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

Percentage Accurate: 93.4% → 95.9%

Time: 9.8s

Alternatives: 10

Speedup: 1.0×

• 25.5% 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: 95.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+271}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 -1e+271) (+ x (* y (/ (- z t) a))) (+ t_1 x))))

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 <= -1e+271) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if (t_1 <= (-1d+271)) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = t_1 + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -1e+271) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = t_1 + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -1e+271:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = t_1 + x
	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 <= -1e+271)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(t_1 + x);
	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 <= -1e+271)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = t_1 + x;
	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[LessEqual[t$95$1, -1e+271], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -9.99999999999999953e270

   1. Initial program 76.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   if -9.99999999999999953e270 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 98.5%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -1 \cdot 10^{+271}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a} + x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 65.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-25} \lor \neg \left(y \leq -4.5 \cdot 10^{-130} \lor \neg \left(y \leq -3 \cdot 10^{-229}\right) \land y \leq 5.2 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7.5e-25)
         (not (or (<= y -4.5e-130) (and (not (<= y -3e-229)) (<= y 5.2e+14)))))
   (* y (/ (- z t) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7.5e-25) || !((y <= -4.5e-130) || (!(y <= -3e-229) && (y <= 5.2e+14)))) {
		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 <= (-7.5d-25)) .or. (.not. (y <= (-4.5d-130)) .or. (.not. (y <= (-3d-229))) .and. (y <= 5.2d+14))) 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 <= -7.5e-25) || !((y <= -4.5e-130) || (!(y <= -3e-229) && (y <= 5.2e+14)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7.5e-25) or not ((y <= -4.5e-130) or (not (y <= -3e-229) and (y <= 5.2e+14))):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7.5e-25) || !((y <= -4.5e-130) || (!(y <= -3e-229) && (y <= 5.2e+14))))
		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 <= -7.5e-25) || ~(((y <= -4.5e-130) || (~((y <= -3e-229)) && (y <= 5.2e+14)))))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7.5e-25], N[Not[Or[LessEqual[y, -4.5e-130], And[N[Not[LessEqual[y, -3e-229]], $MachinePrecision], LessEqual[y, 5.2e+14]]]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999989e-25 or -4.5e-130 < y < -3.00000000000000002e-229 or 5.2e14 < y

   1. Initial program 88.3%

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

      1. associate-/l* 97.3%

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

   3. Simplified 97.3%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-*r/ 95.9%

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

   7. Simplified 95.9%

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

   8. Taylor expanded in x around 0 88.3%

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

      1. +-commutative 88.3%

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

      2. associate-/l* 97.3%

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

   10. Simplified 97.3%

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

   11. Taylor expanded in y around inf 77.8%

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

       1. div-sub 79.2%

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

   13. Simplified 79.2%

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

   if -7.49999999999999989e-25 < y < -4.5e-130 or -3.00000000000000002e-229 < y < 5.2e14

   1. Initial program 99.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 64.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-25} \lor \neg \left(y \leq -4.5 \cdot 10^{-130} \lor \neg \left(y \leq -3 \cdot 10^{-229}\right) \land y \leq 5.2 \cdot 10^{+14}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{-y}}\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a (- y)))))
   (if (<= t -2.8e+17)
     t_1
     (if (<= t 8.8e-275)
       x
       (if (<= t 2.7e-80) (/ y (/ a z)) (if (<= t 9.5e+76) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / -y);
	double tmp;
	if (t <= -2.8e+17) {
		tmp = t_1;
	} else if (t <= 8.8e-275) {
		tmp = x;
	} else if (t <= 2.7e-80) {
		tmp = y / (a / z);
	} else if (t <= 9.5e+76) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (a / -y)
    if (t <= (-2.8d+17)) then
        tmp = t_1
    else if (t <= 8.8d-275) then
        tmp = x
    else if (t <= 2.7d-80) then
        tmp = y / (a / z)
    else if (t <= 9.5d+76) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / -y);
	double tmp;
	if (t <= -2.8e+17) {
		tmp = t_1;
	} else if (t <= 8.8e-275) {
		tmp = x;
	} else if (t <= 2.7e-80) {
		tmp = y / (a / z);
	} else if (t <= 9.5e+76) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / -y)
	tmp = 0
	if t <= -2.8e+17:
		tmp = t_1
	elif t <= 8.8e-275:
		tmp = x
	elif t <= 2.7e-80:
		tmp = y / (a / z)
	elif t <= 9.5e+76:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / Float64(-y)))
	tmp = 0.0
	if (t <= -2.8e+17)
		tmp = t_1;
	elseif (t <= 8.8e-275)
		tmp = x;
	elseif (t <= 2.7e-80)
		tmp = Float64(y / Float64(a / z));
	elseif (t <= 9.5e+76)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / -y);
	tmp = 0.0;
	if (t <= -2.8e+17)
		tmp = t_1;
	elseif (t <= 8.8e-275)
		tmp = x;
	elseif (t <= 2.7e-80)
		tmp = y / (a / z);
	elseif (t <= 9.5e+76)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+17], t$95$1, If[LessEqual[t, 8.8e-275], x, If[LessEqual[t, 2.7e-80], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e+76], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8e17 or 9.5000000000000003e76 < t

   1. Initial program 93.2%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in y around 0 93.2%

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

      1. *-commutative 93.2%

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

      2. associate-*r/ 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in z around 0 82.5%

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

      1. associate-*l/ 79.0%

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

      2. *-commutative 79.0%

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

      3. neg-mul-1 79.0%

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

      4. sub-neg 79.0%

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

      5. *-commutative 79.0%

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

      6. associate-*l/ 82.5%

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

      7. associate-*r/ 85.8%

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

   10. Simplified 85.8%

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

       1. *-commutative 85.8%

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

       2. associate-*l/ 82.5%

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

   12. Applied egg-rr 82.5%

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

   13. Taylor expanded in x around 0 63.5%

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

       1. mul-1-neg 63.5%

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

       2. associate-*l/ 60.0%

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

       3. associate-/r/ 65.9%

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

   15. Simplified 65.9%

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

   if -2.8e17 < t < 8.79999999999999955e-275 or 2.7000000000000002e-80 < t < 9.5000000000000003e76

   1. Initial program 95.4%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf 58.4%

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

   if 8.79999999999999955e-275 < t < 2.7000000000000002e-80

   1. Initial program 87.8%

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

      1. associate-/l* 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in y around 0 87.8%

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

      1. *-commutative 87.8%

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

      2. associate-*r/ 97.4%

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

   7. Simplified 97.4%

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

   8. Taylor expanded in x around 0 87.8%

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

      1. +-commutative 87.8%

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

      2. associate-/l* 92.6%

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

   10. Simplified 92.6%

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

   11. Taylor expanded in z around inf 49.5%

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

       1. associate-*r/ 54.3%

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

   13. Simplified 54.3%

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

       1. clear-num 54.3%

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

       2. un-div-inv 56.6%

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

   15. Applied egg-rr 56.6%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-275}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-80}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4000000000 \lor \neg \left(y \leq 6.6 \cdot 10^{+39}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4000000000.0) (not (<= y 6.6e+39)))
   (* y (/ (- z t) a))
   (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4000000000.0) || !(y <= 6.6e+39)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4000000000.0d0)) .or. (.not. (y <= 6.6d+39))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4000000000.0) || !(y <= 6.6e+39)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4000000000.0) or not (y <= 6.6e+39):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4000000000.0) || !(y <= 6.6e+39))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4000000000.0) || ~((y <= 6.6e+39)))
		tmp = y * ((z - t) / a);
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4000000000.0], N[Not[LessEqual[y, 6.6e+39]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4e9 or 6.60000000000000042e39 < y

   1. Initial program 85.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 85.9%

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

      1. *-commutative 85.9%

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

      2. associate-*r/ 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in x around 0 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-/l* 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in y around inf 83.3%

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

       1. div-sub 84.1%

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

   13. Simplified 84.1%

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

   if -4e9 < y < 6.60000000000000042e39

   1. Initial program 99.9%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in z around inf 80.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4000000000 \lor \neg \left(y \leq 6.6 \cdot 10^{+39}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+101} \lor \neg \left(z \leq 2.6 \cdot 10^{+155}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.4e+101) (not (<= z 2.6e+155)))
   (+ x (/ y (/ a z)))
   (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e+101) || !(z <= 2.6e+155)) {
		tmp = x + (y / (a / z));
	} 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 <= (-6.4d+101)) .or. (.not. (z <= 2.6d+155))) then
        tmp = x + (y / (a / z))
    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 <= -6.4e+101) || !(z <= 2.6e+155)) {
		tmp = x + (y / (a / z));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.4e+101) or not (z <= 2.6e+155):
		tmp = x + (y / (a / z))
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.4e+101) || !(z <= 2.6e+155))
		tmp = Float64(x + Float64(y / Float64(a / z)));
	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 <= -6.4e+101) || ~((z <= 2.6e+155)))
		tmp = x + (y / (a / z));
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.4e+101], N[Not[LessEqual[z, 2.6e+155]], $MachinePrecision]], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.4000000000000001e101 or 2.6000000000000002e155 < z

   1. Initial program 83.4%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in t around 0 78.6%

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

      1. +-commutative 78.6%

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

      2. associate-/l* 83.4%

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

   7. Simplified 83.4%

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

      1. clear-num 62.5%

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

      2. un-div-inv 64.5%

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

   9. Applied egg-rr 85.4%

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

   if -6.4000000000000001e101 < z < 2.6000000000000002e155

   1. Initial program 97.8%

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

      1. associate-/l* 95.1%

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

   3. Simplified 95.1%

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

   5. Taylor expanded in y around 0 97.8%

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

      1. *-commutative 97.8%

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

      2. associate-*r/ 96.8%

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

   7. Simplified 96.8%

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

   8. Taylor expanded in z around 0 88.4%

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

      1. associate-*l/ 85.7%

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

      2. *-commutative 85.7%

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

      3. neg-mul-1 85.7%

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

      4. sub-neg 85.7%

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

      5. *-commutative 85.7%

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

      6. associate-*l/ 88.4%

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

      7. associate-*r/ 89.6%

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

   10. Simplified 89.6%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+101} \lor \neg \left(z \leq 2.6 \cdot 10^{+155}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+104} \lor \neg \left(y \leq 9 \cdot 10^{+39}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.4e+104) (not (<= y 9e+39))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.4e+104) || !(y <= 9e+39)) {
		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 <= (-2.4d+104)) .or. (.not. (y <= 9d+39))) 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 <= -2.4e+104) || !(y <= 9e+39)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.4e+104) or not (y <= 9e+39):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.4e+104) || !(y <= 9e+39))
		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 <= -2.4e+104) || ~((y <= 9e+39)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.4e+104], N[Not[LessEqual[y, 9e+39]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e104 or 8.99999999999999991e39 < y

   1. Initial program 85.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 85.1%

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

      1. *-commutative 85.1%

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

      2. associate-*r/ 95.7%

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

   7. Simplified 95.7%

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

   8. Taylor expanded in x around 0 85.1%

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

      1. +-commutative 85.1%

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

      2. associate-/l* 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in z around inf 39.0%

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

       1. associate-*r/ 47.8%

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

   13. Simplified 47.8%

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

   if -2.4e104 < y < 8.99999999999999991e39

   1. Initial program 99.3%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around inf 56.7%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+104} \lor \neg \left(y \leq 9 \cdot 10^{+39}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+117} \lor \neg \left(z \leq 8.8 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.05e+117) (not (<= z 8.8e+113))) (/ y (/ a z)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.05e+117) || !(z <= 8.8e+113)) {
		tmp = y / (a / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.05d+117)) .or. (.not. (z <= 8.8d+113))) then
        tmp = y / (a / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.05e+117) || !(z <= 8.8e+113)) {
		tmp = y / (a / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.05e+117) or not (z <= 8.8e+113):
		tmp = y / (a / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.05e+117) || !(z <= 8.8e+113))
		tmp = Float64(y / Float64(a / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.05e+117) || ~((z <= 8.8e+113)))
		tmp = y / (a / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.05e+117], N[Not[LessEqual[z, 8.8e+113]], $MachinePrecision]], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -3.0500000000000002e117 or 8.80000000000000041e113 < z

   1. Initial program 83.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around 0 83.8%

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

      1. *-commutative 83.8%

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

      2. associate-*r/ 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in x around 0 83.8%

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

      1. +-commutative 83.8%

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

      2. associate-/l* 89.5%

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

   10. Simplified 89.5%

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

   11. Taylor expanded in z around inf 57.7%

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

       1. associate-*r/ 61.2%

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

   13. Simplified 61.2%

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

       1. clear-num 61.1%

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

       2. un-div-inv 63.1%

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

   15. Applied egg-rr 63.1%

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

   if -3.0500000000000002e117 < z < 8.80000000000000041e113

   1. Initial program 97.8%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in x around inf 48.4%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.05 \cdot 10^{+117} \lor \neg \left(z \leq 8.8 \cdot 10^{+113}\right):\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 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 93.3%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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. Final simplification 93.7%

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

Alternative 9: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

   1. associate-/l* 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 93.3%

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

   1. *-commutative 93.3%

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

   2. associate-*r/ 96.9%

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

7. Simplified 96.9%

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

8. Final simplification 96.9%

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

Alternative 10: 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 93.3%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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 39.5%

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

6. Final simplification 39.5%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024072 
(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)))