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

Percentage Accurate: 93.3% → 98.8%

Time: 10.2s

Alternatives: 12

Speedup: 1.0×

• 25.3% 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: 93.3% 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: 98.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+72}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+72)))
     (+ x (* y (/ (- t z) a)))
     (+ x (/ (* y (- t z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+72)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+72)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+72):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y * (t - z)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+72))
		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)
	t_1 = y * (z - t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+72)))
		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_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+72]], $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 (*.f64 y (-.f64 z t)) < -inf.0 or 1.99999999999999989e72 < (*.f64 y (-.f64 z t))

   1. Initial program 81.5%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

      3. clear-num 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 1.99999999999999989e72

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -\infty \lor \neg \left(y \cdot \left(z - t\right) \leq 2 \cdot 10^{+72}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-47}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+56} \lor \neg \left(z \leq 3.3 \cdot 10^{+104}\right) \land z \leq 2.1 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e-47)
   (- x (/ z (/ a y)))
   (if (or (<= z 3.2e+56) (and (not (<= z 3.3e+104)) (<= z 2.1e+125)))
     (+ x (* y (/ t a)))
     (- x (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e-47) {
		tmp = x - (z / (a / y));
	} else if ((z <= 3.2e+56) || (!(z <= 3.3e+104) && (z <= 2.1e+125))) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1d-47)) then
        tmp = x - (z / (a / y))
    else if ((z <= 3.2d+56) .or. (.not. (z <= 3.3d+104)) .and. (z <= 2.1d+125)) then
        tmp = x + (y * (t / a))
    else
        tmp = x - (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e-47) {
		tmp = x - (z / (a / y));
	} else if ((z <= 3.2e+56) || (!(z <= 3.3e+104) && (z <= 2.1e+125))) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e-47:
		tmp = x - (z / (a / y))
	elif (z <= 3.2e+56) or (not (z <= 3.3e+104) and (z <= 2.1e+125)):
		tmp = x + (y * (t / a))
	else:
		tmp = x - (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e-47)
		tmp = Float64(x - Float64(z / Float64(a / y)));
	elseif ((z <= 3.2e+56) || (!(z <= 3.3e+104) && (z <= 2.1e+125)))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e-47)
		tmp = x - (z / (a / y));
	elseif ((z <= 3.2e+56) || (~((z <= 3.3e+104)) && (z <= 2.1e+125)))
		tmp = x + (y * (t / a));
	else
		tmp = x - (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e-47], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.2e+56], And[N[Not[LessEqual[z, 3.3e+104]], $MachinePrecision], LessEqual[z, 2.1e+125]]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.9999999999999997e-48

   1. Initial program 92.4%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around inf 76.7%

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

      1. associate-*l/ 80.2%

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

      2. *-commutative 80.2%

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

   7. Simplified 80.2%

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

      1. clear-num 80.2%

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

      2. div-inv 80.2%

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

   9. Applied egg-rr 80.2%

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

   if -9.9999999999999997e-48 < z < 3.20000000000000003e56 or 3.29999999999999985e104 < z < 2.1000000000000001e125

   1. Initial program 96.0%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

      1. *-commutative 95.3%

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

      2. clear-num 94.7%

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

      3. un-div-inv 94.7%

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

   6. Applied egg-rr 94.7%

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

   7. Taylor expanded in z around 0 90.4%

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

      1. mul-1-neg 90.4%

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

      2. associate-*l/ 90.9%

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

      3. distribute-rgt-neg-in 90.9%

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

   9. Simplified 90.9%

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

   if 3.20000000000000003e56 < z < 3.29999999999999985e104 or 2.1000000000000001e125 < z

   1. Initial program 85.1%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 79.1%

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

      1. associate-*l/ 91.7%

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

      2. *-commutative 91.7%

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

   7. Simplified 91.7%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{-47}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+56} \lor \neg \left(z \leq 3.3 \cdot 10^{+104}\right) \land z \leq 2.1 \cdot 10^{+125}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-48}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+55}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+103} \lor \neg \left(z \leq 2.3 \cdot 10^{+125}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.5e-48)
   (- x (/ z (/ a y)))
   (if (<= z 4.4e+55)
     (- x (/ y (/ (- a) t)))
     (if (or (<= z 9e+103) (not (<= z 2.3e+125)))
       (- x (* z (/ y a)))
       (+ x (* y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e-48) {
		tmp = x - (z / (a / y));
	} else if (z <= 4.4e+55) {
		tmp = x - (y / (-a / t));
	} else if ((z <= 9e+103) || !(z <= 2.3e+125)) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-3.5d-48)) then
        tmp = x - (z / (a / y))
    else if (z <= 4.4d+55) then
        tmp = x - (y / (-a / t))
    else if ((z <= 9d+103) .or. (.not. (z <= 2.3d+125))) then
        tmp = x - (z * (y / a))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.5e-48) {
		tmp = x - (z / (a / y));
	} else if (z <= 4.4e+55) {
		tmp = x - (y / (-a / t));
	} else if ((z <= 9e+103) || !(z <= 2.3e+125)) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.5e-48:
		tmp = x - (z / (a / y))
	elif z <= 4.4e+55:
		tmp = x - (y / (-a / t))
	elif (z <= 9e+103) or not (z <= 2.3e+125):
		tmp = x - (z * (y / a))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.5e-48)
		tmp = Float64(x - Float64(z / Float64(a / y)));
	elseif (z <= 4.4e+55)
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	elseif ((z <= 9e+103) || !(z <= 2.3e+125))
		tmp = Float64(x - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -3.5e-48)
		tmp = x - (z / (a / y));
	elseif (z <= 4.4e+55)
		tmp = x - (y / (-a / t));
	elseif ((z <= 9e+103) || ~((z <= 2.3e+125)))
		tmp = x - (z * (y / a));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.5e-48], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+55], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 9e+103], N[Not[LessEqual[z, 2.3e+125]], $MachinePrecision]], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.49999999999999991e-48

   1. Initial program 92.4%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around inf 76.7%

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

      1. associate-*l/ 80.2%

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

      2. *-commutative 80.2%

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

   7. Simplified 80.2%

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

      1. clear-num 80.2%

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

      2. div-inv 80.2%

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

   9. Applied egg-rr 80.2%

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

   if -3.49999999999999991e-48 < z < 4.40000000000000021e55

   1. Initial program 96.4%

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

      1. associate-/l* 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in z around 0 90.6%

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

      1. associate-*r/ 90.6%

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

      2. neg-mul-1 90.6%

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

   7. Simplified 90.6%

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

   if 4.40000000000000021e55 < z < 9.00000000000000002e103 or 2.30000000000000013e125 < z

   1. Initial program 85.1%

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

      1. associate-*l/ 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 79.1%

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

      1. associate-*l/ 91.7%

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

      2. *-commutative 91.7%

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

   7. Simplified 91.7%

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

   if 9.00000000000000002e103 < z < 2.30000000000000013e125

   1. Initial program 90.1%

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

      1. associate-*l/ 89.4%

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

   3. Simplified 89.4%

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

      1. *-commutative 89.4%

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

      2. clear-num 89.2%

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

      3. un-div-inv 89.2%

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

   6. Applied egg-rr 89.2%

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

   7. Taylor expanded in z around 0 90.1%

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

      1. mul-1-neg 90.1%

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

      2. associate-*l/ 99.7%

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

      3. distribute-rgt-neg-in 99.7%

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

   9. Simplified 99.7%

      \[\leadsto x - \color{blue}{\frac{t}{a} \cdot \left(-y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{-48}:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+55}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+103} \lor \neg \left(z \leq 2.3 \cdot 10^{+125}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 83.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+141}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -9.4e+101)
   (+ x (/ (* y t) a))
   (if (<= t 1.7e+141) (- x (* z (/ y a))) (- x (/ y (/ (- a) t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.4e+101) {
		tmp = x + ((y * t) / a);
	} else if (t <= 1.7e+141) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x - (y / (-a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-9.4d+101)) then
        tmp = x + ((y * t) / a)
    else if (t <= 1.7d+141) then
        tmp = x - (z * (y / a))
    else
        tmp = x - (y / (-a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -9.4e+101) {
		tmp = x + ((y * t) / a);
	} else if (t <= 1.7e+141) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x - (y / (-a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -9.4e+101:
		tmp = x + ((y * t) / a)
	elif t <= 1.7e+141:
		tmp = x - (z * (y / a))
	else:
		tmp = x - (y / (-a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -9.4e+101)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	elseif (t <= 1.7e+141)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - Float64(y / Float64(Float64(-a) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -9.4e+101)
		tmp = x + ((y * t) / a);
	elseif (t <= 1.7e+141)
		tmp = x - (z * (y / a));
	else
		tmp = x - (y / (-a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -9.4e+101], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.7e+141], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[((-a) / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.39999999999999941e101

   1. Initial program 97.2%

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

   3. Taylor expanded in z around 0 91.2%

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

      1. mul-1-neg 91.2%

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

      2. distribute-lft-neg-out 91.2%

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

      3. *-commutative 91.2%

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

   5. Simplified 91.2%

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

   if -9.39999999999999941e101 < t < 1.6999999999999999e141

   1. Initial program 91.7%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in z around inf 79.0%

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

      1. associate-*l/ 83.7%

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

      2. *-commutative 83.7%

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

   7. Simplified 83.7%

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

   if 1.6999999999999999e141 < t

   1. Initial program 95.5%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in z around 0 90.4%

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

      1. associate-*r/ 90.4%

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

      2. neg-mul-1 90.4%

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

   7. Simplified 90.4%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.4 \cdot 10^{+101}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{+141}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{-a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-67} \lor \neg \left(z \leq 2.6 \cdot 10^{+66}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.4e-67) (not (<= z 2.6e+66)))
   (* z (/ y (- a)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e-67) || !(z <= 2.6e+66)) {
		tmp = z * (y / -a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.4d-67)) .or. (.not. (z <= 2.6d+66))) then
        tmp = z * (y / -a)
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.4e-67) || !(z <= 2.6e+66)) {
		tmp = z * (y / -a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.4e-67) or not (z <= 2.6e+66):
		tmp = z * (y / -a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.4e-67) || !(z <= 2.6e+66))
		tmp = Float64(z * Float64(y / Float64(-a)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.4e-67) || ~((z <= 2.6e+66)))
		tmp = z * (y / -a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.4e-67], N[Not[LessEqual[z, 2.6e+66]], $MachinePrecision]], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.40000000000000043e-67 or 2.60000000000000012e66 < z

   1. Initial program 89.1%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around inf 74.5%

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

      1. associate-*l/ 82.3%

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

      2. *-commutative 82.3%

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

   7. Simplified 82.3%

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

      1. clear-num 81.7%

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

      2. div-inv 81.7%

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

   9. Applied egg-rr 81.7%

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

   10. Taylor expanded in x around 0 51.2%

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

       1. mul-1-neg 51.2%

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

       2. associate-*l/ 58.6%

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

       3. distribute-rgt-neg-out 58.6%

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

       4. associate-/r/ 54.8%

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

   12. Simplified 54.8%

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

       1. frac-2neg 54.8%

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

       2. remove-double-neg 54.8%

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

       3. associate-/r/ 58.6%

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

   14. Applied egg-rr 58.6%

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

   if -6.40000000000000043e-67 < z < 2.60000000000000012e66

   1. Initial program 96.4%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 62.3%

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

      1. associate-*l/ 62.4%

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

      2. *-commutative 62.4%

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

   7. Simplified 62.4%

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

      1. clear-num 62.4%

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

      2. div-inv 61.7%

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

   9. Applied egg-rr 61.7%

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

       1. sub-neg 61.7%

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

       2. +-commutative 61.7%

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

       3. associate-/r/ 62.3%

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

       4. distribute-rgt-neg-in 62.3%

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

       5. add-sqr-sqrt 39.6%

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

       6. sqrt-unprod 54.9%

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

       7. sqr-neg 54.9%

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

       8. sqrt-unprod 19.1%

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

       9. add-sqr-sqrt 55.3%

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

       10. associate-/r/ 57.5%

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

       11. div-inv 58.2%

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

       12. clear-num 58.2%

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

   11. Applied egg-rr 58.2%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{-67} \lor \neg \left(z \leq 2.6 \cdot 10^{+66}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+95} \lor \neg \left(y \leq 4.1 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.6e+95) (not (<= y 4.1e-19))) (* y (/ (- z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.6e+95) || !(y <= 4.1e-19)) {
		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 <= (-1.6d+95)) .or. (.not. (y <= 4.1d-19))) 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 <= -1.6e+95) || !(y <= 4.1e-19)) {
		tmp = y * (-z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.6e+95) or not (y <= 4.1e-19):
		tmp = y * (-z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.6e+95) || !(y <= 4.1e-19))
		tmp = Float64(y * Float64(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 <= -1.6e+95) || ~((y <= 4.1e-19)))
		tmp = y * (-z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.6e+95], N[Not[LessEqual[y, 4.1e-19]], $MachinePrecision]], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.6e95 or 4.09999999999999985e-19 < y

   1. Initial program 84.7%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in z around inf 57.8%

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

      1. associate-*l/ 67.5%

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

      2. *-commutative 67.5%

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

   7. Simplified 67.5%

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

      1. clear-num 67.5%

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

      2. div-inv 66.7%

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

   9. Applied egg-rr 66.7%

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

   10. Taylor expanded in x around 0 42.1%

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

       1. mul-1-neg 42.1%

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

       2. associate-*r/ 50.0%

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

       3. distribute-rgt-neg-in 50.0%

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

       4. distribute-frac-neg 50.0%

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

   12. Simplified 50.0%

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

   if -1.6e95 < y < 4.09999999999999985e-19

   1. Initial program 99.9%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 76.5%

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

      1. associate-*l/ 75.2%

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

      2. *-commutative 75.2%

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

   7. Simplified 75.2%

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

      1. clear-num 74.7%

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

      2. div-inv 74.7%

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

   9. Applied egg-rr 74.7%

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

   10. Taylor expanded in x around inf 59.6%

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

4. Final simplification 55.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+95} \lor \neg \left(y \leq 4.1 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-67} \lor \neg \left(z \leq 4.9 \cdot 10^{+63}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -7.2e-67) (not (<= z 4.9e+63))) (* z (/ y (- a))) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -7.2e-67) || !(z <= 4.9e+63)) {
		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 ((z <= (-7.2d-67)) .or. (.not. (z <= 4.9d+63))) 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 ((z <= -7.2e-67) || !(z <= 4.9e+63)) {
		tmp = z * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -7.2e-67) or not (z <= 4.9e+63):
		tmp = z * (y / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -7.2e-67) || !(z <= 4.9e+63))
		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 ((z <= -7.2e-67) || ~((z <= 4.9e+63)))
		tmp = z * (y / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -7.2e-67], N[Not[LessEqual[z, 4.9e+63]], $MachinePrecision]], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -7.19999999999999998e-67 or 4.8999999999999997e63 < z

   1. Initial program 89.1%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   5. Taylor expanded in z around inf 74.5%

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

      1. associate-*l/ 82.3%

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

      2. *-commutative 82.3%

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

   7. Simplified 82.3%

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

      1. clear-num 81.7%

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

      2. div-inv 81.7%

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

   9. Applied egg-rr 81.7%

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

   10. Taylor expanded in x around 0 51.2%

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

       1. mul-1-neg 51.2%

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

       2. associate-*l/ 58.6%

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

       3. distribute-rgt-neg-out 58.6%

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

       4. associate-/r/ 54.8%

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

   12. Simplified 54.8%

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

       1. frac-2neg 54.8%

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

       2. remove-double-neg 54.8%

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

       3. associate-/r/ 58.6%

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

   14. Applied egg-rr 58.6%

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

   if -7.19999999999999998e-67 < z < 4.8999999999999997e63

   1. Initial program 96.4%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 62.3%

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

      1. associate-*l/ 62.4%

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

      2. *-commutative 62.4%

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

   7. Simplified 62.4%

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

      1. clear-num 62.4%

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

      2. div-inv 61.7%

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

   9. Applied egg-rr 61.7%

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

   10. Taylor expanded in x around inf 54.5%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.2 \cdot 10^{-67} \lor \neg \left(z \leq 4.9 \cdot 10^{+63}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-158}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.2e-158) (+ x (* y (/ (- t z) a))) (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.2e-158) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.2d-158)) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + ((y / a) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.2e-158) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.2e-158:
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.2e-158)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.2e-158)
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.2e-158], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2000000000000001e-158

   1. Initial program 91.8%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

      1. clear-num 99.3%

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

      2. associate-/r/ 99.0%

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

      3. clear-num 99.1%

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

   6. Applied egg-rr 99.1%

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

   if -2.2000000000000001e-158 < y

   1. Initial program 94.0%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-158}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 96.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-164}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.6e-164) (- x (/ y (/ a (- z t)))) (+ x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.6e-164) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-4.6d-164)) then
        tmp = x - (y / (a / (z - t)))
    else
        tmp = x + ((y / a) * (t - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.6e-164) {
		tmp = x - (y / (a / (z - t)));
	} else {
		tmp = x + ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.6e-164:
		tmp = x - (y / (a / (z - t)))
	else:
		tmp = x + ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.6e-164)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -4.6e-164)
		tmp = x - (y / (a / (z - t)));
	else
		tmp = x + ((y / a) * (t - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.6e-164], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.59999999999999971e-164

   1. Initial program 91.8%

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

      1. associate-/l* 99.4%

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

   3. Simplified 99.4%

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

   if -4.59999999999999971e-164 < y

   1. Initial program 94.0%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-164}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.0%

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

   1. associate-*l/ 96.4%

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

3. Simplified 96.4%

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

5. Final simplification 96.4%

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

Alternative 11: 71.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.0%

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

   1. associate-*l/ 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in z around inf 68.0%

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

   1. associate-*l/ 71.7%

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

   2. *-commutative 71.7%

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

7. Simplified 71.7%

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

8. Final simplification 71.7%

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

Alternative 12: 39.3% 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 93.0%

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

   1. associate-*l/ 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in z around inf 68.0%

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

   1. associate-*l/ 71.7%

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

   2. *-commutative 71.7%

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

7. Simplified 71.7%

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

   1. clear-num 71.4%

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

   2. div-inv 71.1%

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

9. Applied egg-rr 71.1%

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

10. Taylor expanded in x around inf 41.1%

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

11. Final simplification 41.1%

    \[\leadsto x \]
12. Add Preprocessing

Developer target: 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 2024021 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (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)))