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

Percentage Accurate: 92.7% → 93.8%

Time: 10.4s

Alternatives: 13

Speedup: 1.0×

• 24.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 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 94.3%

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

   1. associate-/l* 96.6%

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

3. Simplified 96.6%

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

   1. clear-num 96.6%

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

   2. un-div-inv 97.3%

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

6. Applied egg-rr 97.3%

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

7. Final simplification 97.3%

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

Alternative 2: 49.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\frac{a}{y}}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+192}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ t (/ a y))))
   (if (<= y -1.05e+96)
     t_1
     (if (<= y 1.7e-64) x (if (<= y 1e+192) (* z (/ y (- a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (y <= -1.05e+96) {
		tmp = t_1;
	} else if (y <= 1.7e-64) {
		tmp = x;
	} else if (y <= 1e+192) {
		tmp = z * (y / -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / (a / y)
    if (y <= (-1.05d+96)) then
        tmp = t_1
    else if (y <= 1.7d-64) then
        tmp = x
    else if (y <= 1d+192) then
        tmp = z * (y / -a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t / (a / y);
	double tmp;
	if (y <= -1.05e+96) {
		tmp = t_1;
	} else if (y <= 1.7e-64) {
		tmp = x;
	} else if (y <= 1e+192) {
		tmp = z * (y / -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t / (a / y)
	tmp = 0
	if y <= -1.05e+96:
		tmp = t_1
	elif y <= 1.7e-64:
		tmp = x
	elif y <= 1e+192:
		tmp = z * (y / -a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t / Float64(a / y))
	tmp = 0.0
	if (y <= -1.05e+96)
		tmp = t_1;
	elseif (y <= 1.7e-64)
		tmp = x;
	elseif (y <= 1e+192)
		tmp = Float64(z * Float64(y / Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t / (a / y);
	tmp = 0.0;
	if (y <= -1.05e+96)
		tmp = t_1;
	elseif (y <= 1.7e-64)
		tmp = x;
	elseif (y <= 1e+192)
		tmp = z * (y / -a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+96], t$95$1, If[LessEqual[y, 1.7e-64], x, If[LessEqual[y, 1e+192], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0500000000000001e96 or 1.00000000000000004e192 < y

   1. Initial program 86.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 50.0%

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

      1. associate-/l* 60.6%

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

   7. Simplified 60.6%

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

      1. clear-num 60.6%

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

      2. un-div-inv 60.6%

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

   9. Applied egg-rr 60.6%

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

   if -1.0500000000000001e96 < y < 1.70000000000000006e-64

   1. Initial program 99.2%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in x around inf 66.4%

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

   if 1.70000000000000006e-64 < y < 1.00000000000000004e192

   1. Initial program 93.3%

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

      1. associate-/l* 98.4%

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

   3. Simplified 98.4%

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

   5. Taylor expanded in z around inf 51.1%

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

      1. mul-1-neg 51.1%

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

      2. associate-/l* 54.4%

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

      3. distribute-rgt-neg-in 54.4%

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

      4. distribute-neg-frac2 54.4%

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

   7. Simplified 54.4%

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

      1. associate-*r/ 51.1%

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

      2. frac-2neg 51.1%

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

      3. distribute-rgt-neg-in 51.1%

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

      4. remove-double-neg 51.1%

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

   9. Applied egg-rr 51.1%

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

   10. Taylor expanded in y around 0 51.1%

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

       1. neg-mul-1 51.1%

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

       2. distribute-neg-frac2 51.1%

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

       3. *-commutative 51.1%

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

       4. associate-*r/ 55.9%

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

   12. Simplified 55.9%

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

Alternative 3: 50.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+96}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5e+96)
   (/ t (/ a y))
   (if (<= y 6.5e-64) x (if (<= y 1.15e+58) (* (/ z a) (- y)) (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5e+96) {
		tmp = t / (a / y);
	} else if (y <= 6.5e-64) {
		tmp = x;
	} else if (y <= 1.15e+58) {
		tmp = (z / a) * -y;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-5d+96)) then
        tmp = t / (a / y)
    else if (y <= 6.5d-64) then
        tmp = x
    else if (y <= 1.15d+58) then
        tmp = (z / a) * -y
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5e+96) {
		tmp = t / (a / y);
	} else if (y <= 6.5e-64) {
		tmp = x;
	} else if (y <= 1.15e+58) {
		tmp = (z / a) * -y;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5e+96:
		tmp = t / (a / y)
	elif y <= 6.5e-64:
		tmp = x
	elif y <= 1.15e+58:
		tmp = (z / a) * -y
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5e+96)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 6.5e-64)
		tmp = x;
	elseif (y <= 1.15e+58)
		tmp = Float64(Float64(z / a) * Float64(-y));
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5e+96)
		tmp = t / (a / y);
	elseif (y <= 6.5e-64)
		tmp = x;
	elseif (y <= 1.15e+58)
		tmp = (z / a) * -y;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5e+96], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-64], x, If[LessEqual[y, 1.15e+58], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.0000000000000004e96

   1. Initial program 87.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 46.9%

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

      1. associate-/l* 56.6%

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

   7. Simplified 56.6%

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

      1. clear-num 56.6%

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

      2. un-div-inv 56.6%

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

   9. Applied egg-rr 56.6%

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

   if -5.0000000000000004e96 < y < 6.5000000000000004e-64

   1. Initial program 99.2%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in x around inf 66.4%

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

   if 6.5000000000000004e-64 < y < 1.15000000000000001e58

   1. Initial program 99.9%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   5. Taylor expanded in z around inf 59.3%

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

      1. mul-1-neg 59.3%

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

      2. associate-/l* 59.2%

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

      3. distribute-rgt-neg-in 59.2%

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

      4. distribute-neg-frac2 59.2%

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

   7. Simplified 59.2%

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

   if 1.15000000000000001e58 < y

   1. Initial program 85.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around inf 50.1%

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

      1. associate-/l* 57.9%

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

   7. Simplified 57.9%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+96}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+58}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+65} \lor \neg \left(t \leq 2.1 \cdot 10^{+45}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.5e+65) (not (<= t 2.1e+45)))
   (+ x (* t (/ y a)))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.5e+65) || !(t <= 2.1e+45)) {
		tmp = x + (t * (y / 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 <= (-4.5d+65)) .or. (.not. (t <= 2.1d+45))) then
        tmp = x + (t * (y / 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 <= -4.5e+65) || !(t <= 2.1e+45)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.5e+65) or not (t <= 2.1e+45):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.5e+65) || !(t <= 2.1e+45))
		tmp = Float64(x + Float64(t * Float64(y / 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 <= -4.5e+65) || ~((t <= 2.1e+45)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.5e+65], N[Not[LessEqual[t, 2.1e+45]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e65 or 2.09999999999999995e45 < t

   1. Initial program 91.2%

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

      1. sub-neg 91.2%

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

      2. distribute-frac-neg2 91.2%

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

      3. +-commutative 91.2%

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

      4. associate-/l* 95.2%

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

      5. fma-define 95.2%

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

      6. distribute-frac-neg2 95.2%

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

      7. distribute-neg-frac 95.2%

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

      8. sub-neg 95.2%

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

      9. distribute-neg-in 95.2%

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

      10. remove-double-neg 95.2%

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

      11. +-commutative 95.2%

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

      12. sub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 82.4%

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

      1. associate-*r/ 90.1%

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

      2. *-commutative 90.1%

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

   7. Applied egg-rr 90.1%

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

   if -4.5e65 < t < 2.09999999999999995e45

   1. Initial program 96.3%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

      1. clear-num 97.5%

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

      2. un-div-inv 98.6%

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

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in z around inf 91.1%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+65} \lor \neg \left(t \leq 2.1 \cdot 10^{+45}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+65} \lor \neg \left(t \leq 1.05 \cdot 10^{+45}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5e+65) (not (<= t 1.05e+45)))
   (+ x (* t (/ y a)))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e+65) || !(t <= 1.05e+45)) {
		tmp = x + (t * (y / 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 <= (-5d+65)) .or. (.not. (t <= 1.05d+45))) then
        tmp = x + (t * (y / 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 <= -5e+65) || !(t <= 1.05e+45)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5e+65) or not (t <= 1.05e+45):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5e+65) || !(t <= 1.05e+45))
		tmp = Float64(x + Float64(t * Float64(y / 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 <= -5e+65) || ~((t <= 1.05e+45)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5e+65], N[Not[LessEqual[t, 1.05e+45]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.99999999999999973e65 or 1.04999999999999997e45 < t

   1. Initial program 91.2%

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

      1. sub-neg 91.2%

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

      2. distribute-frac-neg2 91.2%

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

      3. +-commutative 91.2%

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

      4. associate-/l* 95.2%

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

      5. fma-define 95.2%

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

      6. distribute-frac-neg2 95.2%

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

      7. distribute-neg-frac 95.2%

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

      8. sub-neg 95.2%

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

      9. distribute-neg-in 95.2%

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

      10. remove-double-neg 95.2%

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

      11. +-commutative 95.2%

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

      12. sub-neg 95.2%

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

   3. Simplified 95.2%

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

   5. Taylor expanded in z around 0 82.4%

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

      1. associate-*r/ 90.1%

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

      2. *-commutative 90.1%

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

   7. Applied egg-rr 90.1%

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

   if -4.99999999999999973e65 < t < 1.04999999999999997e45

   1. Initial program 96.3%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   5. Taylor expanded in z around inf 88.9%

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

      1. associate-/l* 90.5%

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

   7. Simplified 90.5%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+65} \lor \neg \left(t \leq 1.05 \cdot 10^{+45}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+20} \lor \neg \left(z \leq 1.2 \cdot 10^{+118}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.4e+20) (not (<= z 1.2e+118)))
   (* (/ y a) (- t z))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e+20) || !(z <= 1.2e+118)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-3.4d+20)) .or. (.not. (z <= 1.2d+118))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -3.4e+20) || !(z <= 1.2e+118)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -3.4e+20) or not (z <= 1.2e+118):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -3.4e+20) || !(z <= 1.2e+118))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -3.4e+20) || ~((z <= 1.2e+118)))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -3.4e+20], N[Not[LessEqual[z, 1.2e+118]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.4e20 or 1.2e118 < z

   1. Initial program 87.4%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

      1. clear-num 95.6%

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

      2. un-div-inv 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in x around 0 68.9%

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

      1. mul-1-neg 68.9%

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

      2. associate-*l/ 79.1%

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

      3. sub-neg 79.1%

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

      4. distribute-lft-out 72.5%

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

      5. associate-*l/ 61.0%

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

      6. associate-*r/ 70.3%

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

      7. +-commutative 70.3%

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

      8. *-commutative 70.3%

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

      9. distribute-lft-neg-out 70.3%

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

      10. associate-/l* 67.4%

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

      11. mul-1-neg 67.4%

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

      12. distribute-neg-in 67.4%

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

      13. mul-1-neg 67.4%

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

      14. remove-double-neg 67.4%

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

      15. sub-neg 67.4%

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

      16. *-commutative 67.4%

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

      17. associate-*l/ 62.1%

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

      18. associate-*r/ 69.5%

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

      19. associate-/l* 72.5%

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

      20. distribute-rgt-out-- 79.1%

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

   9. Simplified 79.1%

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

   if -3.4e20 < z < 1.2e118

   1. Initial program 98.1%

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

      1. sub-neg 98.1%

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

      2. distribute-frac-neg2 98.1%

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

      3. +-commutative 98.1%

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

      4. associate-/l* 97.1%

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

      5. fma-define 97.2%

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

      6. distribute-frac-neg2 97.2%

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

      7. distribute-neg-frac 97.2%

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

      8. sub-neg 97.2%

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

      9. distribute-neg-in 97.2%

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

      10. remove-double-neg 97.2%

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

      11. +-commutative 97.2%

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

      12. sub-neg 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in z around 0 85.9%

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

      1. associate-*r/ 89.3%

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

      2. *-commutative 89.3%

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

   7. Applied egg-rr 89.3%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+20} \lor \neg \left(z \leq 1.2 \cdot 10^{+118}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+35} \lor \neg \left(y \leq 2.6 \cdot 10^{-64}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.4e+35) (not (<= y 2.6e-64))) (* y (/ (- t z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.4e+35) || !(y <= 2.6e-64)) {
		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 <= (-6.4d+35)) .or. (.not. (y <= 2.6d-64))) 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 <= -6.4e+35) || !(y <= 2.6e-64)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.4e+35) or not (y <= 2.6e-64):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.4e+35) || !(y <= 2.6e-64))
		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 <= -6.4e+35) || ~((y <= 2.6e-64)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.4e+35], N[Not[LessEqual[y, 2.6e-64]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.39999999999999965e35 or 2.6e-64 < y

   1. Initial program 90.3%

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

      1. associate-/l* 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 73.6%

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

      1. associate-*r/ 73.6%

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

      2. neg-mul-1 73.6%

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

      3. distribute-rgt-neg-in 73.6%

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

      4. sub-neg 73.6%

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

      5. distribute-neg-in 73.6%

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

      6. remove-double-neg 73.6%

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

      7. +-commutative 73.6%

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

      8. sub-neg 73.6%

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

      9. associate-*r/ 79.9%

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

   7. Simplified 79.9%

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

   if -6.39999999999999965e35 < y < 2.6e-64

   1. Initial program 99.9%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf 71.9%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+35} \lor \neg \left(y \leq 2.6 \cdot 10^{-64}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} + \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+43}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e+64)
   (* t (+ (/ x t) (/ y a)))
   (if (<= t 2.6e+43) (- x (/ y (/ a z))) (+ x (* t (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+64) {
		tmp = t * ((x / t) + (y / a));
	} else if (t <= 2.6e+43) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.5d+64)) then
        tmp = t * ((x / t) + (y / a))
    else if (t <= 2.6d+43) then
        tmp = x - (y / (a / z))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+64) {
		tmp = t * ((x / t) + (y / a));
	} else if (t <= 2.6e+43) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e+64:
		tmp = t * ((x / t) + (y / a))
	elif t <= 2.6e+43:
		tmp = x - (y / (a / z))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e+64)
		tmp = Float64(t * Float64(Float64(x / t) + Float64(y / a)));
	elseif (t <= 2.6e+43)
		tmp = Float64(x - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.5e+64)
		tmp = t * ((x / t) + (y / a));
	elseif (t <= 2.6e+43)
		tmp = x - (y / (a / z));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+64], N[(t * N[(N[(x / t), $MachinePrecision] + N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+43], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.50000000000000007e64

   1. Initial program 90.3%

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

      1. sub-neg 90.3%

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

      2. distribute-frac-neg2 90.3%

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

      3. +-commutative 90.3%

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

      4. associate-/l* 96.1%

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

      5. fma-define 96.1%

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

      6. distribute-frac-neg2 96.1%

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

      7. distribute-neg-frac 96.1%

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

      8. sub-neg 96.1%

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

      9. distribute-neg-in 96.1%

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

      10. remove-double-neg 96.1%

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

      11. +-commutative 96.1%

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

      12. sub-neg 96.1%

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

   3. Simplified 96.1%

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

   5. Taylor expanded in z around 0 80.7%

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

   6. Taylor expanded in t around inf 90.1%

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

   if -6.50000000000000007e64 < t < 2.60000000000000021e43

   1. Initial program 96.3%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

      1. clear-num 97.5%

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

      2. un-div-inv 98.6%

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

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in z around inf 91.1%

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

   if 2.60000000000000021e43 < t

   1. Initial program 92.1%

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

      1. sub-neg 92.1%

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

      2. distribute-frac-neg2 92.1%

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

      3. +-commutative 92.1%

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

      4. associate-/l* 94.2%

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

      5. fma-define 94.2%

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

      6. distribute-frac-neg2 94.2%

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

      7. distribute-neg-frac 94.2%

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

      8. sub-neg 94.2%

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

      9. distribute-neg-in 94.2%

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

      10. remove-double-neg 94.2%

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

      11. +-commutative 94.2%

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

      12. sub-neg 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around 0 84.2%

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

      1. associate-*r/ 90.0%

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

      2. *-commutative 90.0%

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

   7. Applied egg-rr 90.0%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+64}:\\ \;\;\;\;t \cdot \left(\frac{x}{t} + \frac{y}{a}\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+43}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+36}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.1e+36)
   (* y (/ (- t z) a))
   (if (<= y 3.8e-64) x (* (/ y a) (- t z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.1e+36) {
		tmp = y * ((t - z) / a);
	} else if (y <= 3.8e-64) {
		tmp = x;
	} else {
		tmp = (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 <= (-1.1d+36)) then
        tmp = y * ((t - z) / a)
    else if (y <= 3.8d-64) then
        tmp = x
    else
        tmp = (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 <= -1.1e+36) {
		tmp = y * ((t - z) / a);
	} else if (y <= 3.8e-64) {
		tmp = x;
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.1e+36:
		tmp = y * ((t - z) / a)
	elif y <= 3.8e-64:
		tmp = x
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.1e+36)
		tmp = Float64(y * Float64(Float64(t - z) / a));
	elseif (y <= 3.8e-64)
		tmp = x;
	else
		tmp = 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 <= -1.1e+36)
		tmp = y * ((t - z) / a);
	elseif (y <= 3.8e-64)
		tmp = x;
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.1e+36], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-64], x, N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e36

   1. Initial program 90.5%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 69.5%

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

      1. associate-*r/ 69.5%

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

      2. neg-mul-1 69.5%

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

      3. distribute-rgt-neg-in 69.5%

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

      4. sub-neg 69.5%

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

      5. distribute-neg-in 69.5%

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

      6. remove-double-neg 69.5%

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

      7. +-commutative 69.5%

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

      8. sub-neg 69.5%

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

      9. associate-*r/ 77.3%

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

   7. Simplified 77.3%

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

   if -1.1e36 < y < 3.8000000000000002e-64

   1. Initial program 99.9%

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

      1. associate-/l* 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in x around inf 71.9%

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

   if 3.8000000000000002e-64 < y

   1. Initial program 90.2%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

      1. clear-num 98.9%

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

      2. un-div-inv 99.0%

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

   6. Applied egg-rr 99.0%

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

   7. Taylor expanded in x around 0 76.2%

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

      1. mul-1-neg 76.2%

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

      2. associate-*l/ 82.5%

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

      3. sub-neg 82.5%

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

      4. distribute-lft-out 74.7%

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

      5. associate-*l/ 72.8%

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

      6. associate-*r/ 79.2%

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

      7. +-commutative 79.2%

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

      8. *-commutative 79.2%

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

      9. distribute-lft-neg-out 79.2%

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

      10. associate-/l* 76.0%

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

      11. mul-1-neg 76.0%

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

      12. distribute-neg-in 76.0%

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

      13. mul-1-neg 76.0%

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

      14. remove-double-neg 76.0%

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

      15. sub-neg 76.0%

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

      16. *-commutative 76.0%

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

      17. associate-*l/ 71.7%

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

      18. associate-*r/ 71.5%

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

      19. associate-/l* 74.7%

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

      20. distribute-rgt-out-- 82.5%

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

   9. Simplified 82.5%

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

Alternative 10: 50.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+95} \lor \neg \left(y \leq 7 \cdot 10^{-45}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.8e+95) (not (<= y 7e-45))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.8e+95) || !(y <= 7e-45)) {
		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 ((y <= (-5.8d+95)) .or. (.not. (y <= 7d-45))) 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 ((y <= -5.8e+95) || !(y <= 7e-45)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.8e+95) or not (y <= 7e-45):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.8e+95) || !(y <= 7e-45))
		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 ((y <= -5.8e+95) || ~((y <= 7e-45)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.8e+95], N[Not[LessEqual[y, 7e-45]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.80000000000000027e95 or 7e-45 < y

   1. Initial program 89.2%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around inf 45.3%

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

      1. associate-/l* 52.1%

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

   7. Simplified 52.1%

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

   if -5.80000000000000027e95 < y < 7e-45

   1. Initial program 99.2%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in x around inf 65.2%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+95} \lor \neg \left(y \leq 7 \cdot 10^{-45}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+96}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 10^{-43}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.6e+96) (/ t (/ a y)) (if (<= y 1e-43) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.6e+96) {
		tmp = t / (a / y);
	} else if (y <= 1e-43) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.6d+96)) then
        tmp = t / (a / y)
    else if (y <= 1d-43) then
        tmp = x
    else
        tmp = t * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.6e+96) {
		tmp = t / (a / y);
	} else if (y <= 1e-43) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.6e+96:
		tmp = t / (a / y)
	elif y <= 1e-43:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.6e+96)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 1e-43)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.6e+96)
		tmp = t / (a / y);
	elseif (y <= 1e-43)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.6e+96], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e-43], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.60000000000000013e96

   1. Initial program 87.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 46.9%

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

      1. associate-/l* 56.6%

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

   7. Simplified 56.6%

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

      1. clear-num 56.6%

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

      2. un-div-inv 56.6%

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

   9. Applied egg-rr 56.6%

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

   if -3.60000000000000013e96 < y < 1.00000000000000008e-43

   1. Initial program 99.2%

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

      1. associate-/l* 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in x around inf 65.2%

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

   if 1.00000000000000008e-43 < y

   1. Initial program 89.8%

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

      1. associate-/l* 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in t around inf 44.6%

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

      1. associate-/l* 50.1%

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

   7. Simplified 50.1%

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

Alternative 12: 93.4% 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 94.3%

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

   1. associate-/l* 96.6%

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

3. Simplified 96.6%

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

5. Final simplification 96.6%

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

Alternative 13: 39.7% 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 94.3%

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

   1. associate-/l* 96.6%

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

3. Simplified 96.6%

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

5. Taylor expanded in x around inf 42.5%

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

Developer Target 1: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024181 
(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)))