylor expanded in y around 0 77.5%

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

       1. associate-*l/ 98.7%

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

       2. *-commutative 98.7%

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

   14. Simplified 82.6%

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

   if -4.09999999999999992e-44 < y < 2.75000000000000009e-170 or 6.60000000000000009e-53 < y < 2.49999999999999996e-46

   1. Initial program 99.9%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in x around inf 77.9%

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

   if 2.49999999999999996e-46 < y

   1. Initial program 88.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 88.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   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 y around inf 76.5%

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

   9. Taylor expanded in z around 0 58.3%

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

       1. +-commutative 58.3%

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

       2. associate-*l/ 58.0%

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

       3. mul-1-neg 58.0%

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

       4. associate-/l* 59.8%

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

       5. distribute-lft-neg-in 59.8%

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

       6. *-commutative 59.8%

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

       7. distribute-lft-out 80.0%

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

       8. sub-neg 80.0%

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

       9. *-commutative 80.0%

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

       10. associate-/l* 71.7%

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

       11. associate-*l/ 82.1%

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

       12. *-commutative 82.1%

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

   11. Simplified 82.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-44}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-170}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-53}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-44} \lor \neg \left(y \leq 3.6 \cdot 10^{-141}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6e-44) (not (<= y 3.6e-141))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6e-44) || !(y <= 3.6e-141)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-6d-44)) .or. (.not. (y <= 3.6d-141))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6e-44) || !(y <= 3.6e-141)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6e-44) or not (y <= 3.6e-141):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6e-44) || !(y <= 3.6e-141))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6e-44) || ~((y <= 3.6e-141)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6e-44], N[Not[LessEqual[y, 3.6e-141]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.0000000000000005e-44 or 3.60000000000000015e-141 < y

   1. Initial program 90.0%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in y around 0 90.0%

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

      1. associate-*l/ 97.7%

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

      2. *-commutative 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in y around inf 75.9%

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

   9. Taylor expanded in z around 0 61.7%

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

       1. +-commutative 61.7%

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

       2. associate-*l/ 61.3%

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

       3. mul-1-neg 61.3%

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

       4. associate-/l* 64.4%

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

       5. distribute-lft-neg-in 64.4%

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

       6. *-commutative 64.4%

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

       7. distribute-lft-out 80.8%

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

       8. sub-neg 80.8%

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

       9. *-commutative 80.8%

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

       10. associate-/l* 73.9%

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

       11. associate-*l/ 81.1%

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

       12. *-commutative 81.1%

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

   11. Simplified 81.1%

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

   if -6.0000000000000005e-44 < y < 3.60000000000000015e-141

   1. Initial program 99.9%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in x around inf 73.9%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-44} \lor \neg \left(y \leq 3.6 \cdot 10^{-141}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+183}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+115}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.65e+183)
   (* y (/ (- z t) a))
   (if (<= t 3.2e+115) (+ x (/ (* z y) a)) (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.65e+183) {
		tmp = y * ((z - t) / a);
	} else if (t <= 3.2e+115) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.65d+183)) then
        tmp = y * ((z - t) / a)
    else if (t <= 3.2d+115) then
        tmp = x + ((z * y) / a)
    else
        tmp = (z - t) * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.65e+183) {
		tmp = y * ((z - t) / a);
	} else if (t <= 3.2e+115) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.65e+183:
		tmp = y * ((z - t) / a)
	elif t <= 3.2e+115:
		tmp = x + ((z * y) / a)
	else:
		tmp = (z - t) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.65e+183)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 3.2e+115)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	else
		tmp = Float64(Float64(z - t) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.65e+183)
		tmp = y * ((z - t) / a);
	elseif (t <= 3.2e+115)
		tmp = x + ((z * y) / a);
	else
		tmp = (z - t) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.65e+183], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e+115], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6500000000000001e183

   1. Initial program 93.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around 0 93.2%

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

      1. associate-*l/ 96.5%

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

      2. *-commutative 96.5%

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

   7. Simplified 96.5%

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

   8. Taylor expanded in y around inf 71.6%

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

   9. Taylor expanded in z around 0 57.8%

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

       1. +-commutative 57.8%

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

       2. associate-*l/ 54.3%

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

       3. mul-1-neg 54.3%

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

       4. associate-/l* 57.5%

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

       5. distribute-lft-neg-in 57.5%

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

       6. *-commutative 57.5%

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

       7. distribute-lft-out 86.1%

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

       8. sub-neg 86.1%

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

       9. *-commutative 86.1%

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

       10. associate-/l* 82.8%

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

       11. associate-*l/ 86.1%

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

       12. *-commutative 86.1%

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

   11. Simplified 86.1%

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

   if -2.6500000000000001e183 < t < 3.2e115

   1. Initial program 95.3%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around inf 83.7%

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

   if 3.2e115 < t

   1. Initial program 85.3%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around 0 85.3%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around inf 78.0%

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

   9. Taylor expanded in z around 0 60.6%

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

       1. +-commutative 60.6%

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

       2. associate-*l/ 56.1%

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

       3. mul-1-neg 56.1%

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

       4. associate-/l* 68.6%

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

       5. distribute-lft-neg-in 68.6%

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

       6. *-commutative 68.6%

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

       7. distribute-lft-out 89.1%

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

       8. sub-neg 89.1%

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

       9. *-commutative 89.1%

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

       10. associate-/l* 76.5%

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

       11. associate-*l/ 84.8%

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

       12. *-commutative 84.8%

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

   11. Simplified 84.8%

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

   12. Taylor expanded in y around 0 76.5%

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

       1. associate-*l/ 99.9%

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

       2. *-commutative 99.9%

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

   14. Simplified 89.1%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.65 \cdot 10^{+183}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+115}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+114}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.2e+172)
   (* y (/ (- z t) a))
   (if (<= t 5.5e+114) (+ x (* z (/ y a))) (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+172) {
		tmp = y * ((z - t) / a);
	} else if (t <= 5.5e+114) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.2d+172)) then
        tmp = y * ((z - t) / a)
    else if (t <= 5.5d+114) then
        tmp = x + (z * (y / a))
    else
        tmp = (z - t) * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.2e+172) {
		tmp = y * ((z - t) / a);
	} else if (t <= 5.5e+114) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.2e+172:
		tmp = y * ((z - t) / a)
	elif t <= 5.5e+114:
		tmp = x + (z * (y / a))
	else:
		tmp = (z - t) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.2e+172)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 5.5e+114)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(Float64(z - t) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.2e+172)
		tmp = y * ((z - t) / a);
	elseif (t <= 5.5e+114)
		tmp = x + (z * (y / a));
	else
		tmp = (z - t) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.2e+172], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.5e+114], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.19999999999999976e172

   1. Initial program 93.7%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around 0 93.7%

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

      1. associate-*l/ 96.8%

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

      2. *-commutative 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in y around inf 70.4%

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

   9. Taylor expanded in z around 0 57.5%

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

       1. +-commutative 57.5%

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

       2. associate-*l/ 50.9%

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

       3. mul-1-neg 50.9%

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

       4. associate-/l* 53.9%

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

       5. distribute-lft-neg-in 53.9%

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

       6. *-commutative 53.9%

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

       7. distribute-lft-out 83.9%

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

       8. sub-neg 83.9%

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

       9. *-commutative 83.9%

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

       10. associate-/l* 80.8%

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

       11. associate-*l/ 83.9%

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

       12. *-commutative 83.9%

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

   11. Simplified 83.9%

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

   if -6.19999999999999976e172 < t < 5.5000000000000001e114

   1. Initial program 95.2%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around 0 84.1%

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

      1. +-commutative 84.1%

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

      2. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

      1. *-commutative 40.5%

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

      2. associate-*l/ 41.0%

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

   9. Applied egg-rr 84.1%

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

       1. *-commutative 84.1%

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

       2. associate-*l/ 88.2%

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

   11. Applied egg-rr 88.2%

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

   if 5.5000000000000001e114 < t

   1. Initial program 85.3%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around 0 85.3%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around inf 78.0%

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

   9. Taylor expanded in z around 0 60.6%

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

       1. +-commutative 60.6%

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

       2. associate-*l/ 56.1%

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

       3. mul-1-neg 56.1%

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

       4. associate-/l* 68.6%

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

       5. distribute-lft-neg-in 68.6%

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

       6. *-commutative 68.6%

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

       7. distribute-lft-out 89.1%

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

       8. sub-neg 89.1%

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

       9. *-commutative 89.1%

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

       10. associate-/l* 76.5%

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

       11. associate-*l/ 84.8%

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

       12. *-commutative 84.8%

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

   11. Simplified 84.8%

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

   12. Taylor expanded in y around 0 76.5%

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

       1. associate-*l/ 99.9%

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

       2. *-commutative 99.9%

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

   14. Simplified 89.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+172}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+114}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+137}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.3e+137)
   (- x (* t (/ y a)))
   (if (<= t 2.05e+114) (+ x (* z (/ y a))) (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.3e+137) {
		tmp = x - (t * (y / a));
	} else if (t <= 2.05e+114) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.3d+137)) then
        tmp = x - (t * (y / a))
    else if (t <= 2.05d+114) then
        tmp = x + (z * (y / a))
    else
        tmp = (z - t) * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.3e+137) {
		tmp = x - (t * (y / a));
	} else if (t <= 2.05e+114) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.3e+137:
		tmp = x - (t * (y / a))
	elif t <= 2.05e+114:
		tmp = x + (z * (y / a))
	else:
		tmp = (z - t) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.3e+137)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (t <= 2.05e+114)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(Float64(z - t) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.3e+137)
		tmp = x - (t * (y / a));
	elseif (t <= 2.05e+114)
		tmp = x + (z * (y / a));
	else
		tmp = (z - t) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.3e+137], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.05e+114], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.29999999999999965e137

   1. Initial program 94.4%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in y around 0 94.4%

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

      1. associate-*l/ 97.1%

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

      2. *-commutative 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around 0 85.6%

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

      1. associate-*l/ 85.6%

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

      2. *-commutative 85.6%

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

      3. neg-mul-1 85.6%

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

      4. sub-neg 85.6%

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

      5. associate-*r/ 85.6%

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

      6. associate-*l/ 88.3%

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

      7. *-commutative 88.3%

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

   10. Simplified 88.3%

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

   if -4.29999999999999965e137 < t < 2.05e114

   1. Initial program 95.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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* 83.3%

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

   7. Simplified 83.3%

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

      1. *-commutative 40.8%

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

      2. associate-*l/ 41.3%

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

   9. Applied egg-rr 83.8%

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

       1. *-commutative 83.8%

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

       2. associate-*l/ 88.0%

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

   11. Applied egg-rr 88.0%

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

   if 2.05e114 < t

   1. Initial program 85.3%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around 0 85.3%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around inf 78.0%

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

   9. Taylor expanded in z around 0 60.6%

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

       1. +-commutative 60.6%

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

       2. associate-*l/ 56.1%

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

       3. mul-1-neg 56.1%

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

       4. associate-/l* 68.6%

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

       5. distribute-lft-neg-in 68.6%

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

       6. *-commutative 68.6%

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

       7. distribute-lft-out 89.1%

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

       8. sub-neg 89.1%

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

       9. *-commutative 89.1%

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

       10. associate-/l* 76.5%

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

       11. associate-*l/ 84.8%

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

       12. *-commutative 84.8%

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

   11. Simplified 84.8%

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

   12. Taylor expanded in y around 0 76.5%

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

       1. associate-*l/ 99.9%

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

       2. *-commutative 99.9%

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

   14. Simplified 89.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+137}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-36} \lor \neg \left(y \leq 1.75 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.5e-36) (not (<= y 1.75e+34))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.5e-36) || !(y <= 1.75e+34)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-2.5d-36)) .or. (.not. (y <= 1.75d+34))) then
        tmp = y * (z / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.5e-36) || !(y <= 1.75e+34)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.5e-36) or not (y <= 1.75e+34):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.5e-36) || !(y <= 1.75e+34))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.5e-36) || ~((y <= 1.75e+34)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.5e-36], N[Not[LessEqual[y, 1.75e+34]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.50000000000000002e-36 or 1.74999999999999999e34 < y

   1. Initial program 87.4%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around 0 87.4%

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

      1. associate-*l/ 97.7%

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

      2. *-commutative 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in y around inf 79.0%

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

   9. Taylor expanded in z around inf 52.7%

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

   if -2.50000000000000002e-36 < y < 1.74999999999999999e34

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 61.5%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-36} \lor \neg \left(y \leq 1.75 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.5e-36) (/ (* z y) a) (if (<= y 1.55e+34) x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.5e-36) {
		tmp = (z * y) / a;
	} else if (y <= 1.55e+34) {
		tmp = x;
	} else {
		tmp = 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 (y <= (-2.5d-36)) then
        tmp = (z * y) / a
    else if (y <= 1.55d+34) then
        tmp = x
    else
        tmp = 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 (y <= -2.5e-36) {
		tmp = (z * y) / a;
	} else if (y <= 1.55e+34) {
		tmp = x;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.5e-36:
		tmp = (z * y) / a
	elif y <= 1.55e+34:
		tmp = x
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.5e-36)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= 1.55e+34)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.5e-36)
		tmp = (z * y) / a;
	elseif (y <= 1.55e+34)
		tmp = x;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.5e-36], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.55e+34], x, N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.50000000000000002e-36

   1. Initial program 89.7%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in y around 0 89.7%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 80.5%

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

   9. Taylor expanded in z around inf 57.2%

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

       1. *-commutative 57.2%

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

       2. associate-*l/ 61.4%

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

   11. Applied egg-rr 61.4%

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

   if -2.50000000000000002e-36 < y < 1.54999999999999989e34

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 61.5%

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

   if 1.54999999999999989e34 < y

   1. Initial program 85.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around 0 85.3%

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

      1. associate-*l/ 95.9%

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

      2. *-commutative 95.9%

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

   7. Simplified 95.9%

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

   8. Taylor expanded in y around inf 77.7%

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

   9. Taylor expanded in z around inf 48.6%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-36}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.0% 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 93.3%

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

   1. associate-/l* 94.3%

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

3. Simplified 94.3%

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

5. Final simplification 94.3%

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

Alternative 12: 38.5% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

   1. associate-/l* 94.3%

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

3. Simplified 94.3%

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

5. Taylor expanded in x around inf 36.8%

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

6. Final simplification 36.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.9% 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 2024096 
(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)))