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

Percentage Accurate: 93.1% → 99.1%

Time: 9.5s

Alternatives: 15

Speedup: 1.0×

• 24.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+250}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+107}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 -5e+250)
     (+ x (* y (/ (- t z) a)))
     (if (<= t_1 2e+107)
       (+ x (/ (* y (- t z)) a))
       (- x (/ y (/ a (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -5e+250) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 2e+107) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x - (y / (a / (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) :: t_1
    real(8) :: tmp
    t_1 = y * (z - t)
    if (t_1 <= (-5d+250)) then
        tmp = x + (y * ((t - z) / a))
    else if (t_1 <= 2d+107) then
        tmp = x + ((y * (t - z)) / a)
    else
        tmp = x - (y / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -5e+250) {
		tmp = x + (y * ((t - z) / a));
	} else if (t_1 <= 2e+107) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = x - (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -5e+250:
		tmp = x + (y * ((t - z) / a))
	elif t_1 <= 2e+107:
		tmp = x + ((y * (t - z)) / a)
	else:
		tmp = x - (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -5e+250)
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	elseif (t_1 <= 2e+107)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -5e+250)
		tmp = x + (y * ((t - z) / a));
	elseif (t_1 <= 2e+107)
		tmp = x + ((y * (t - z)) / a);
	else
		tmp = x - (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+250], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+107], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -5.0000000000000002e250

   1. Initial program 77.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   if -5.0000000000000002e250 < (*.f64 y (-.f64 z t)) < 1.9999999999999999e107

   1. Initial program 99.9%

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

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

   1. Initial program 82.2%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -5 \cdot 10^{+250}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 2 \cdot 10^{+107}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+86} \lor \neg \left(t \leq 1.8 \cdot 10^{+144}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.2e+86) (not (<= t 1.8e+144)))
   (+ x (* y (/ t a)))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e+86) || !(t <= 1.8e+144)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y / (a / 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 ((t <= (-5.2d+86)) .or. (.not. (t <= 1.8d+144))) then
        tmp = x + (y * (t / a))
    else
        tmp = x - (y / (a / 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 ((t <= -5.2e+86) || !(t <= 1.8e+144)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.2e+86) or not (t <= 1.8e+144):
		tmp = x + (y * (t / a))
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.2e+86) || !(t <= 1.8e+144))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.2e+86) || ~((t <= 1.8e+144)))
		tmp = x + (y * (t / a));
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.2e+86], N[Not[LessEqual[t, 1.8e+144]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.1999999999999995e86 or 1.7999999999999999e144 < t

   1. Initial program 85.2%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

      1. clear-num 91.3%

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

      2. un-div-inv 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in z around 0 77.7%

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

      1. cancel-sign-sub-inv 77.7%

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

      2. metadata-eval 77.7%

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

      3. *-commutative 77.7%

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

      4. associate-*r/ 83.7%

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

      5. *-lft-identity 83.7%

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

   9. Simplified 83.7%

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

   if -5.1999999999999995e86 < t < 1.7999999999999999e144

   1. Initial program 95.2%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

      1. clear-num 96.2%

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

      2. un-div-inv 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in z around inf 91.0%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+86} \lor \neg \left(t \leq 1.8 \cdot 10^{+144}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+82} \lor \neg \left(t \leq 2.9 \cdot 10^{+148}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.5e+82) (not (<= t 2.9e+148)))
   (+ x (* y (/ t a)))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+82) || !(t <= 2.9e+148)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4.5d+82)) .or. (.not. (t <= 2.9d+148))) then
        tmp = x + (y * (t / a))
    else
        tmp = x - (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+82) || !(t <= 2.9e+148)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.5e+82) or not (t <= 2.9e+148):
		tmp = x + (y * (t / a))
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.5e+82) || !(t <= 2.9e+148))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(x - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4.5e+82) || ~((t <= 2.9e+148)))
		tmp = x + (y * (t / a));
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.5e+82], N[Not[LessEqual[t, 2.9e+148]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4999999999999997e82 or 2.9e148 < t

   1. Initial program 85.2%

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

      1. associate-/l* 91.3%

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

   3. Simplified 91.3%

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

      1. clear-num 91.3%

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

      2. un-div-inv 92.6%

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

   6. Applied egg-rr 92.6%

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

   7. Taylor expanded in z around 0 77.7%

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

      1. cancel-sign-sub-inv 77.7%

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

      2. metadata-eval 77.7%

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

      3. *-commutative 77.7%

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

      4. associate-*r/ 83.7%

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

      5. *-lft-identity 83.7%

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

   9. Simplified 83.7%

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

   if -4.4999999999999997e82 < t < 2.9e148

   1. Initial program 95.2%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around inf 88.7%

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

      1. associate-/l* 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+82} \lor \neg \left(t \leq 2.9 \cdot 10^{+148}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+91} \lor \neg \left(z \leq 2.1 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+91) (not (<= z 2.1e+31)))
   (* (/ y a) (- t z))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4e+91) || !(z <= 2.1e+31)) {
		tmp = (y / a) * (t - z);
	} 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 <= (-4d+91)) .or. (.not. (z <= 2.1d+31))) then
        tmp = (y / a) * (t - z)
    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 <= -4e+91) || !(z <= 2.1e+31)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4e+91) or not (z <= 2.1e+31):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4e+91) || !(z <= 2.1e+31))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	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 <= -4e+91) || ~((z <= 2.1e+31)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4e+91], N[Not[LessEqual[z, 2.1e+31]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.00000000000000032e91 or 2.09999999999999979e31 < z

   1. Initial program 86.7%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in x around 0 71.6%

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

      1. associate-*r/ 71.6%

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

      2. neg-mul-1 71.6%

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

      3. *-commutative 71.6%

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

      4. distribute-lft-neg-in 71.6%

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

      5. associate-*r/ 81.1%

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

      6. *-commutative 81.1%

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

      7. neg-sub0 81.1%

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

      8. sub-neg 81.1%

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

      9. +-commutative 81.1%

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

      10. associate--r+ 81.1%

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

      11. neg-sub0 81.1%

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

      12. remove-double-neg 81.1%

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

   7. Simplified 81.1%

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

   if -4.00000000000000032e91 < z < 2.09999999999999979e31

   1. Initial program 96.1%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

      1. clear-num 96.0%

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

      2. un-div-inv 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in z around 0 80.8%

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

      1. cancel-sign-sub-inv 80.8%

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

      2. metadata-eval 80.8%

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

      3. *-commutative 80.8%

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

      4. associate-*r/ 81.4%

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

      5. *-lft-identity 81.4%

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

   9. Simplified 81.4%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+91} \lor \neg \left(z \leq 2.1 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-59} \lor \neg \left(y \leq 2.1 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.06e-59) (not (<= y 2.1e-6))) (* y (/ (- t z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.06e-59) || !(y <= 2.1e-6)) {
		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 <= (-1.06d-59)) .or. (.not. (y <= 2.1d-6))) 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 <= -1.06e-59) || !(y <= 2.1e-6)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.06e-59) or not (y <= 2.1e-6):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.06e-59) || !(y <= 2.1e-6))
		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 <= -1.06e-59) || ~((y <= 2.1e-6)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.06e-59], N[Not[LessEqual[y, 2.1e-6]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e-59 or 2.0999999999999998e-6 < y

   1. Initial program 86.4%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in x around 0 66.4%

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

      1. associate-*r/ 66.4%

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

      2. neg-mul-1 66.4%

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

      3. *-commutative 66.4%

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

      4. distribute-lft-neg-in 66.4%

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

      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%

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

      1. *-commutative 74.0%

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

      2. clear-num 73.9%

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

      3. un-div-inv 73.9%

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

   9. Applied egg-rr 73.9%

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

       1. associate-/r/ 75.3%

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

   11. Applied egg-rr 75.3%

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

   if -1.06e-59 < y < 2.0999999999999998e-6

   1. Initial program 99.9%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in x around inf 65.0%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-59} \lor \neg \left(y \leq 2.1 \cdot 10^{-6}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-59} \lor \neg \left(y \leq 1.36 \cdot 10^{-204}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.12e-59) (not (<= y 1.36e-204))) (* (/ y a) (- t z)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.12e-59) || !(y <= 1.36e-204)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.12d-59)) .or. (.not. (y <= 1.36d-204))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.12e-59) || !(y <= 1.36e-204)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.12e-59) or not (y <= 1.36e-204):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.12e-59) || !(y <= 1.36e-204))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.12e-59) || ~((y <= 1.36e-204)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.12e-59], N[Not[LessEqual[y, 1.36e-204]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.1200000000000001e-59 or 1.3600000000000001e-204 < y

   1. Initial program 89.4%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in x around 0 63.2%

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

      1. associate-*r/ 63.2%

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

      2. neg-mul-1 63.2%

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

      3. *-commutative 63.2%

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

      4. distribute-lft-neg-in 63.2%

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

      5. associate-*r/ 69.1%

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

      6. *-commutative 69.1%

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

      7. neg-sub0 69.1%

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

      8. sub-neg 69.1%

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

      9. +-commutative 69.1%

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

      10. associate--r+ 69.1%

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

      11. neg-sub0 69.1%

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

      12. remove-double-neg 69.1%

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

   7. Simplified 69.1%

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

   if -1.1200000000000001e-59 < y < 1.3600000000000001e-204

   1. Initial program 100.0%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in x around inf 73.5%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{-59} \lor \neg \left(y \leq 1.36 \cdot 10^{-204}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+146}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.6e+79)
   (+ x (* y (/ t a)))
   (if (<= t 2.6e+146) (- x (/ y (/ a z))) (+ x (/ y (/ a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.6e+79) {
		tmp = x + (y * (t / a));
	} else if (t <= 2.6e+146) {
		tmp = x - (y / (a / z));
	} 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 <= (-3.6d+79)) then
        tmp = x + (y * (t / a))
    else if (t <= 2.6d+146) then
        tmp = x - (y / (a / z))
    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 <= -3.6e+79) {
		tmp = x + (y * (t / a));
	} else if (t <= 2.6e+146) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3.6e+79:
		tmp = x + (y * (t / a))
	elif t <= 2.6e+146:
		tmp = x - (y / (a / z))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.6e+79)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t <= 2.6e+146)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3.6e+79)
		tmp = x + (y * (t / a));
	elseif (t <= 2.6e+146)
		tmp = x - (y / (a / z));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.6e+79], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+146], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.5999999999999999e79

   1. Initial program 85.3%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

      1. clear-num 92.7%

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

      2. un-div-inv 92.7%

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

   6. Applied egg-rr 92.7%

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

   7. Taylor expanded in z around 0 80.3%

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

      1. cancel-sign-sub-inv 80.3%

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

      2. metadata-eval 80.3%

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

      3. *-commutative 80.3%

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

      4. associate-*r/ 88.0%

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

      5. *-lft-identity 88.0%

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

   9. Simplified 88.0%

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

   if -3.5999999999999999e79 < t < 2.60000000000000014e146

   1. Initial program 95.2%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

      1. clear-num 96.2%

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

      2. un-div-inv 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in z around inf 91.0%

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

   if 2.60000000000000014e146 < t

   1. Initial program 85.1%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

      1. clear-num 89.8%

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

      2. un-div-inv 92.5%

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

   6. Applied egg-rr 92.5%

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

   7. Taylor expanded in z around 0 81.9%

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

      1. associate-*r/ 81.9%

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

      2. neg-mul-1 81.9%

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

   9. Simplified 81.9%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{+79}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+146}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+112} \lor \neg \left(z \leq 2.8 \cdot 10^{+31}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.5e+112) (not (<= z 2.8e+31))) (* z (/ y (- a))) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.5e+112) || !(z <= 2.8e+31)) {
		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 <= (-1.5d+112)) .or. (.not. (z <= 2.8d+31))) 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 <= -1.5e+112) || !(z <= 2.8e+31)) {
		tmp = z * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.5e+112) or not (z <= 2.8e+31):
		tmp = z * (y / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.5e+112) || !(z <= 2.8e+31))
		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 <= -1.5e+112) || ~((z <= 2.8e+31)))
		tmp = z * (y / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.5e+112], N[Not[LessEqual[z, 2.8e+31]], $MachinePrecision]], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.4999999999999999e112 or 2.80000000000000017e31 < z

   1. Initial program 87.3%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in x around 0 71.7%

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

      1. associate-*r/ 71.7%

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

      2. neg-mul-1 71.7%

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

      3. *-commutative 71.7%

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

      4. distribute-lft-neg-in 71.7%

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

      5. associate-*r/ 80.5%

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

      6. *-commutative 80.5%

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

      7. neg-sub0 80.5%

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

      8. sub-neg 80.5%

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

      9. +-commutative 80.5%

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

      10. associate--r+ 80.5%

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

      11. neg-sub0 80.5%

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

      12. remove-double-neg 80.5%

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

   7. Simplified 80.5%

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

   8. Taylor expanded in t around 0 69.4%

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

      1. neg-mul-1 69.4%

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

   10. Simplified 69.4%

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

   if -1.4999999999999999e112 < z < 2.80000000000000017e31

   1. Initial program 95.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 56.4%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+112} \lor \neg \left(z \leq 2.8 \cdot 10^{+31}\right):\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+107} \lor \neg \left(z \leq 1.15 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.3e+107) (not (<= z 1.15e+31))) (* (/ z a) (- y)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e+107) || !(z <= 1.15e+31)) {
		tmp = (z / a) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4.3d+107)) .or. (.not. (z <= 1.15d+31))) then
        tmp = (z / a) * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.3e+107) || !(z <= 1.15e+31)) {
		tmp = (z / a) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.3e+107) or not (z <= 1.15e+31):
		tmp = (z / a) * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.3e+107) || !(z <= 1.15e+31))
		tmp = Float64(Float64(z / a) * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4.3e+107) || ~((z <= 1.15e+31)))
		tmp = (z / a) * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.3e+107], N[Not[LessEqual[z, 1.15e+31]], $MachinePrecision]], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -4.3e107 or 1.15e31 < z

   1. Initial program 87.3%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in z around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. associate-/l* 65.1%

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

      3. distribute-rgt-neg-in 65.1%

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

      4. distribute-frac-neg2 65.1%

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

   7. Simplified 65.1%

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

   if -4.3e107 < z < 1.15e31

   1. Initial program 95.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 56.4%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+107} \lor \neg \left(z \leq 1.15 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -5.6e+101)
   (* z (/ y (- a)))
   (if (<= z 5.9e+32) x (/ (- z) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5.6e+101) {
		tmp = z * (y / -a);
	} else if (z <= 5.9e+32) {
		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 (z <= (-5.6d+101)) then
        tmp = z * (y / -a)
    else if (z <= 5.9d+32) 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 (z <= -5.6e+101) {
		tmp = z * (y / -a);
	} else if (z <= 5.9e+32) {
		tmp = x;
	} else {
		tmp = -z / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5.6e+101:
		tmp = z * (y / -a)
	elif z <= 5.9e+32:
		tmp = x
	else:
		tmp = -z / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5.6e+101)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (z <= 5.9e+32)
		tmp = x;
	else
		tmp = Float64(Float64(-z) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5.6e+101)
		tmp = z * (y / -a);
	elseif (z <= 5.9e+32)
		tmp = x;
	else
		tmp = -z / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -5.6e+101], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.9e+32], x, N[((-z) / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.59999999999999962e101

   1. Initial program 77.6%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in x around 0 62.5%

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

      1. associate-*r/ 62.5%

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

      2. neg-mul-1 62.5%

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

      3. *-commutative 62.5%

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

      4. distribute-lft-neg-in 62.5%

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

      5. associate-*r/ 77.3%

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

      6. *-commutative 77.3%

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

      7. neg-sub0 77.3%

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

      8. sub-neg 77.3%

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

      9. +-commutative 77.3%

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

      10. associate--r+ 77.3%

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

      11. neg-sub0 77.3%

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

      12. remove-double-neg 77.3%

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

   7. Simplified 77.3%

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

   8. Taylor expanded in t around 0 69.6%

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

      1. neg-mul-1 69.6%

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

   10. Simplified 69.6%

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

   if -5.59999999999999962e101 < z < 5.89999999999999965e32

   1. Initial program 95.5%

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

      1. associate-/l* 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in x around inf 56.4%

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

   if 5.89999999999999965e32 < z

   1. Initial program 92.8%

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

      1. associate-/l* 92.8%

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

   3. Simplified 92.8%

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

   5. Taylor expanded in z around inf 66.5%

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

      1. mul-1-neg 66.5%

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

      2. associate-/l* 65.2%

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

      3. distribute-rgt-neg-in 65.2%

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

      4. distribute-frac-neg2 65.2%

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

   7. Simplified 65.2%

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

      1. associate-*r/ 66.5%

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

      2. add-sqr-sqrt 29.3%

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

      3. sqrt-unprod 26.7%

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

      4. sqr-neg 26.7%

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

      5. sqrt-unprod 0.4%

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

      6. add-sqr-sqrt 5.5%

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

      7. associate-*l/ 5.7%

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

      8. *-commutative 5.7%

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

      9. clear-num 5.7%

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

      10. div-inv 5.7%

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

      11. frac-2neg 5.7%

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

      12. distribute-neg-frac 5.7%

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

      13. add-sqr-sqrt 5.2%

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

      14. sqrt-unprod 42.1%

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

      15. sqr-neg 42.1%

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

      16. sqrt-unprod 38.6%

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

      17. add-sqr-sqrt 69.5%

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

   9. Applied egg-rr 69.5%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+99} \lor \neg \left(t \leq 3.1 \cdot 10^{+159}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.3e+99) (not (<= t 3.1e+159))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.3e+99) || !(t <= 3.1e+159)) {
		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 <= (-2.3d+99)) .or. (.not. (t <= 3.1d+159))) 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 <= -2.3e+99) || !(t <= 3.1e+159)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.3e+99) or not (t <= 3.1e+159):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.3e+99) || !(t <= 3.1e+159))
		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 <= -2.3e+99) || ~((t <= 3.1e+159)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.3e+99], N[Not[LessEqual[t, 3.1e+159]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.30000000000000019e99 or 3.0999999999999998e159 < t

   1. Initial program 85.5%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in x around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. neg-mul-1 69.2%

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

      3. *-commutative 69.2%

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

      4. distribute-lft-neg-in 69.2%

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

      5. associate-*r/ 79.3%

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

      6. *-commutative 79.3%

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

      7. neg-sub0 79.3%

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

      8. sub-neg 79.3%

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

      9. +-commutative 79.3%

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

      10. associate--r+ 79.3%

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

      11. neg-sub0 79.3%

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

      12. remove-double-neg 79.3%

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

   7. Simplified 79.3%

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

   8. Taylor expanded in t around inf 70.0%

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

   if -2.30000000000000019e99 < t < 3.0999999999999998e159

   1. Initial program 94.8%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf 49.9%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+99} \lor \neg \left(t \leq 3.1 \cdot 10^{+159}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 48.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+98} \lor \neg \left(t \leq 9 \cdot 10^{+158}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.15e+98) (not (<= t 9e+158))) (* y (/ t a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.15e+98) || !(t <= 9e+158)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.15d+98)) .or. (.not. (t <= 9d+158))) then
        tmp = y * (t / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.15e+98) || !(t <= 9e+158)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.15e+98) or not (t <= 9e+158):
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.15e+98) || !(t <= 9e+158))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.15e+98) || ~((t <= 9e+158)))
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.15e+98], N[Not[LessEqual[t, 9e+158]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.1500000000000001e98 or 9.00000000000000092e158 < t

   1. Initial program 85.5%

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

      1. associate-/l* 90.7%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in t around inf 61.2%

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

      1. *-commutative 61.2%

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

      2. associate-/l* 66.0%

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

   7. Simplified 66.0%

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

   if -2.1500000000000001e98 < t < 9.00000000000000092e158

   1. Initial program 94.8%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in x around inf 49.9%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+98} \lor \neg \left(t \leq 9 \cdot 10^{+158}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 93.8% accurate, 1.0× speedup

Math

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

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(y / Float64(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[(y / N[(a / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.2%

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

   1. associate-/l* 94.8%

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

3. Simplified 94.8%

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

   1. clear-num 94.7%

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

   2. un-div-inv 95.6%

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

6. Applied egg-rr 95.6%

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

7. Final simplification 95.6%

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

Alternative 14: 93.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.2%

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

   1. associate-/l* 94.8%

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

3. Simplified 94.8%

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

5. Final simplification 94.8%

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

Alternative 15: 39.0% 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 92.2%

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

   1. associate-/l* 94.8%

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

3. Simplified 94.8%

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

5. Taylor expanded in x around inf 41.8%

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

Developer Target 1: 99.1% 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 2024185 
(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)))