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

Percentage Accurate: 93.1% → 98.9%

Time: 7.9s

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: 98.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+220} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+107}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (or (<= t_1 -5e+220) (not (<= t_1 2e+107)))
     (+ x (* y (/ (- z t) a)))
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -5e+220) || !(t_1 <= 2e+107)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + (t_1 / 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
    if ((t_1 <= (-5d+220)) .or. (.not. (t_1 <= 2d+107))) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = x + (t_1 / 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;
	double tmp;
	if ((t_1 <= -5e+220) || !(t_1 <= 2e+107)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	tmp = 0
	if (t_1 <= -5e+220) or not (t_1 <= 2e+107):
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * y)
	tmp = 0.0
	if ((t_1 <= -5e+220) || !(t_1 <= 2e+107))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * y;
	tmp = 0.0;
	if ((t_1 <= -5e+220) || ~((t_1 <= 2e+107)))
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+220], N[Not[LessEqual[t$95$1, 2e+107]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -5.0000000000000002e220 or 1.9999999999999999e107 < (*.f64 y (-.f64 z t))

   1. Initial program 84.4%

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

      1. associate-/l* 100.0%

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

      2. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

   if -5.0000000000000002e220 < (*.f64 y (-.f64 z t)) < 1.9999999999999999e107

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -5 \cdot 10^{+220} \lor \neg \left(\left(z - t\right) \cdot y \leq 2 \cdot 10^{+107}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a}\\ \mathbf{if}\;y \leq -1.8 \cdot 10^{+165}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+65} \lor \neg \left(y \leq 1.88 \cdot 10^{+130}\right):\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z a))))
   (if (<= y -1.8e+165)
     (/ (* z y) a)
     (if (<= y -3.5e+53)
       (* t (/ (- y) a))
       (if (<= y -2.7e-36)
         t_1
         (if (<= y 2.8e-44)
           x
           (if (or (<= y 8.5e+65) (not (<= y 1.88e+130)))
             (* (- y) (/ t a))
             t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (y <= -1.8e+165) {
		tmp = (z * y) / a;
	} else if (y <= -3.5e+53) {
		tmp = t * (-y / a);
	} else if (y <= -2.7e-36) {
		tmp = t_1;
	} else if (y <= 2.8e-44) {
		tmp = x;
	} else if ((y <= 8.5e+65) || !(y <= 1.88e+130)) {
		tmp = -y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / a)
    if (y <= (-1.8d+165)) then
        tmp = (z * y) / a
    else if (y <= (-3.5d+53)) then
        tmp = t * (-y / a)
    else if (y <= (-2.7d-36)) then
        tmp = t_1
    else if (y <= 2.8d-44) then
        tmp = x
    else if ((y <= 8.5d+65) .or. (.not. (y <= 1.88d+130))) then
        tmp = -y * (t / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / a);
	double tmp;
	if (y <= -1.8e+165) {
		tmp = (z * y) / a;
	} else if (y <= -3.5e+53) {
		tmp = t * (-y / a);
	} else if (y <= -2.7e-36) {
		tmp = t_1;
	} else if (y <= 2.8e-44) {
		tmp = x;
	} else if ((y <= 8.5e+65) || !(y <= 1.88e+130)) {
		tmp = -y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / a)
	tmp = 0
	if y <= -1.8e+165:
		tmp = (z * y) / a
	elif y <= -3.5e+53:
		tmp = t * (-y / a)
	elif y <= -2.7e-36:
		tmp = t_1
	elif y <= 2.8e-44:
		tmp = x
	elif (y <= 8.5e+65) or not (y <= 1.88e+130):
		tmp = -y * (t / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (y <= -1.8e+165)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= -3.5e+53)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (y <= -2.7e-36)
		tmp = t_1;
	elseif (y <= 2.8e-44)
		tmp = x;
	elseif ((y <= 8.5e+65) || !(y <= 1.88e+130))
		tmp = Float64(Float64(-y) * Float64(t / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / a);
	tmp = 0.0;
	if (y <= -1.8e+165)
		tmp = (z * y) / a;
	elseif (y <= -3.5e+53)
		tmp = t * (-y / a);
	elseif (y <= -2.7e-36)
		tmp = t_1;
	elseif (y <= 2.8e-44)
		tmp = x;
	elseif ((y <= 8.5e+65) || ~((y <= 1.88e+130)))
		tmp = -y * (t / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.8e+165], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -3.5e+53], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e-36], t$95$1, If[LessEqual[y, 2.8e-44], x, If[Or[LessEqual[y, 8.5e+65], N[Not[LessEqual[y, 1.88e+130]], $MachinePrecision]], N[((-y) * N[(t / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.7999999999999999e165

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 82.1%

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

   4. Taylor expanded in z around inf 72.6%

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

   if -1.7999999999999999e165 < y < -3.50000000000000019e53

   1. Initial program 85.4%

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

   3. Taylor expanded in x around 0 73.3%

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

   4. Taylor expanded in z around 0 62.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{t \cdot y}{a}} \]
   5. 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-rgt-neg-in 77.2%

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

      4. mul-1-neg 77.2%

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

      5. associate-*r/ 77.2%

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

      6. mul-1-neg 77.2%

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

   6. Simplified 77.2%

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

   if -3.50000000000000019e53 < y < -2.70000000000000007e-36 or 8.50000000000000075e65 < y < 1.88000000000000003e130

   1. Initial program 89.4%

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

   3. Taylor expanded in x around 0 75.9%

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

   4. Taylor expanded in z around inf 65.0%

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

      1. associate-/l* 85.6%

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

   6. Simplified 70.1%

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

   if -2.70000000000000007e-36 < y < 2.8e-44

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 67.3%

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

   if 2.8e-44 < y < 8.50000000000000075e65 or 1.88000000000000003e130 < y

   1. Initial program 89.5%

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

   3. Taylor expanded in x around 0 73.0%

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

   4. Taylor expanded in z around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. associate-/l* 53.0%

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

      3. distribute-rgt-neg-in 53.0%

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

      4. mul-1-neg 53.0%

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

      5. associate-*r/ 53.0%

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

      6. mul-1-neg 53.0%

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

   6. Simplified 53.0%

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

   7. Taylor expanded in t around 0 49.2%

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

      1. mul-1-neg 49.2%

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

      2. *-commutative 49.2%

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

      3. distribute-frac-neg2 49.2%

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

      4. associate-/l* 54.2%

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

   9. Simplified 54.2%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+165}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+65} \lor \neg \left(y \leq 1.88 \cdot 10^{+130}\right):\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-y}{a}\\ t_2 := y \cdot \frac{z}{a}\\ \mathbf{if}\;y \leq -6.5 \cdot 10^{+167}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y) a))) (t_2 (* y (/ z a))))
   (if (<= y -6.5e+167)
     (/ (* z y) a)
     (if (<= y -4.5e+53)
       t_1
       (if (<= y -2.7e-36)
         t_2
         (if (<= y 1.75e-44) x (if (<= y 5.6e+65) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double t_2 = y * (z / a);
	double tmp;
	if (y <= -6.5e+167) {
		tmp = (z * y) / a;
	} else if (y <= -4.5e+53) {
		tmp = t_1;
	} else if (y <= -2.7e-36) {
		tmp = t_2;
	} else if (y <= 1.75e-44) {
		tmp = x;
	} else if (y <= 5.6e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (-y / a)
    t_2 = y * (z / a)
    if (y <= (-6.5d+167)) then
        tmp = (z * y) / a
    else if (y <= (-4.5d+53)) then
        tmp = t_1
    else if (y <= (-2.7d-36)) then
        tmp = t_2
    else if (y <= 1.75d-44) then
        tmp = x
    else if (y <= 5.6d+65) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double t_2 = y * (z / a);
	double tmp;
	if (y <= -6.5e+167) {
		tmp = (z * y) / a;
	} else if (y <= -4.5e+53) {
		tmp = t_1;
	} else if (y <= -2.7e-36) {
		tmp = t_2;
	} else if (y <= 1.75e-44) {
		tmp = x;
	} else if (y <= 5.6e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-y / a)
	t_2 = y * (z / a)
	tmp = 0
	if y <= -6.5e+167:
		tmp = (z * y) / a
	elif y <= -4.5e+53:
		tmp = t_1
	elif y <= -2.7e-36:
		tmp = t_2
	elif y <= 1.75e-44:
		tmp = x
	elif y <= 5.6e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-y) / a))
	t_2 = Float64(y * Float64(z / a))
	tmp = 0.0
	if (y <= -6.5e+167)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= -4.5e+53)
		tmp = t_1;
	elseif (y <= -2.7e-36)
		tmp = t_2;
	elseif (y <= 1.75e-44)
		tmp = x;
	elseif (y <= 5.6e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-y / a);
	t_2 = y * (z / a);
	tmp = 0.0;
	if (y <= -6.5e+167)
		tmp = (z * y) / a;
	elseif (y <= -4.5e+53)
		tmp = t_1;
	elseif (y <= -2.7e-36)
		tmp = t_2;
	elseif (y <= 1.75e-44)
		tmp = x;
	elseif (y <= 5.6e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.5e+167], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -4.5e+53], t$95$1, If[LessEqual[y, -2.7e-36], t$95$2, If[LessEqual[y, 1.75e-44], x, If[LessEqual[y, 5.6e+65], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.5e167

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 82.1%

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

   4. Taylor expanded in z around inf 72.6%

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

   if -6.5e167 < y < -4.5000000000000002e53 or 1.7499999999999999e-44 < y < 5.5999999999999998e65

   1. Initial program 95.0%

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

   3. Taylor expanded in x around 0 74.9%

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

   4. Taylor expanded in z around 0 57.0%

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

      1. mul-1-neg 57.0%

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

      2. associate-/l* 61.7%

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

      3. distribute-rgt-neg-in 61.7%

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

      4. mul-1-neg 61.7%

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

      5. associate-*r/ 61.7%

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

      6. mul-1-neg 61.7%

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

   6. Simplified 61.7%

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

   if -4.5000000000000002e53 < y < -2.70000000000000007e-36 or 5.5999999999999998e65 < y

   1. Initial program 86.2%

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

   3. Taylor expanded in x around 0 73.4%

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

   4. Taylor expanded in z around inf 49.3%

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

      1. associate-/l* 68.8%

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

   6. Simplified 56.2%

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

   if -2.70000000000000007e-36 < y < 1.7499999999999999e-44

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 67.3%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+167}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+30} \lor \neg \left(t\_1 \leq 10^{+114}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) a)))
   (if (or (<= t_1 -4e+30) (not (<= t_1 1e+114)))
     (* (- z t) (/ y a))
     (+ x (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double tmp;
	if ((t_1 <= -4e+30) || !(t_1 <= 1e+114)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((z - t) * y) / a
    if ((t_1 <= (-4d+30)) .or. (.not. (t_1 <= 1d+114))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double tmp;
	if ((t_1 <= -4e+30) || !(t_1 <= 1e+114)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / a
	tmp = 0
	if (t_1 <= -4e+30) or not (t_1 <= 1e+114):
		tmp = (z - t) * (y / a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / a)
	tmp = 0.0
	if ((t_1 <= -4e+30) || !(t_1 <= 1e+114))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(z * Float64(y / 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 ((t_1 <= -4e+30) || ~((t_1 <= 1e+114)))
		tmp = (z - t) * (y / a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+30], N[Not[LessEqual[t$95$1, 1e+114]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -4.0000000000000001e30 or 1e114 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 88.3%

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

   3. Taylor expanded in x around 0 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-/l* 91.3%

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

   5. Applied egg-rr 91.3%

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

   if -4.0000000000000001e30 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1e114

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-/l* 98.2%

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

   4. Applied egg-rr 98.2%

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

   5. Taylor expanded in z around inf 89.6%

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

      1. associate-*l/ 88.7%

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

      2. *-commutative 88.7%

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

   7. Simplified 88.7%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a} \leq -4 \cdot 10^{+30} \lor \neg \left(\frac{\left(z - t\right) \cdot y}{a} \leq 10^{+114}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-43} \lor \neg \left(y \leq 1.8 \cdot 10^{-167}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.7e-43) (not (<= y 1.8e-167))) (* (- z t) (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.7e-43) || !(y <= 1.8e-167)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.7d-43)) .or. (.not. (y <= 1.8d-167))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.7e-43) || !(y <= 1.8e-167)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.7e-43) or not (y <= 1.8e-167):
		tmp = (z - t) * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.7e-43) || !(y <= 1.8e-167))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.7e-43) || ~((y <= 1.8e-167)))
		tmp = (z - t) * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.7e-43], N[Not[LessEqual[y, 1.8e-167]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e-43 or 1.8e-167 < y

   1. Initial program 90.5%

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

   3. Taylor expanded in x around 0 72.9%

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

      1. *-commutative 72.9%

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

      2. associate-/l* 79.5%

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

   5. Applied egg-rr 79.5%

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

   if -1.7e-43 < y < 1.8e-167

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 76.7%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-43} \lor \neg \left(y \leq 1.8 \cdot 10^{-167}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+183}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+114}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.6e+183)
   (* y (/ (- z t) a))
   (if (<= t 2.3e+114) (+ x (* y (/ z a))) (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.6e+183) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.3e+114) {
		tmp = x + (y * (z / 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 <= (-2.6d+183)) then
        tmp = y * ((z - t) / a)
    else if (t <= 2.3d+114) then
        tmp = x + (y * (z / 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 <= -2.6e+183) {
		tmp = y * ((z - t) / a);
	} else if (t <= 2.3e+114) {
		tmp = x + (y * (z / a));
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.6e+183:
		tmp = y * ((z - t) / a)
	elif t <= 2.3e+114:
		tmp = x + (y * (z / a))
	else:
		tmp = (z - t) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.6e+183)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 2.3e+114)
		tmp = Float64(x + Float64(y * Float64(z / 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 <= -2.6e+183)
		tmp = y * ((z - t) / a);
	elseif (t <= 2.3e+114)
		tmp = x + (y * (z / a));
	else
		tmp = (z - t) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.6e+183], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.3e+114], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5999999999999999e183

   1. Initial program 93.2%

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

   3. Taylor expanded in x around 0 82.8%

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

      1. associate-/l* 93.2%

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

      2. *-commutative 93.2%

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

   5. Applied egg-rr 86.1%

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

   if -2.5999999999999999e183 < t < 2.3e114

   1. Initial program 95.3%

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

   3. Taylor expanded in z around inf 83.7%

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

      1. associate-/l* 83.2%

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

   5. Simplified 83.2%

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

   if 2.3e114 < t

   1. Initial program 85.3%

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

   3. Taylor expanded in x around 0 76.5%

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

      1. *-commutative 76.5%

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

      2. associate-/l* 89.1%

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

   5. Applied egg-rr 89.1%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+183}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+114}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-43}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.8e-43)
   (* (- z t) (/ y a))
   (if (<= y 1.7e-139) x (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.8e-43) {
		tmp = (z - t) * (y / a);
	} else if (y <= 1.7e-139) {
		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) :: tmp
    if (y <= (-3.8d-43)) then
        tmp = (z - t) * (y / a)
    else if (y <= 1.7d-139) 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 tmp;
	if (y <= -3.8e-43) {
		tmp = (z - t) * (y / a);
	} else if (y <= 1.7e-139) {
		tmp = x;
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.8e-43:
		tmp = (z - t) * (y / a)
	elif y <= 1.7e-139:
		tmp = x
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.8e-43)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif (y <= 1.7e-139)
		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)
	tmp = 0.0;
	if (y <= -3.8e-43)
		tmp = (z - t) * (y / a);
	elseif (y <= 1.7e-139)
		tmp = x;
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.8e-43], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-139], x, N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7999999999999997e-43

   1. Initial program 89.8%

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

   3. Taylor expanded in x around 0 80.6%

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

      1. *-commutative 80.6%

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

      2. associate-/l* 87.8%

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

   5. Applied egg-rr 87.8%

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

   if -3.7999999999999997e-43 < y < 1.69999999999999999e-139

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 73.9%

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

   if 1.69999999999999999e-139 < y

   1. Initial program 90.2%

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

   3. Taylor expanded in x around 0 69.9%

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

      1. associate-/l* 99.0%

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

      2. *-commutative 99.0%

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

   5. Applied egg-rr 78.0%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-43}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-139}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-36} \lor \neg \left(y \leq 1.05 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.75e-36) (not (<= y 1.05e+33))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.75e-36) || !(y <= 1.05e+33)) {
		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 <= (-2.75d-36)) .or. (.not. (y <= 1.05d+33))) 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 <= -2.75e-36) || !(y <= 1.05e+33)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.75e-36) or not (y <= 1.05e+33):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.75e-36) || !(y <= 1.05e+33))
		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 <= -2.75e-36) || ~((y <= 1.05e+33)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.75e-36], N[Not[LessEqual[y, 1.05e+33]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.74999999999999992e-36 or 1.05e33 < y

   1. Initial program 87.4%

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

   3. Taylor expanded in x around 0 76.1%

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

   4. Taylor expanded in z around inf 50.5%

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

      1. associate-/l* 65.2%

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

   6. Simplified 52.7%

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

   if -2.74999999999999992e-36 < y < 1.05e33

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 61.5%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-36} \lor \neg \left(y \leq 1.05 \cdot 10^{+33}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-36}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.75e-36) (/ (* z y) a) (if (<= y 1.1e+34) x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.75e-36) {
		tmp = (z * y) / a;
	} else if (y <= 1.1e+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 <= (-2.75d-36)) then
        tmp = (z * y) / a
    else if (y <= 1.1d+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 <= -2.75e-36) {
		tmp = (z * y) / a;
	} else if (y <= 1.1e+34) {
		tmp = x;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.75e-36:
		tmp = (z * y) / a
	elif y <= 1.1e+34:
		tmp = x
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.75e-36)
		tmp = Float64(Float64(z * y) / a);
	elseif (y <= 1.1e+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 <= -2.75e-36)
		tmp = (z * y) / a;
	elseif (y <= 1.1e+34)
		tmp = x;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.75e-36], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.1e+34], x, N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.74999999999999992e-36

   1. Initial program 89.7%

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

   3. Taylor expanded in x around 0 81.0%

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

   4. Taylor expanded in z around inf 61.4%

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

   if -2.74999999999999992e-36 < y < 1.1000000000000001e34

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 61.5%

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

   if 1.1000000000000001e34 < y

   1. Initial program 85.3%

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

   3. Taylor expanded in x around 0 71.6%

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

   4. Taylor expanded in z around inf 40.6%

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

      1. associate-/l* 62.6%

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

   6. Simplified 48.6%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-36}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

   1. +-commutative 93.3%

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

   2. *-commutative 93.3%

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

   3. associate-/l* 98.0%

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

4. Applied egg-rr 98.0%

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

   1. associate-/l* 94.3%

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

   2. *-commutative 94.3%

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

4. Applied egg-rr 94.3%

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

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. Add Preprocessing

3. Taylor expanded in x around inf 36.8%

   \[\leadsto \color{blue}{x} \]
4. 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)))