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

Percentage Accurate: 93.7% → 98.7%

Time: 11.1s

Alternatives: 13

Speedup: 0.5×

• 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: 93.7% 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: 98.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-26} \lor \neg \left(y \leq 2.3 \cdot 10^{-108}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3e-26) (not (<= y 2.3e-108)))
   (+ x (* y (/ (- t z) a)))
   (+ x (/ -1.0 (/ a (* y (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e-26) || !(y <= 2.3e-108)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (-1.0 / (a / (y * (z - t))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3d-26)) .or. (.not. (y <= 2.3d-108))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + ((-1.0d0) / (a / (y * (z - t))))
    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 <= -3e-26) || !(y <= 2.3e-108)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + (-1.0 / (a / (y * (z - t))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3e-26) or not (y <= 2.3e-108):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + (-1.0 / (a / (y * (z - t))))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3e-26) || !(y <= 2.3e-108))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(-1.0 / Float64(a / Float64(y * Float64(z - t)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3e-26) || ~((y <= 2.3e-108)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + (-1.0 / (a / (y * (z - t))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3e-26], N[Not[LessEqual[y, 2.3e-108]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-1.0 / N[(a / N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.00000000000000012e-26 or 2.29999999999999996e-108 < y

   1. Initial program 88.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -3.00000000000000012e-26 < y < 2.29999999999999996e-108

   1. Initial program 99.5%

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

      1. associate-/l* 85.5%

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

   3. Simplified 85.5%

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

      1. associate-*r/ 99.5%

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

      2. clear-num 99.6%

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

   6. Applied egg-rr 99.6%

      \[\leadsto x - \color{blue}{\frac{1}{\frac{a}{y \cdot \left(z - t\right)}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-26} \lor \neg \left(y \leq 2.3 \cdot 10^{-108}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-7} \lor \neg \left(y \leq 3 \cdot 10^{-108}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.85e-7) (not (<= y 3e-108)))
   (+ x (* y (/ (- t z) a)))
   (+ x (/ (* y (- t z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.85e-7) || !(y <= 3e-108)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * (t - 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 <= (-1.85d-7)) .or. (.not. (y <= 3d-108))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + ((y * (t - 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 <= -1.85e-7) || !(y <= 3e-108)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.85e-7) or not (y <= 3e-108):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y * (t - z)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.85e-7) || !(y <= 3e-108))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.85e-7) || ~((y <= 3e-108)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((y * (t - z)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.85e-7], N[Not[LessEqual[y, 3e-108]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85000000000000002e-7 or 2.99999999999999993e-108 < y

   1. Initial program 87.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -1.85000000000000002e-7 < y < 2.99999999999999993e-108

   1. Initial program 99.6%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-7} \lor \neg \left(y \leq 3 \cdot 10^{-108}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-124} \lor \neg \left(y \leq 9.5 \cdot 10^{-216}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.1e-124) (not (<= y 9.5e-216)))
   (+ x (* y (/ (- t z) a)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.1e-124) || !(y <= 9.5e-216)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.1d-124)) .or. (.not. (y <= 9.5d-216))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.1e-124) || !(y <= 9.5e-216)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.1e-124) or not (y <= 9.5e-216):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.1e-124) || !(y <= 9.5e-216))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.1e-124) || ~((y <= 9.5e-216)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.1e-124], N[Not[LessEqual[y, 9.5e-216]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0999999999999999e-124 or 9.49999999999999943e-216 < y

   1. Initial program 91.3%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   if -1.0999999999999999e-124 < y < 9.49999999999999943e-216

   1. Initial program 99.3%

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

      1. associate-/l* 77.7%

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

   3. Simplified 77.7%

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

   5. Taylor expanded in z around 0 92.0%

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

      1. associate-*r/ 92.0%

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

      2. mul-1-neg 92.0%

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

      3. distribute-lft-neg-out 92.0%

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

      4. *-commutative 92.0%

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

   7. Simplified 92.0%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-124} \lor \neg \left(y \leq 9.5 \cdot 10^{-216}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+89}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z - t\right) \cdot \frac{-1}{a}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.7e+72)
   (* y (/ (- t z) a))
   (if (<= y 3.8e+89) (+ x (/ (* y t) a)) (* y (* (- z t) (/ -1.0 a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.7e+72) {
		tmp = y * ((t - z) / a);
	} else if (y <= 3.8e+89) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y * ((z - t) * (-1.0 / 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 <= (-1.7d+72)) then
        tmp = y * ((t - z) / a)
    else if (y <= 3.8d+89) then
        tmp = x + ((y * t) / a)
    else
        tmp = y * ((z - t) * ((-1.0d0) / 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 <= -1.7e+72) {
		tmp = y * ((t - z) / a);
	} else if (y <= 3.8e+89) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y * ((z - t) * (-1.0 / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.7e+72:
		tmp = y * ((t - z) / a)
	elif y <= 3.8e+89:
		tmp = x + ((y * t) / a)
	else:
		tmp = y * ((z - t) * (-1.0 / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.7e+72)
		tmp = Float64(y * Float64(Float64(t - z) / a));
	elseif (y <= 3.8e+89)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(y * Float64(Float64(z - t) * Float64(-1.0 / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.7e+72)
		tmp = y * ((t - z) / a);
	elseif (y <= 3.8e+89)
		tmp = x + ((y * t) / a);
	else
		tmp = y * ((z - t) * (-1.0 / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.7e+72], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e+89], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] * N[(-1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6999999999999999e72

   1. Initial program 84.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 95.9%

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

   6. Taylor expanded in a around 0 82.9%

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

      1. associate-/l* 98.0%

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

      2. *-commutative 98.0%

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

   8. Applied egg-rr 98.0%

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

   if -1.6999999999999999e72 < y < 3.80000000000000023e89

   1. Initial program 97.8%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 82.8%

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

      1. associate-*r/ 82.8%

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

      2. mul-1-neg 82.8%

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

      3. distribute-lft-neg-out 82.8%

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

      4. *-commutative 82.8%

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

   7. Simplified 82.8%

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

   if 3.80000000000000023e89 < y

   1. Initial program 86.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 70.1%

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

      1. mul-1-neg 70.1%

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

      2. distribute-frac-neg2 70.1%

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

      3. associate-*r/ 83.6%

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

   7. Simplified 83.6%

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

      1. div-sub 81.5%

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

      2. sub-neg 81.5%

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

      3. distribute-frac-neg 81.5%

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

      4. frac-2neg 81.5%

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

      5. +-commutative 81.5%

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

      6. distribute-frac-neg2 81.5%

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

      7. sub-neg 81.5%

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

      8. div-inv 81.5%

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

      9. div-inv 81.5%

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

      10. distribute-rgt-out-- 83.6%

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

   9. Applied egg-rr 83.6%

      \[\leadsto y \cdot \color{blue}{\left(\frac{1}{a} \cdot \left(t - z\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+89}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(z - t\right) \cdot \frac{-1}{a}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+72} \lor \neg \left(y \leq 9.2 \cdot 10^{+85}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.65e+72) (not (<= y 9.2e+85)))
   (* y (/ (- t z) a))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.65e+72) || !(y <= 9.2e+85)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.65d+72)) .or. (.not. (y <= 9.2d+85))) then
        tmp = y * ((t - z) / a)
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.65e+72) || !(y <= 9.2e+85)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.65e+72) or not (y <= 9.2e+85):
		tmp = y * ((t - z) / a)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.65e+72) || !(y <= 9.2e+85))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.65e+72) || ~((y <= 9.2e+85)))
		tmp = y * ((t - z) / a);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.65e+72], N[Not[LessEqual[y, 9.2e+85]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.65e72 or 9.1999999999999996e85 < y

   1. Initial program 85.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 88.8%

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

   6. Taylor expanded in a around 0 76.6%

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

      1. associate-/l* 90.8%

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

      2. *-commutative 90.8%

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

   8. Applied egg-rr 90.8%

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

   if -1.65e72 < y < 9.1999999999999996e85

   1. Initial program 97.8%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 82.8%

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

      1. associate-*r/ 82.8%

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

      2. mul-1-neg 82.8%

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

      3. distribute-lft-neg-out 82.8%

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

      4. *-commutative 82.8%

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

   7. Simplified 82.8%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+72} \lor \neg \left(y \leq 9.2 \cdot 10^{+85}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+72} \lor \neg \left(y \leq 4.5 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.6e+72) (not (<= y 4.5e+102)))
   (* y (/ (- t z) a))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.6e+72) || !(y <= 4.5e+102)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.6d+72)) .or. (.not. (y <= 4.5d+102))) then
        tmp = y * ((t - z) / a)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.6e+72) || !(y <= 4.5e+102)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.6e+72) or not (y <= 4.5e+102):
		tmp = y * ((t - z) / a)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.6e+72) || !(y <= 4.5e+102))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.6e+72) || ~((y <= 4.5e+102)))
		tmp = y * ((t - z) / a);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.6e+72], N[Not[LessEqual[y, 4.5e+102]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6000000000000001e72 or 4.50000000000000021e102 < y

   1. Initial program 85.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 89.3%

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

   6. Taylor expanded in a around 0 76.6%

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

      1. associate-/l* 91.5%

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

      2. *-commutative 91.5%

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

   8. Applied egg-rr 91.5%

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

   if -1.6000000000000001e72 < y < 4.50000000000000021e102

   1. Initial program 97.8%

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

      1. associate-*r/ 90.0%

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

      2. *-commutative 90.0%

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

      3. div-inv 89.9%

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

      4. associate-*l* 95.7%

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

   4. Applied egg-rr 95.7%

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

   5. Taylor expanded in z around 0 81.7%

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

      1. neg-mul-1 81.7%

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

   7. Simplified 81.7%

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

      1. cancel-sign-sub 81.7%

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

      2. associate-*l/ 81.7%

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

      3. *-un-lft-identity 81.7%

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

      4. +-commutative 81.7%

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

   9. Applied egg-rr 81.7%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+72} \lor \neg \left(y \leq 4.5 \cdot 10^{+102}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-141} \lor \neg \left(y \leq 3.5 \cdot 10^{-97}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -7.5e-141) (not (<= y 3.5e-97))) (* y (/ (- t z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -7.5e-141) || !(y <= 3.5e-97)) {
		tmp = y * ((t - 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 <= (-7.5d-141)) .or. (.not. (y <= 3.5d-97))) then
        tmp = y * ((t - 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 <= -7.5e-141) || !(y <= 3.5e-97)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -7.5e-141) or not (y <= 3.5e-97):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -7.5e-141) || !(y <= 3.5e-97))
		tmp = Float64(y * Float64(Float64(t - z) / 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-141) || ~((y <= 3.5e-97)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -7.5e-141], N[Not[LessEqual[y, 3.5e-97]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000046e-141 or 3.50000000000000019e-97 < y

   1. Initial program 90.0%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around inf 73.5%

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

   6. Taylor expanded in a around 0 67.7%

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

      1. associate-/l* 76.4%

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

      2. *-commutative 76.4%

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

   8. Applied egg-rr 76.4%

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

   if -7.50000000000000046e-141 < y < 3.50000000000000019e-97

   1. Initial program 99.5%

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

      1. associate-/l* 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in x around inf 63.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-141} \lor \neg \left(y \leq 3.5 \cdot 10^{-97}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-145} \lor \neg \left(y \leq 5.4 \cdot 10^{-98}\right):\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.1e-145) (not (<= y 5.4e-98))) (* (- t z) (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.1e-145) || !(y <= 5.4e-98)) {
		tmp = (t - z) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-6.1d-145)) .or. (.not. (y <= 5.4d-98))) then
        tmp = (t - z) * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.1e-145) || !(y <= 5.4e-98)) {
		tmp = (t - z) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.1e-145) or not (y <= 5.4e-98):
		tmp = (t - z) * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.1e-145) || !(y <= 5.4e-98))
		tmp = Float64(Float64(t - z) * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.1e-145) || ~((y <= 5.4e-98)))
		tmp = (t - z) * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.1e-145], N[Not[LessEqual[y, 5.4e-98]], $MachinePrecision]], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.1e-145 or 5.3999999999999997e-98 < y

   1. Initial program 90.1%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around 0 67.5%

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

      1. associate-*r/ 67.5%

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

      2. neg-mul-1 67.5%

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

      3. *-commutative 67.5%

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

      4. distribute-lft-neg-in 67.5%

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

      5. associate-*r/ 74.0%

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

      6. *-commutative 74.0%

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

      7. neg-sub0 74.0%

         \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(0 - \left(z - t\right)\right)} \]

      8. sub-neg 74.0%

         \[\leadsto \frac{y}{a} \cdot \left(0 - \color{blue}{\left(z + \left(-t\right)\right)}\right) \]

      9. +-commutative 74.0%

         \[\leadsto \frac{y}{a} \cdot \left(0 - \color{blue}{\left(\left(-t\right) + z\right)}\right) \]

      10. associate--r+ 74.0%

          \[\leadsto \frac{y}{a} \cdot \color{blue}{\left(\left(0 - \left(-t\right)\right) - z\right)} \]

      11. neg-sub0 74.0%

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

      12. remove-double-neg 74.0%

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

   7. Simplified 74.0%

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

   if -6.1e-145 < y < 5.3999999999999997e-98

   1. Initial program 99.5%

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

      1. associate-/l* 82.7%

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

   3. Simplified 82.7%

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

   5. Taylor expanded in x around inf 64.3%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{-145} \lor \neg \left(y \leq 5.4 \cdot 10^{-98}\right):\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+63} \lor \neg \left(y \leq 2.45 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.25e+63) (not (<= y 2.45e+14))) (* z (/ y (- a))) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.25e+63) || !(y <= 2.45e+14)) {
		tmp = z * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.25d+63)) .or. (.not. (y <= 2.45d+14))) then
        tmp = z * (y / -a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.25e+63) || !(y <= 2.45e+14)) {
		tmp = z * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.25e+63) or not (y <= 2.45e+14):
		tmp = z * (y / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.25e+63) || !(y <= 2.45e+14))
		tmp = Float64(z * Float64(y / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.25e+63) || ~((y <= 2.45e+14)))
		tmp = z * (y / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.25e+63], N[Not[LessEqual[y, 2.45e+14]], $MachinePrecision]], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.24999999999999996e63 or 2.45e14 < y

   1. Initial program 86.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 49.7%

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

      1. mul-1-neg 49.7%

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

      2. associate-/l* 56.7%

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

      3. distribute-rgt-neg-in 56.7%

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

      4. distribute-frac-neg2 56.7%

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

   7. Simplified 56.7%

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

      1. associate-*r/ 49.7%

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

      2. distribute-frac-neg2 49.7%

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

      3. *-commutative 49.7%

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

      4. add-sqr-sqrt 24.4%

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

      5. sqrt-unprod 27.3%

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

      6. sqr-neg 27.3%

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

      7. sqrt-unprod 4.1%

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

      8. add-sqr-sqrt 6.6%

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

      9. associate-*l/ 6.7%

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

      10. div-inv 6.7%

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

      11. associate-*l* 8.5%

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

      12. add-sqr-sqrt 5.9%

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

      13. sqrt-unprod 30.1%

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

      14. sqr-neg 30.1%

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

      15. sqrt-unprod 29.6%

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

      16. add-sqr-sqrt 59.4%

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

      17. *-commutative 59.4%

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

      18. div-inv 59.4%

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

   9. Applied egg-rr 59.4%

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

   if -3.24999999999999996e63 < y < 2.45e14

   1. Initial program 97.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 56.2%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.25 \cdot 10^{+63} \lor \neg \left(y \leq 2.45 \cdot 10^{+14}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{-y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.35e+61)
   (* z (/ y (- a)))
   (if (<= y 9.5e+16) x (/ z (/ a (- y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.35e+61) {
		tmp = z * (y / -a);
	} else if (y <= 9.5e+16) {
		tmp = x;
	} else {
		tmp = z / (a / -y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.35d+61)) then
        tmp = z * (y / -a)
    else if (y <= 9.5d+16) then
        tmp = x
    else
        tmp = z / (a / -y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.35e+61) {
		tmp = z * (y / -a);
	} else if (y <= 9.5e+16) {
		tmp = x;
	} else {
		tmp = z / (a / -y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.35e+61:
		tmp = z * (y / -a)
	elif y <= 9.5e+16:
		tmp = x
	else:
		tmp = z / (a / -y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.35e+61)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (y <= 9.5e+16)
		tmp = x;
	else
		tmp = Float64(z / Float64(a / Float64(-y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.35e+61)
		tmp = z * (y / -a);
	elseif (y <= 9.5e+16)
		tmp = x;
	else
		tmp = z / (a / -y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.35e+61], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+16], x, N[(z / N[(a / (-y)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3499999999999999e61

   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 z around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. associate-/l* 68.8%

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

      3. distribute-rgt-neg-in 68.8%

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

      4. distribute-frac-neg2 68.8%

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

   7. Simplified 68.8%

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

      1. associate-*r/ 61.5%

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

      2. distribute-frac-neg2 61.5%

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

      3. *-commutative 61.5%

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

      4. add-sqr-sqrt 30.7%

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

      5. sqrt-unprod 30.9%

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

      6. sqr-neg 30.9%

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

      7. sqrt-unprod 0.3%

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

      8. add-sqr-sqrt 2.8%

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

      9. associate-*l/ 2.9%

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

      10. div-inv 2.9%

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

      11. associate-*l* 4.8%

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

      12. add-sqr-sqrt 2.2%

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

      13. sqrt-unprod 36.6%

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

      14. sqr-neg 36.6%

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

      15. sqrt-unprod 34.3%

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

      16. add-sqr-sqrt 70.7%

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

      17. *-commutative 70.7%

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

      18. div-inv 70.8%

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

   9. Applied egg-rr 70.8%

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

   if -2.3499999999999999e61 < y < 9.5e16

   1. Initial program 97.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 56.2%

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

   if 9.5e16 < y

   1. Initial program 88.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 39.2%

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

      1. mul-1-neg 39.2%

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

      2. associate-/l* 46.0%

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

      3. distribute-rgt-neg-in 46.0%

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

      4. distribute-frac-neg2 46.0%

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

   7. Simplified 46.0%

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

      1. associate-*r/ 39.2%

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

      2. distribute-frac-neg2 39.2%

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

      3. *-commutative 39.2%

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

      4. add-sqr-sqrt 18.9%

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

      5. sqrt-unprod 24.1%

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

      6. sqr-neg 24.1%

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

      7. sqrt-unprod 7.5%

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

      8. add-sqr-sqrt 10.0%

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

      9. associate-*l/ 10.0%

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

      10. div-inv 10.0%

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

      11. associate-*l* 11.8%

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

      12. add-sqr-sqrt 9.3%

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

      13. sqrt-unprod 24.2%

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

      14. sqr-neg 24.2%

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

      15. sqrt-unprod 25.4%

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

      16. add-sqr-sqrt 49.2%

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

      17. *-commutative 49.2%

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

      18. div-inv 49.2%

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

   9. Applied egg-rr 49.2%

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

       1. distribute-lft-neg-in 49.2%

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

       2. clear-num 49.2%

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

       3. un-div-inv 49.7%

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

   11. Applied egg-rr 49.7%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{a}{-y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+32} \lor \neg \left(t \leq 4.4 \cdot 10^{+73}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.05e+32) (not (<= t 4.4e+73))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.05e+32) || !(t <= 4.4e+73)) {
		tmp = 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 ((t <= (-3.05d+32)) .or. (.not. (t <= 4.4d+73))) then
        tmp = 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 ((t <= -3.05e+32) || !(t <= 4.4e+73)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.05e+32) or not (t <= 4.4e+73):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.05e+32) || !(t <= 4.4e+73))
		tmp = Float64(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 ((t <= -3.05e+32) || ~((t <= 4.4e+73)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.05e+32], N[Not[LessEqual[t, 4.4e+73]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -3.05000000000000014e32 or 4.4e73 < t

   1. Initial program 91.4%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in x around 0 76.0%

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

      1. mul-1-neg 76.0%

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

      2. distribute-frac-neg2 76.0%

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

      3. associate-*r/ 75.7%

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

   7. Simplified 75.7%

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

   8. Taylor expanded in z around 0 62.9%

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

      1. associate-/l* 64.1%

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

   10. Simplified 64.1%

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

   if -3.05000000000000014e32 < t < 4.4e73

   1. Initial program 94.3%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf 51.2%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.05 \cdot 10^{+32} \lor \neg \left(t \leq 4.4 \cdot 10^{+73}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.42 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+69}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.42e+23) (/ t (/ a y)) (if (<= t 4e+69) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.42e+23) {
		tmp = t / (a / y);
	} else if (t <= 4e+69) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.42d+23)) then
        tmp = t / (a / y)
    else if (t <= 4d+69) then
        tmp = x
    else
        tmp = 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 <= -1.42e+23) {
		tmp = t / (a / y);
	} else if (t <= 4e+69) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.42e+23:
		tmp = t / (a / y)
	elif t <= 4e+69:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.42e+23)
		tmp = Float64(t / Float64(a / y));
	elseif (t <= 4e+69)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.42e+23)
		tmp = t / (a / y);
	elseif (t <= 4e+69)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.42e+23], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4e+69], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.42000000000000004e23

   1. Initial program 94.2%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around 0 78.8%

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

      1. mul-1-neg 78.8%

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

      2. distribute-frac-neg2 78.8%

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

      3. associate-*r/ 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in z around 0 62.3%

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

      1. associate-/l* 62.9%

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

   10. Simplified 62.9%

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

       1. clear-num 62.8%

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

       2. un-div-inv 62.9%

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

   12. Applied egg-rr 62.9%

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

   if -1.42000000000000004e23 < t < 4.0000000000000003e69

   1. Initial program 94.3%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around inf 51.2%

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

   if 4.0000000000000003e69 < t

   1. Initial program 88.6%

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

      1. associate-/l* 88.4%

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

   3. Simplified 88.4%

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

   5. Taylor expanded in x around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. distribute-frac-neg2 73.1%

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

      3. associate-*r/ 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in z around 0 63.6%

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

      1. associate-/l* 65.3%

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

   10. Simplified 65.3%

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

Alternative 13: 40.2% 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 93.2%

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

   1. associate-/l* 93.6%

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

3. Simplified 93.6%

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

5. Taylor expanded in x around inf 38.2%

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

Developer Target 1: 99.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024157 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

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

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