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

Percentage Accurate: 93.4% → 98.2%

Time: 11.5s

Alternatives: 17

Speedup: 1.0×

• 24.8% 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: 93.4% 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: 98.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+224}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+253}:\\ \;\;\;\;x + \frac{1}{\frac{a}{t\_1}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 -5e+224)
     (+ x (/ y (/ a (- z t))))
     (if (<= t_1 2e+253) (+ x (/ 1.0 (/ a t_1))) (* y (/ (- z t) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -5e+224) {
		tmp = x + (y / (a / (z - t)));
	} else if (t_1 <= 2e+253) {
		tmp = x + (1.0 / (a / t_1));
	} 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 = y * (z - t)
    if (t_1 <= (-5d+224)) then
        tmp = x + (y / (a / (z - t)))
    else if (t_1 <= 2d+253) then
        tmp = x + (1.0d0 / (a / t_1))
    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 = y * (z - t);
	double tmp;
	if (t_1 <= -5e+224) {
		tmp = x + (y / (a / (z - t)));
	} else if (t_1 <= 2e+253) {
		tmp = x + (1.0 / (a / t_1));
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -5e+224:
		tmp = x + (y / (a / (z - t)))
	elif t_1 <= 2e+253:
		tmp = x + (1.0 / (a / t_1))
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+224)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (t_1 <= 2e+253)
		tmp = Float64(x + Float64(1.0 / Float64(a / t_1)));
	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 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+224)
		tmp = x + (y / (a / (z - t)));
	elseif (t_1 <= 2e+253)
		tmp = x + (1.0 / (a / t_1));
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+224], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+253], N[(x + N[(1.0 / N[(a / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -4.99999999999999964e224

   1. Initial program 81.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 81.0%

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

      1. associate-*l/ 99.8%

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

      2. associate-/r/ 99.9%

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

   7. Simplified 99.9%

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

   if -4.99999999999999964e224 < (*.f64 y (-.f64 z t)) < 1.9999999999999999e253

   1. Initial program 99.8%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

      1. associate-*r/ 99.8%

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

      2. clear-num 99.8%

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

   6. Applied egg-rr 99.8%

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

   if 1.9999999999999999e253 < (*.f64 y (-.f64 z t))

   1. Initial program 80.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around inf 93.0%

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

      1. associate--l+ 93.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 93.0%

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

      1. div-sub 100.0%

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

   10. Simplified 100.0%

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

Alternative 2: 84.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+152} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+281}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -2e+152) (not (<= t_1 5e+281)))
     (* (- z t) (/ y a))
     (- x (/ (* y t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -2e+152) || !(t_1 <= 5e+281)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x - ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if ((t_1 <= (-2d+152)) .or. (.not. (t_1 <= 5d+281))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x - ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -2e+152) || !(t_1 <= 5e+281)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x - ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if (t_1 <= -2e+152) or not (t_1 <= 5e+281):
		tmp = (z - t) * (y / a)
	else:
		tmp = x - ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -2e+152) || !(t_1 <= 5e+281))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x - Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if ((t_1 <= -2e+152) || ~((t_1 <= 5e+281)))
		tmp = (z - t) * (y / a);
	else
		tmp = x - ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+152], N[Not[LessEqual[t$95$1, 5e+281]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2.0000000000000001e152 or 5.00000000000000016e281 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 84.9%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in a around 0 83.0%

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

   6. Taylor expanded in a around 0 81.0%

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

      1. *-commutative 81.0%

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

      2. associate-/l* 90.4%

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

   8. Applied egg-rr 90.4%

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

   if -2.0000000000000001e152 < (/.f64 (*.f64 y (-.f64 z t)) a) < 5.00000000000000016e281

   1. Initial program 99.8%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in z around 0 88.9%

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

      1. +-commutative 88.9%

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

      2. associate-*r/ 88.9%

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

      3. mul-1-neg 88.9%

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

      4. distribute-lft-neg-out 88.9%

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

      5. *-commutative 88.9%

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

   7. Simplified 88.9%

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

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -2 \cdot 10^{+152} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 5 \cdot 10^{+281}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+152} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+253}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -2e+152) (not (<= t_1 4e+253)))
     (* (- z t) (/ y a))
     (- x (/ y (/ a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -2e+152) || !(t_1 <= 4e+253)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if ((t_1 <= (-2d+152)) .or. (.not. (t_1 <= 4d+253))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x - (y / (a / t))
    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 * (z - t)) / a;
	double tmp;
	if ((t_1 <= -2e+152) || !(t_1 <= 4e+253)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x - (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if (t_1 <= -2e+152) or not (t_1 <= 4e+253):
		tmp = (z - t) * (y / a)
	else:
		tmp = x - (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -2e+152) || !(t_1 <= 4e+253))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x - Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if ((t_1 <= -2e+152) || ~((t_1 <= 4e+253)))
		tmp = (z - t) * (y / a);
	else
		tmp = x - (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+152], N[Not[LessEqual[t$95$1, 4e+253]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2.0000000000000001e152 or 3.9999999999999997e253 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 85.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 a around 0 83.6%

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

   6. Taylor expanded in a around 0 81.6%

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

      1. *-commutative 81.6%

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

      2. associate-/l* 90.7%

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

   8. Applied egg-rr 90.7%

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

   if -2.0000000000000001e152 < (/.f64 (*.f64 y (-.f64 z t)) a) < 3.9999999999999997e253

   1. Initial program 99.8%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around 0 88.6%

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

      1. mul-1-neg 88.6%

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

      2. unsub-neg 88.6%

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

      3. *-commutative 88.6%

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

      4. associate-/l* 83.6%

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

   7. Simplified 83.6%

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

      1. clear-num 83.5%

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

      2. un-div-inv 86.1%

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

   9. Applied egg-rr 86.1%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -2 \cdot 10^{+152} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 4 \cdot 10^{+253}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+224}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+253}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 -5e+224)
     (+ x (/ y (/ a (- z t))))
     (if (<= t_1 2e+253) (+ x (/ t_1 a)) (* y (/ (- z t) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -5e+224) {
		tmp = x + (y / (a / (z - t)));
	} else if (t_1 <= 2e+253) {
		tmp = x + (t_1 / a);
	} 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 = y * (z - t)
    if (t_1 <= (-5d+224)) then
        tmp = x + (y / (a / (z - t)))
    else if (t_1 <= 2d+253) then
        tmp = x + (t_1 / a)
    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 = y * (z - t);
	double tmp;
	if (t_1 <= -5e+224) {
		tmp = x + (y / (a / (z - t)));
	} else if (t_1 <= 2e+253) {
		tmp = x + (t_1 / a);
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -5e+224:
		tmp = x + (y / (a / (z - t)))
	elif t_1 <= 2e+253:
		tmp = x + (t_1 / a)
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+224)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (t_1 <= 2e+253)
		tmp = Float64(x + Float64(t_1 / a));
	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 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+224)
		tmp = x + (y / (a / (z - t)));
	elseif (t_1 <= 2e+253)
		tmp = x + (t_1 / a);
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+224], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+253], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -4.99999999999999964e224

   1. Initial program 81.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 81.0%

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

      1. associate-*l/ 99.8%

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

      2. associate-/r/ 99.9%

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

   7. Simplified 99.9%

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

   if -4.99999999999999964e224 < (*.f64 y (-.f64 z t)) < 1.9999999999999999e253

   1. Initial program 99.8%

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

   if 1.9999999999999999e253 < (*.f64 y (-.f64 z t))

   1. Initial program 80.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around inf 93.0%

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

      1. associate--l+ 93.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 93.0%

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

      1. div-sub 100.0%

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

   10. Simplified 100.0%

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

Alternative 5: 83.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+202} \lor \neg \left(z \leq 3.5 \cdot 10^{+19}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.6e+202) (not (<= z 3.5e+19)))
   (+ x (* z (/ y a)))
   (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+202) || !(z <= 3.5e+19)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.6d+202)) .or. (.not. (z <= 3.5d+19))) then
        tmp = x + (z * (y / a))
    else
        tmp = x - (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.6e+202) || !(z <= 3.5e+19)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.6e+202) or not (z <= 3.5e+19):
		tmp = x + (z * (y / a))
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.6e+202) || !(z <= 3.5e+19))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.6e+202) || ~((z <= 3.5e+19)))
		tmp = x + (z * (y / a));
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.6e+202], N[Not[LessEqual[z, 3.5e+19]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6000000000000002e202 or 3.5e19 < z

   1. Initial program 90.6%

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

      1. +-commutative 90.6%

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

      2. associate-/l* 90.7%

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

      3. fma-define 90.7%

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

   3. Simplified 90.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 90.7%

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

      2. associate-*r/ 90.6%

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

      3. *-commutative 90.6%

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

      4. associate-/l* 93.3%

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

   6. Applied egg-rr 93.3%

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

   7. Taylor expanded in z around inf 82.7%

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

   if -2.6000000000000002e202 < z < 3.5e19

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-/l* 95.1%

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

      3. fma-define 95.1%

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

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 95.1%

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

      2. associate-*r/ 94.9%

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

      3. *-commutative 94.9%

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

      4. associate-/l* 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in z around 0 84.7%

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

      1. mul-1-neg 84.7%

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

      2. sub-neg 84.7%

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

      3. associate-/l* 87.4%

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

   9. Simplified 87.4%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+202} \lor \neg \left(z \leq 3.5 \cdot 10^{+19}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{-52} \lor \neg \left(y \leq 6.2 \cdot 10^{-44}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.62e-52) (not (<= y 6.2e-44))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.62e-52) || !(y <= 6.2e-44)) {
		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 <= (-1.62d-52)) .or. (.not. (y <= 6.2d-44))) 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 <= -1.62e-52) || !(y <= 6.2e-44)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.62e-52) or not (y <= 6.2e-44):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.62e-52) || !(y <= 6.2e-44))
		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 <= -1.62e-52) || ~((y <= 6.2e-44)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.62e-52], N[Not[LessEqual[y, 6.2e-44]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.61999999999999995e-52 or 6.19999999999999968e-44 < y

   1. Initial program 89.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 95.4%

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

      1. associate--l+ 95.4%

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

      2. div-sub 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in x around 0 73.7%

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

      1. div-sub 76.2%

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

   10. Simplified 76.2%

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

   if -1.61999999999999995e-52 < y < 6.19999999999999968e-44

   1. Initial program 99.8%

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

      1. associate-/l* 85.8%

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

   3. Simplified 85.8%

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

   5. Taylor expanded in x around inf 69.5%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{-52} \lor \neg \left(y \leq 6.2 \cdot 10^{-44}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+119}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4.2e+123)
   (* (- z t) (/ y a))
   (if (<= t 3.3e+119) (+ x (* z (/ y a))) (/ t (/ a (- y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+123) {
		tmp = (z - t) * (y / a);
	} else if (t <= 3.3e+119) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t / (a / -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-4.2d+123)) then
        tmp = (z - t) * (y / a)
    else if (t <= 3.3d+119) then
        tmp = x + (z * (y / a))
    else
        tmp = t / (a / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4.2e+123) {
		tmp = (z - t) * (y / a);
	} else if (t <= 3.3e+119) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t / (a / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -4.2e+123:
		tmp = (z - t) * (y / a)
	elif t <= 3.3e+119:
		tmp = x + (z * (y / a))
	else:
		tmp = t / (a / -y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4.2e+123)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (t <= 3.3e+119)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(t / Float64(a / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -4.2e+123)
		tmp = (z - t) * (y / a);
	elseif (t <= 3.3e+119)
		tmp = x + (z * (y / a));
	else
		tmp = t / (a / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4.2e+123], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.3e+119], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(a / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.19999999999999988e123

   1. Initial program 83.3%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around 0 79.0%

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

   6. Taylor expanded in a around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 82.0%

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

   8. Applied egg-rr 82.0%

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

   if -4.19999999999999988e123 < t < 3.3000000000000002e119

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-/l* 95.4%

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

      3. fma-define 95.4%

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

   3. Simplified 95.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 95.4%

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

      2. associate-*r/ 96.8%

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

      3. *-commutative 96.8%

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

      4. associate-/l* 95.2%

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

   6. Applied egg-rr 95.2%

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

   7. Taylor expanded in z around inf 82.4%

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

   if 3.3000000000000002e119 < t

   1. Initial program 87.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. div-sub 84.1%

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

   7. Simplified 84.1%

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

   8. Taylor expanded in t around inf 60.0%

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

      1. neg-mul-1 60.0%

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

      2. distribute-frac-neg2 60.0%

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

   10. Simplified 60.0%

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

       1. *-commutative 60.0%

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

       2. div-inv 60.0%

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

       3. associate-*l* 69.2%

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

       4. add-sqr-sqrt 29.1%

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

       5. sqrt-unprod 22.3%

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

       6. sqr-neg 22.3%

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

       7. sqrt-unprod 0.8%

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

       8. add-sqr-sqrt 0.9%

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

       9. associate-/r/ 0.9%

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

       10. div-inv 0.9%

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

       11. frac-2neg 0.9%

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

       12. distribute-neg-frac 0.9%

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

       13. add-sqr-sqrt 0.2%

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

       14. sqrt-unprod 30.3%

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

       15. sqr-neg 30.3%

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

       16. sqrt-unprod 40.1%

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

       17. add-sqr-sqrt 69.3%

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

   12. Applied egg-rr 69.3%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{+123}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3.3 \cdot 10^{+119}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+123}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+119}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.15e+123)
   (* (- z t) (/ y a))
   (if (<= t 5e+119) (+ x (* y (/ z a))) (/ t (/ a (- y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.15e+123) {
		tmp = (z - t) * (y / a);
	} else if (t <= 5e+119) {
		tmp = x + (y * (z / a));
	} else {
		tmp = t / (a / -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.15d+123)) then
        tmp = (z - t) * (y / a)
    else if (t <= 5d+119) then
        tmp = x + (y * (z / a))
    else
        tmp = t / (a / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.15e+123) {
		tmp = (z - t) * (y / a);
	} else if (t <= 5e+119) {
		tmp = x + (y * (z / a));
	} else {
		tmp = t / (a / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.15e+123:
		tmp = (z - t) * (y / a)
	elif t <= 5e+119:
		tmp = x + (y * (z / a))
	else:
		tmp = t / (a / -y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.15e+123)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (t <= 5e+119)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	else
		tmp = Float64(t / Float64(a / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.15e+123)
		tmp = (z - t) * (y / a);
	elseif (t <= 5e+119)
		tmp = x + (y * (z / a));
	else
		tmp = t / (a / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.15e+123], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e+119], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t / N[(a / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.14999999999999993e123

   1. Initial program 83.3%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around 0 79.0%

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

   6. Taylor expanded in a around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 82.0%

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

   8. Applied egg-rr 82.0%

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

   if -2.14999999999999993e123 < t < 4.9999999999999999e119

   1. Initial program 96.8%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in t around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-/l* 82.0%

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

   7. Simplified 82.0%

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

   if 4.9999999999999999e119 < t

   1. Initial program 87.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. div-sub 84.1%

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

   7. Simplified 84.1%

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

   8. Taylor expanded in t around inf 60.0%

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

      1. neg-mul-1 60.0%

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

      2. distribute-frac-neg2 60.0%

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

   10. Simplified 60.0%

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

       1. *-commutative 60.0%

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

       2. div-inv 60.0%

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

       3. associate-*l* 69.2%

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

       4. add-sqr-sqrt 29.1%

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

       5. sqrt-unprod 22.3%

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

       6. sqr-neg 22.3%

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

       7. sqrt-unprod 0.8%

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

       8. add-sqr-sqrt 0.9%

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

       9. associate-/r/ 0.9%

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

       10. div-inv 0.9%

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

       11. frac-2neg 0.9%

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

       12. distribute-neg-frac 0.9%

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

       13. add-sqr-sqrt 0.2%

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

       14. sqrt-unprod 30.3%

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

       15. sqr-neg 30.3%

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

       16. sqrt-unprod 40.1%

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

       17. add-sqr-sqrt 69.3%

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

   12. Applied egg-rr 69.3%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+123}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+119}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+123}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+120}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.1e+123)
   (* (- z t) (/ y a))
   (if (<= t 4.4e+120) (+ x (/ (* y z) a)) (/ t (/ a (- y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+123) {
		tmp = (z - t) * (y / a);
	} else if (t <= 4.4e+120) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t / (a / -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.1d+123)) then
        tmp = (z - t) * (y / a)
    else if (t <= 4.4d+120) then
        tmp = x + ((y * z) / a)
    else
        tmp = t / (a / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.1e+123) {
		tmp = (z - t) * (y / a);
	} else if (t <= 4.4e+120) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = t / (a / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.1e+123:
		tmp = (z - t) * (y / a)
	elif t <= 4.4e+120:
		tmp = x + ((y * z) / a)
	else:
		tmp = t / (a / -y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.1e+123)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (t <= 4.4e+120)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(t / Float64(a / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.1e+123)
		tmp = (z - t) * (y / a);
	elseif (t <= 4.4e+120)
		tmp = x + ((y * z) / a);
	else
		tmp = t / (a / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.1e+123], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.4e+120], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(t / N[(a / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.09999999999999994e123

   1. Initial program 83.3%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

   5. Taylor expanded in a around 0 79.0%

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

   6. Taylor expanded in a around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-/l* 82.0%

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

   8. Applied egg-rr 82.0%

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

   if -2.09999999999999994e123 < t < 4.4000000000000003e120

   1. Initial program 96.8%

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

      1. associate-/l* 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 81.5%

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

   if 4.4000000000000003e120 < t

   1. Initial program 87.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. div-sub 84.1%

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

   7. Simplified 84.1%

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

   8. Taylor expanded in t around inf 60.0%

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

      1. neg-mul-1 60.0%

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

      2. distribute-frac-neg2 60.0%

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

   10. Simplified 60.0%

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

       1. *-commutative 60.0%

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

       2. div-inv 60.0%

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

       3. associate-*l* 69.2%

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

       4. add-sqr-sqrt 29.1%

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

       5. sqrt-unprod 22.3%

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

       6. sqr-neg 22.3%

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

       7. sqrt-unprod 0.8%

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

       8. add-sqr-sqrt 0.9%

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

       9. associate-/r/ 0.9%

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

       10. div-inv 0.9%

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

       11. frac-2neg 0.9%

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

       12. distribute-neg-frac 0.9%

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

       13. add-sqr-sqrt 0.2%

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

       14. sqrt-unprod 30.3%

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

       15. sqr-neg 30.3%

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

       16. sqrt-unprod 40.1%

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

       17. add-sqr-sqrt 69.3%

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

   12. Applied egg-rr 69.3%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+123}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+120}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+122} \lor \neg \left(y \leq 4.8 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -9.2e+122) (not (<= y 4.8e+49))) (/ z (/ a y)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -9.2e+122) || !(y <= 4.8e+49)) {
		tmp = z / (a / y);
	} 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 <= (-9.2d+122)) .or. (.not. (y <= 4.8d+49))) then
        tmp = z / (a / y)
    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 <= -9.2e+122) || !(y <= 4.8e+49)) {
		tmp = z / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -9.2e+122) or not (y <= 4.8e+49):
		tmp = z / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -9.2e+122) || !(y <= 4.8e+49))
		tmp = Float64(z / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -9.2e+122) || ~((y <= 4.8e+49)))
		tmp = z / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -9.2e+122], N[Not[LessEqual[y, 4.8e+49]], $MachinePrecision]], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.2000000000000002e122 or 4.8e49 < y

   1. Initial program 87.5%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around inf 93.4%

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

      1. associate--l+ 93.4%

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

      2. div-sub 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. associate-/r/ 50.6%

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

   10. Applied egg-rr 50.6%

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

   if -9.2000000000000002e122 < y < 4.8e49

   1. Initial program 97.8%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around inf 60.0%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+122} \lor \neg \left(y \leq 4.8 \cdot 10^{+49}\right):\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+120} \lor \neg \left(y \leq 5.8 \cdot 10^{+53}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.1e+120) (not (<= y 5.8e+53))) (* z (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.1e+120) || !(y <= 5.8e+53)) {
		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 ((y <= (-5.1d+120)) .or. (.not. (y <= 5.8d+53))) 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 ((y <= -5.1e+120) || !(y <= 5.8e+53)) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.1e+120) or not (y <= 5.8e+53):
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.1e+120) || !(y <= 5.8e+53))
		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 ((y <= -5.1e+120) || ~((y <= 5.8e+53)))
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.1e+120], N[Not[LessEqual[y, 5.8e+53]], $MachinePrecision]], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.10000000000000027e120 or 5.8000000000000004e53 < y

   1. Initial program 87.5%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in a around 0 84.7%

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

   6. Taylor expanded in z around inf 43.9%

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

      1. div-inv 43.9%

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

      2. *-commutative 43.9%

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

      3. associate-*l* 50.5%

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

      4. div-inv 50.5%

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

   8. Applied egg-rr 50.5%

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

   if -5.10000000000000027e120 < y < 5.8000000000000004e53

   1. Initial program 97.8%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around inf 60.0%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.1 \cdot 10^{+120} \lor \neg \left(y \leq 5.8 \cdot 10^{+53}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+119} \lor \neg \left(y \leq 1.6 \cdot 10^{+50}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.95e+119) (not (<= y 1.6e+50))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.95e+119) || !(y <= 1.6e+50)) {
		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 <= (-2.95d+119)) .or. (.not. (y <= 1.6d+50))) 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 <= -2.95e+119) || !(y <= 1.6e+50)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.95e+119) or not (y <= 1.6e+50):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.95e+119) || !(y <= 1.6e+50))
		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 <= -2.95e+119) || ~((y <= 1.6e+50)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.95e+119], N[Not[LessEqual[y, 1.6e+50]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.95e119 or 1.59999999999999991e50 < y

   1. Initial program 87.5%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in y around inf 93.4%

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

      1. associate--l+ 93.4%

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

      2. div-sub 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around inf 49.5%

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

   if -2.95e119 < y < 1.59999999999999991e50

   1. Initial program 97.8%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around inf 60.0%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+119} \lor \neg \left(y \leq 1.6 \cdot 10^{+50}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5600000000000:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5600000000000.0)
   (/ t (/ a (- y)))
   (if (<= y 8e+50) x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5600000000000.0) {
		tmp = t / (a / -y);
	} else if (y <= 8e+50) {
		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 (y <= (-5600000000000.0d0)) then
        tmp = t / (a / -y)
    else if (y <= 8d+50) 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 (y <= -5600000000000.0) {
		tmp = t / (a / -y);
	} else if (y <= 8e+50) {
		tmp = x;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5600000000000.0:
		tmp = t / (a / -y)
	elif y <= 8e+50:
		tmp = x
	else:
		tmp = z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5600000000000.0)
		tmp = Float64(t / Float64(a / Float64(-y)));
	elseif (y <= 8e+50)
		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 (y <= -5600000000000.0)
		tmp = t / (a / -y);
	elseif (y <= 8e+50)
		tmp = x;
	else
		tmp = z / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5600000000000.0], N[(t / N[(a / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+50], x, N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6e12

   1. Initial program 92.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 94.0%

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

      1. associate--l+ 94.0%

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

      2. div-sub 95.5%

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

   7. Simplified 95.5%

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

   8. Taylor expanded in t around inf 49.3%

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

      1. neg-mul-1 49.3%

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

      2. distribute-frac-neg2 49.3%

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

   10. Simplified 49.3%

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

       1. *-commutative 49.3%

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

       2. div-inv 49.3%

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

       3. associate-*l* 50.9%

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

       4. add-sqr-sqrt 18.6%

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

       5. sqrt-unprod 19.4%

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

       6. sqr-neg 19.4%

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

       7. sqrt-unprod 2.6%

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

       8. add-sqr-sqrt 4.4%

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

       9. associate-/r/ 4.4%

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

       10. div-inv 4.4%

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

       11. frac-2neg 4.4%

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

       12. distribute-neg-frac 4.4%

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

       13. add-sqr-sqrt 1.8%

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

       14. sqrt-unprod 27.1%

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

       15. sqr-neg 27.1%

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

       16. sqrt-unprod 32.2%

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

       17. add-sqr-sqrt 51.2%

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

   12. Applied egg-rr 51.2%

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

   if -5.6e12 < y < 8.0000000000000006e50

   1. Initial program 98.3%

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

      1. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in x around inf 62.5%

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

   if 8.0000000000000006e50 < y

   1. Initial program 84.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 94.8%

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

      1. associate--l+ 94.8%

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

      2. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 53.9%

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

      1. *-commutative 53.9%

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

      2. associate-/r/ 54.1%

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

   10. Applied egg-rr 54.1%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5600000000000:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4500000000000:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4500000000000.0)
   (* (/ t a) (- y))
   (if (<= y 1.05e+52) x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4500000000000.0) {
		tmp = (t / a) * -y;
	} else if (y <= 1.05e+52) {
		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 (y <= (-4500000000000.0d0)) then
        tmp = (t / a) * -y
    else if (y <= 1.05d+52) 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 (y <= -4500000000000.0) {
		tmp = (t / a) * -y;
	} else if (y <= 1.05e+52) {
		tmp = x;
	} else {
		tmp = z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4500000000000.0:
		tmp = (t / a) * -y
	elif y <= 1.05e+52:
		tmp = x
	else:
		tmp = z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4500000000000.0)
		tmp = Float64(Float64(t / a) * Float64(-y));
	elseif (y <= 1.05e+52)
		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 (y <= -4500000000000.0)
		tmp = (t / a) * -y;
	elseif (y <= 1.05e+52)
		tmp = x;
	else
		tmp = z / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4500000000000.0], N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[y, 1.05e+52], x, N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5e12

   1. Initial program 92.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 94.0%

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

      1. associate--l+ 94.0%

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

      2. div-sub 95.5%

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

   7. Simplified 95.5%

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

   8. Taylor expanded in t around inf 49.3%

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

      1. neg-mul-1 49.3%

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

      2. distribute-frac-neg2 49.3%

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

   10. Simplified 49.3%

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

   if -4.5e12 < y < 1.05e52

   1. Initial program 98.3%

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

      1. associate-/l* 88.9%

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

   3. Simplified 88.9%

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

   5. Taylor expanded in x around inf 62.5%

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

   if 1.05e52 < y

   1. Initial program 84.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 94.8%

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

      1. associate--l+ 94.8%

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

      2. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 53.9%

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

      1. *-commutative 53.9%

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

      2. associate-/r/ 54.1%

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

   10. Applied egg-rr 54.1%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4500000000000:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 93.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

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

   1. associate-/l* 93.7%

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

3. Simplified 93.7%

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

5. Taylor expanded in y around 0 93.5%

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

   1. associate-*l/ 95.6%

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

   2. associate-/r/ 95.1%

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

7. Simplified 95.1%

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

Alternative 16: 93.3% 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 93.5%

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

   1. associate-/l* 93.7%

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

3. Simplified 93.7%

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

Alternative 17: 39.2% 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 93.5%

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

   1. associate-/l* 93.7%

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

3. Simplified 93.7%

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

5. Taylor expanded in x around inf 41.5%

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

Developer Target 1: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (+ x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (+ x (/ (* y (- z t)) a))
       (+ x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x + (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x + (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x + Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x + (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x + N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024186 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

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

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