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

Percentage Accurate: 93.8% → 99.1%

Time: 10.6s

Alternatives: 14

Speedup: 0.3×

• 25.0% 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: 93.8% 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

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+115} \lor \neg \left(t\_1 \leq 10^{+258}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -5e+115) (not (<= t_1 1e+258)))
     (+ x (* y (/ (- t z) a)))
     (+ x (/ (* y (- t z)) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -5e+115) || !(t_1 <= 1e+258)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z - t)
    if ((t_1 <= (-5d+115)) .or. (.not. (t_1 <= 1d+258))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + ((y * (t - z)) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -5e+115) || !(t_1 <= 1e+258)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if (t_1 <= -5e+115) or not (t_1 <= 1e+258):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y * (t - z)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -5e+115) || !(t_1 <= 1e+258))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if ((t_1 <= -5e+115) || ~((t_1 <= 1e+258)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((y * (t - z)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+115], N[Not[LessEqual[t$95$1, 1e+258]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -5.00000000000000008e115 or 1.00000000000000006e258 < (*.f64 y (-.f64 z t))

   1. Initial program 77.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -5.00000000000000008e115 < (*.f64 y (-.f64 z t)) < 1.00000000000000006e258

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -5 \cdot 10^{+115} \lor \neg \left(y \cdot \left(z - t\right) \leq 10^{+258}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+137}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-193}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 11:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= t -6.5e+137)
     t_1
     (if (<= t -8.5e-49)
       x
       (if (<= t -7.2e-193)
         (/ (* y z) (- a))
         (if (<= t 3.6e-271)
           x
           (if (<= t 11.0) (* z (/ y (- a))) (if (<= t 1.02e+117) x t_1))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -6.5e+137) {
		tmp = t_1;
	} else if (t <= -8.5e-49) {
		tmp = x;
	} else if (t <= -7.2e-193) {
		tmp = (y * z) / -a;
	} else if (t <= 3.6e-271) {
		tmp = x;
	} else if (t <= 11.0) {
		tmp = z * (y / -a);
	} else if (t <= 1.02e+117) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (t <= (-6.5d+137)) then
        tmp = t_1
    else if (t <= (-8.5d-49)) then
        tmp = x
    else if (t <= (-7.2d-193)) then
        tmp = (y * z) / -a
    else if (t <= 3.6d-271) then
        tmp = x
    else if (t <= 11.0d0) then
        tmp = z * (y / -a)
    else if (t <= 1.02d+117) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -6.5e+137) {
		tmp = t_1;
	} else if (t <= -8.5e-49) {
		tmp = x;
	} else if (t <= -7.2e-193) {
		tmp = (y * z) / -a;
	} else if (t <= 3.6e-271) {
		tmp = x;
	} else if (t <= 11.0) {
		tmp = z * (y / -a);
	} else if (t <= 1.02e+117) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if t <= -6.5e+137:
		tmp = t_1
	elif t <= -8.5e-49:
		tmp = x
	elif t <= -7.2e-193:
		tmp = (y * z) / -a
	elif t <= 3.6e-271:
		tmp = x
	elif t <= 11.0:
		tmp = z * (y / -a)
	elif t <= 1.02e+117:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t <= -6.5e+137)
		tmp = t_1;
	elseif (t <= -8.5e-49)
		tmp = x;
	elseif (t <= -7.2e-193)
		tmp = Float64(Float64(y * z) / Float64(-a));
	elseif (t <= 3.6e-271)
		tmp = x;
	elseif (t <= 11.0)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (t <= 1.02e+117)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (t <= -6.5e+137)
		tmp = t_1;
	elseif (t <= -8.5e-49)
		tmp = x;
	elseif (t <= -7.2e-193)
		tmp = (y * z) / -a;
	elseif (t <= 3.6e-271)
		tmp = x;
	elseif (t <= 11.0)
		tmp = z * (y / -a);
	elseif (t <= 1.02e+117)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+137], t$95$1, If[LessEqual[t, -8.5e-49], x, If[LessEqual[t, -7.2e-193], N[(N[(y * z), $MachinePrecision] / (-a)), $MachinePrecision], If[LessEqual[t, 3.6e-271], x, If[LessEqual[t, 11.0], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+117], x, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.5000000000000002e137 or 1.02e117 < t

   1. Initial program 84.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 63.5%

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

      1. *-commutative 63.5%

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

   7. Simplified 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-/l* 74.3%

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

   9. Applied egg-rr 74.3%

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

   if -6.5000000000000002e137 < t < -8.50000000000000069e-49 or -7.1999999999999998e-193 < t < 3.5999999999999998e-271 or 11 < t < 1.02e117

   1. Initial program 91.9%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf 60.4%

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

   if -8.50000000000000069e-49 < t < -7.1999999999999998e-193

   1. Initial program 99.8%

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

      1. associate-/l* 87.6%

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

   3. Simplified 87.6%

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

      1. clear-num 87.4%

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

      2. un-div-inv 88.4%

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

   6. Applied egg-rr 88.4%

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

   7. Taylor expanded in z around inf 62.6%

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

      1. associate-*r/ 50.4%

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

      2. neg-mul-1 50.4%

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

      3. distribute-lft-neg-in 50.4%

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

   9. Simplified 50.4%

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

       1. distribute-lft-neg-out 50.4%

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

       2. associate-/l* 62.6%

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

       3. distribute-neg-frac2 62.6%

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

       4. *-commutative 62.6%

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

   11. Applied egg-rr 62.6%

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

   if 3.5999999999999998e-271 < t < 11

   1. Initial program 96.4%

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

   3. Taylor expanded in z around inf 94.8%

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

      1. mul-1-neg 94.8%

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

      2. unsub-neg 94.8%

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

      3. *-commutative 94.8%

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

      4. associate-/l* 94.8%

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

   5. Simplified 94.8%

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

   6. Taylor expanded in z around inf 59.0%

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

      1. mul-1-neg 59.0%

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

      2. associate-*l/ 62.6%

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

      3. distribute-rgt-neg-in 62.6%

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

   8. Simplified 62.6%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+137}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-193}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 11:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ t_2 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -5.2 \cdot 10^{+141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 42:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))) (t_2 (* t (/ y a))))
   (if (<= t -5.2e+141)
     t_2
     (if (<= t -9e-49)
       x
       (if (<= t -6e-195)
         t_1
         (if (<= t 2.5e-271)
           x
           (if (<= t 42.0) t_1 (if (<= t 1.2e+117) x t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double t_2 = t * (y / a);
	double tmp;
	if (t <= -5.2e+141) {
		tmp = t_2;
	} else if (t <= -9e-49) {
		tmp = x;
	} else if (t <= -6e-195) {
		tmp = t_1;
	} else if (t <= 2.5e-271) {
		tmp = x;
	} else if (t <= 42.0) {
		tmp = t_1;
	} else if (t <= 1.2e+117) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = z * (y / -a)
    t_2 = t * (y / a)
    if (t <= (-5.2d+141)) then
        tmp = t_2
    else if (t <= (-9d-49)) then
        tmp = x
    else if (t <= (-6d-195)) then
        tmp = t_1
    else if (t <= 2.5d-271) then
        tmp = x
    else if (t <= 42.0d0) then
        tmp = t_1
    else if (t <= 1.2d+117) then
        tmp = x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double t_2 = t * (y / a);
	double tmp;
	if (t <= -5.2e+141) {
		tmp = t_2;
	} else if (t <= -9e-49) {
		tmp = x;
	} else if (t <= -6e-195) {
		tmp = t_1;
	} else if (t <= 2.5e-271) {
		tmp = x;
	} else if (t <= 42.0) {
		tmp = t_1;
	} else if (t <= 1.2e+117) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	t_2 = t * (y / a)
	tmp = 0
	if t <= -5.2e+141:
		tmp = t_2
	elif t <= -9e-49:
		tmp = x
	elif t <= -6e-195:
		tmp = t_1
	elif t <= 2.5e-271:
		tmp = x
	elif t <= 42.0:
		tmp = t_1
	elif t <= 1.2e+117:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	t_2 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t <= -5.2e+141)
		tmp = t_2;
	elseif (t <= -9e-49)
		tmp = x;
	elseif (t <= -6e-195)
		tmp = t_1;
	elseif (t <= 2.5e-271)
		tmp = x;
	elseif (t <= 42.0)
		tmp = t_1;
	elseif (t <= 1.2e+117)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	t_2 = t * (y / a);
	tmp = 0.0;
	if (t <= -5.2e+141)
		tmp = t_2;
	elseif (t <= -9e-49)
		tmp = x;
	elseif (t <= -6e-195)
		tmp = t_1;
	elseif (t <= 2.5e-271)
		tmp = x;
	elseif (t <= 42.0)
		tmp = t_1;
	elseif (t <= 1.2e+117)
		tmp = x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.2e+141], t$95$2, If[LessEqual[t, -9e-49], x, If[LessEqual[t, -6e-195], t$95$1, If[LessEqual[t, 2.5e-271], x, If[LessEqual[t, 42.0], t$95$1, If[LessEqual[t, 1.2e+117], x, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.1999999999999999e141 or 1.1999999999999999e117 < t

   1. Initial program 84.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 63.5%

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

      1. *-commutative 63.5%

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

   7. Simplified 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-/l* 74.3%

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

   9. Applied egg-rr 74.3%

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

   if -5.1999999999999999e141 < t < -9.0000000000000004e-49 or -6e-195 < t < 2.5000000000000001e-271 or 42 < t < 1.1999999999999999e117

   1. Initial program 91.9%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf 60.4%

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

   if -9.0000000000000004e-49 < t < -6e-195 or 2.5000000000000001e-271 < t < 42

   1. Initial program 97.6%

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

   3. Taylor expanded in z around inf 96.6%

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

      1. mul-1-neg 96.6%

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

      2. unsub-neg 96.6%

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

      3. *-commutative 96.6%

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

      4. associate-/l* 96.6%

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

   5. Simplified 96.6%

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

   6. Taylor expanded in z around inf 60.3%

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

      1. mul-1-neg 60.3%

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

      2. associate-*l/ 61.6%

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

      3. distribute-rgt-neg-in 61.6%

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

   8. Simplified 61.6%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+141}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-195}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 42:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{-a}\\ t_2 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+139}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-192}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 30:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a)))) (t_2 (* t (/ y a))))
   (if (<= t -8.8e+139)
     t_2
     (if (<= t -1e-48)
       x
       (if (<= t -2.3e-192)
         t_1
         (if (<= t 3.7e-179)
           x
           (if (<= t 30.0) t_1 (if (<= t 1.02e+117) x t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / -a);
	double t_2 = t * (y / a);
	double tmp;
	if (t <= -8.8e+139) {
		tmp = t_2;
	} else if (t <= -1e-48) {
		tmp = x;
	} else if (t <= -2.3e-192) {
		tmp = t_1;
	} else if (t <= 3.7e-179) {
		tmp = x;
	} else if (t <= 30.0) {
		tmp = t_1;
	} else if (t <= 1.02e+117) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = y * (z / -a)
    t_2 = t * (y / a)
    if (t <= (-8.8d+139)) then
        tmp = t_2
    else if (t <= (-1d-48)) then
        tmp = x
    else if (t <= (-2.3d-192)) then
        tmp = t_1
    else if (t <= 3.7d-179) then
        tmp = x
    else if (t <= 30.0d0) then
        tmp = t_1
    else if (t <= 1.02d+117) then
        tmp = x
    else
        tmp = t_2
    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 / -a);
	double t_2 = t * (y / a);
	double tmp;
	if (t <= -8.8e+139) {
		tmp = t_2;
	} else if (t <= -1e-48) {
		tmp = x;
	} else if (t <= -2.3e-192) {
		tmp = t_1;
	} else if (t <= 3.7e-179) {
		tmp = x;
	} else if (t <= 30.0) {
		tmp = t_1;
	} else if (t <= 1.02e+117) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / -a)
	t_2 = t * (y / a)
	tmp = 0
	if t <= -8.8e+139:
		tmp = t_2
	elif t <= -1e-48:
		tmp = x
	elif t <= -2.3e-192:
		tmp = t_1
	elif t <= 3.7e-179:
		tmp = x
	elif t <= 30.0:
		tmp = t_1
	elif t <= 1.02e+117:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(-a)))
	t_2 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t <= -8.8e+139)
		tmp = t_2;
	elseif (t <= -1e-48)
		tmp = x;
	elseif (t <= -2.3e-192)
		tmp = t_1;
	elseif (t <= 3.7e-179)
		tmp = x;
	elseif (t <= 30.0)
		tmp = t_1;
	elseif (t <= 1.02e+117)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / -a);
	t_2 = t * (y / a);
	tmp = 0.0;
	if (t <= -8.8e+139)
		tmp = t_2;
	elseif (t <= -1e-48)
		tmp = x;
	elseif (t <= -2.3e-192)
		tmp = t_1;
	elseif (t <= 3.7e-179)
		tmp = x;
	elseif (t <= 30.0)
		tmp = t_1;
	elseif (t <= 1.02e+117)
		tmp = x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -8.8e+139], t$95$2, If[LessEqual[t, -1e-48], x, If[LessEqual[t, -2.3e-192], t$95$1, If[LessEqual[t, 3.7e-179], x, If[LessEqual[t, 30.0], t$95$1, If[LessEqual[t, 1.02e+117], x, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -8.7999999999999998e139 or 1.02e117 < t

   1. Initial program 84.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around inf 63.5%

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

      1. *-commutative 63.5%

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

   7. Simplified 63.5%

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

      1. *-commutative 63.5%

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

      2. associate-/l* 74.3%

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

   9. Applied egg-rr 74.3%

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

   if -8.7999999999999998e139 < t < -9.9999999999999997e-49 or -2.30000000000000018e-192 < t < 3.6999999999999999e-179 or 30 < t < 1.02e117

   1. Initial program 93.0%

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

      1. associate-/l* 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in x around inf 57.9%

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

   if -9.9999999999999997e-49 < t < -2.30000000000000018e-192 or 3.6999999999999999e-179 < t < 30

   1. Initial program 97.2%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around inf 62.8%

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

      1. mul-1-neg 62.8%

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

      2. associate-/l* 58.8%

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

      3. distribute-rgt-neg-in 58.8%

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

      4. distribute-frac-neg2 58.8%

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

   7. Simplified 58.8%

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

Alternative 5: 81.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+199}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq -0.019 \lor \neg \left(z \leq 2.6 \cdot 10^{-10}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -3.8e+199)
   (* (/ y a) (- t z))
   (if (or (<= z -0.019) (not (<= z 2.6e-10)))
     (- x (/ y (/ a z)))
     (+ x (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -3.8e+199) {
		tmp = (y / a) * (t - z);
	} else if ((z <= -0.019) || !(z <= 2.6e-10)) {
		tmp = x - (y / (a / 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 <= (-3.8d+199)) then
        tmp = (y / a) * (t - z)
    else if ((z <= (-0.019d0)) .or. (.not. (z <= 2.6d-10))) then
        tmp = x - (y / (a / 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 <= -3.8e+199) {
		tmp = (y / a) * (t - z);
	} else if ((z <= -0.019) || !(z <= 2.6e-10)) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -3.8e+199:
		tmp = (y / a) * (t - z)
	elif (z <= -0.019) or not (z <= 2.6e-10):
		tmp = x - (y / (a / z))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -3.8e+199)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif ((z <= -0.019) || !(z <= 2.6e-10))
		tmp = Float64(x - Float64(y / Float64(a / 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 <= -3.8e+199)
		tmp = (y / a) * (t - z);
	elseif ((z <= -0.019) || ~((z <= 2.6e-10)))
		tmp = x - (y / (a / z));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -3.8e+199], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -0.019], N[Not[LessEqual[z, 2.6e-10]], $MachinePrecision]], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.8e199

   1. Initial program 89.8%

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

      1. associate-/l* 80.2%

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

   3. Simplified 80.2%

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

      1. clear-num 80.1%

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

      2. un-div-inv 80.0%

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

   6. Applied egg-rr 80.0%

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

   7. Taylor expanded in x around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. associate-*r/ 69.9%

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

      3. distribute-rgt-neg-in 69.9%

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

      4. neg-sub0 69.9%

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

      5. div-sub 66.3%

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

      6. associate--r- 66.3%

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

      7. neg-sub0 66.3%

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

      8. mul-1-neg 66.3%

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

      9. +-commutative 66.3%

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

      10. mul-1-neg 66.3%

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

      11. sub-neg 66.3%

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

      12. distribute-rgt-out-- 59.2%

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

      13. associate-*l/ 55.9%

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

      14. *-commutative 55.9%

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

      15. associate-*r/ 68.5%

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

      16. associate-*r/ 68.5%

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

      17. associate-*l/ 78.4%

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

      18. *-commutative 78.4%

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

      19. distribute-rgt-out-- 89.1%

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

   9. Simplified 89.1%

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

   if -3.8e199 < z < -0.0189999999999999995 or 2.59999999999999981e-10 < z

   1. Initial program 91.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 81.8%

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

      1. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

      1. clear-num 83.5%

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

      2. un-div-inv 83.8%

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

   9. Applied egg-rr 83.8%

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

   if -0.0189999999999999995 < z < 2.59999999999999981e-10

   1. Initial program 91.8%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 94.3%

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

      2. un-div-inv 94.3%

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

   6. Applied egg-rr 94.3%

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

   7. Taylor expanded in z around 0 84.9%

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

      1. cancel-sign-sub-inv 84.9%

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

      2. metadata-eval 84.9%

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

      3. associate-*l/ 88.3%

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

      4. *-commutative 88.3%

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

      5. *-lft-identity 88.3%

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

   9. Simplified 88.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{+199}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq -0.019 \lor \neg \left(z \leq 2.6 \cdot 10^{-10}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 81.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+199}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-8} \lor \neg \left(z \leq 1.85 \cdot 10^{-10}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.2e+199)
   (* (/ y a) (- t z))
   (if (or (<= z -5e-8) (not (<= z 1.85e-10)))
     (- x (* y (/ z a)))
     (+ x (* y (/ t a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+199) {
		tmp = (y / a) * (t - z);
	} else if ((z <= -5e-8) || !(z <= 1.85e-10)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.2d+199)) then
        tmp = (y / a) * (t - z)
    else if ((z <= (-5d-8)) .or. (.not. (z <= 1.85d-10))) then
        tmp = x - (y * (z / a))
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.2e+199) {
		tmp = (y / a) * (t - z);
	} else if ((z <= -5e-8) || !(z <= 1.85e-10)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.2e+199:
		tmp = (y / a) * (t - z)
	elif (z <= -5e-8) or not (z <= 1.85e-10):
		tmp = x - (y * (z / a))
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.2e+199)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif ((z <= -5e-8) || !(z <= 1.85e-10))
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.2e+199)
		tmp = (y / a) * (t - z);
	elseif ((z <= -5e-8) || ~((z <= 1.85e-10)))
		tmp = x - (y * (z / a));
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.2e+199], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -5e-8], N[Not[LessEqual[z, 1.85e-10]], $MachinePrecision]], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000007e199

   1. Initial program 89.8%

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

      1. associate-/l* 80.2%

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

   3. Simplified 80.2%

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

      1. clear-num 80.1%

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

      2. un-div-inv 80.0%

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

   6. Applied egg-rr 80.0%

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

   7. Taylor expanded in x around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. associate-*r/ 69.9%

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

      3. distribute-rgt-neg-in 69.9%

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

      4. neg-sub0 69.9%

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

      5. div-sub 66.3%

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

      6. associate--r- 66.3%

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

      7. neg-sub0 66.3%

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

      8. mul-1-neg 66.3%

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

      9. +-commutative 66.3%

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

      10. mul-1-neg 66.3%

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

      11. sub-neg 66.3%

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

      12. distribute-rgt-out-- 59.2%

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

      13. associate-*l/ 55.9%

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

      14. *-commutative 55.9%

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

      15. associate-*r/ 68.5%

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

      16. associate-*r/ 68.5%

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

      17. associate-*l/ 78.4%

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

      18. *-commutative 78.4%

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

      19. distribute-rgt-out-- 89.1%

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

   9. Simplified 89.1%

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

   if -1.20000000000000007e199 < z < -4.9999999999999998e-8 or 1.85000000000000007e-10 < z

   1. Initial program 91.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 81.8%

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

      1. associate-/l* 83.5%

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

   7. Simplified 83.5%

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

   if -4.9999999999999998e-8 < z < 1.85000000000000007e-10

   1. Initial program 91.8%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 94.3%

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

      2. un-div-inv 94.3%

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

   6. Applied egg-rr 94.3%

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

   7. Taylor expanded in z around 0 84.9%

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

      1. cancel-sign-sub-inv 84.9%

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

      2. metadata-eval 84.9%

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

      3. associate-*l/ 88.3%

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

      4. *-commutative 88.3%

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

      5. *-lft-identity 88.3%

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

   9. Simplified 88.3%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+199}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-8} \lor \neg \left(z \leq 1.85 \cdot 10^{-10}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+42} \lor \neg \left(x \leq 4.1 \cdot 10^{-85}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -2.8e+42) (not (<= x 4.1e-85)))
   (+ x (* y (/ t a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -2.8e+42) || !(x <= 4.1e-85)) {
		tmp = x + (y * (t / a));
	} 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 ((x <= (-2.8d+42)) .or. (.not. (x <= 4.1d-85))) then
        tmp = x + (y * (t / a))
    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 ((x <= -2.8e+42) || !(x <= 4.1e-85)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -2.8e+42) or not (x <= 4.1e-85):
		tmp = x + (y * (t / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -2.8e+42) || !(x <= 4.1e-85))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	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 ((x <= -2.8e+42) || ~((x <= 4.1e-85)))
		tmp = x + (y * (t / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -2.8e+42], N[Not[LessEqual[x, 4.1e-85]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.7999999999999999e42 or 4.09999999999999994e-85 < x

   1. Initial program 93.0%

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

      1. associate-/l* 96.4%

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

   3. Simplified 96.4%

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

      1. clear-num 96.4%

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

      2. un-div-inv 96.4%

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

   6. Applied egg-rr 96.4%

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

   7. Taylor expanded in z around 0 78.5%

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

      1. cancel-sign-sub-inv 78.5%

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

      2. metadata-eval 78.5%

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

      3. associate-*l/ 82.0%

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

      4. *-commutative 82.0%

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

      5. *-lft-identity 82.0%

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

   9. Simplified 82.0%

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

   if -2.7999999999999999e42 < x < 4.09999999999999994e-85

   1. Initial program 89.8%

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

      1. clear-num 90.6%

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

      2. un-div-inv 90.9%

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

   6. Applied egg-rr 90.9%

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

   7. Taylor expanded in x around 0 77.9%

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

      1. mul-1-neg 77.9%

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

      2. associate-*r/ 78.8%

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

      3. distribute-rgt-neg-in 78.8%

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

      4. neg-sub0 78.8%

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

      5. div-sub 77.9%

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

      6. associate--r- 77.9%

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

      7. neg-sub0 77.9%

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

      8. mul-1-neg 77.9%

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

      9. +-commutative 77.9%

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

      10. mul-1-neg 77.9%

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

      11. sub-neg 77.9%

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

      12. distribute-rgt-out-- 77.1%

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

      13. associate-*l/ 73.9%

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

      14. *-commutative 73.9%

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

      15. associate-*r/ 76.2%

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

      16. associate-*r/ 76.2%

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

      17. associate-*l/ 77.5%

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

      18. *-commutative 77.5%

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

      19. distribute-rgt-out-- 84.1%

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

   9. Simplified 84.1%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+42} \lor \neg \left(x \leq 4.1 \cdot 10^{-85}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-39} \lor \neg \left(y \leq 5 \cdot 10^{-199}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.5e-39) (not (<= y 5e-199))) (* y (/ (- t z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.5e-39) || !(y <= 5e-199)) {
		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 <= (-1.5d-39)) .or. (.not. (y <= 5d-199))) 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 <= -1.5e-39) || !(y <= 5e-199)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.5e-39) or not (y <= 5e-199):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.5e-39) || !(y <= 5e-199))
		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 <= -1.5e-39) || ~((y <= 5e-199)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.5e-39], N[Not[LessEqual[y, 5e-199]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000014e-39 or 4.9999999999999996e-199 < y

   1. Initial program 87.7%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

      1. clear-num 96.7%

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

      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 x around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-*r/ 75.1%

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

      3. distribute-rgt-neg-in 75.1%

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

      4. neg-sub0 75.1%

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

      5. div-sub 73.9%

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

      6. associate--r- 73.9%

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

      7. neg-sub0 73.9%

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

      8. mul-1-neg 73.9%

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

      9. +-commutative 73.9%

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

      10. mul-1-neg 73.9%

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

      11. sub-neg 73.9%

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

      12. distribute-rgt-out-- 70.0%

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

      13. associate-*l/ 63.6%

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

      14. *-commutative 63.6%

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

      15. associate-*r/ 62.5%

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

      16. associate-*r/ 63.5%

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

      17. associate-*l/ 65.8%

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

      18. *-commutative 65.8%

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

      19. distribute-rgt-out-- 75.0%

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

   9. Simplified 75.0%

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

   10. Taylor expanded in y around 0 67.7%

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

       1. associate-/l* 75.1%

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

   12. Simplified 75.1%

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

   if -1.50000000000000014e-39 < y < 4.9999999999999996e-199

   1. Initial program 99.9%

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

      1. associate-/l* 86.9%

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

   3. Simplified 86.9%

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

   5. Taylor expanded in x around inf 63.6%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-39} \lor \neg \left(y \leq 5 \cdot 10^{-199}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0064:\\ \;\;\;\;x - \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-10}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -0.0064)
   (- x (/ z (/ a y)))
   (if (<= z 1.35e-10) (+ x (* y (/ t a))) (- x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -0.0064) {
		tmp = x - (z / (a / y));
	} else if (z <= 1.35e-10) {
		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 (z <= (-0.0064d0)) then
        tmp = x - (z / (a / y))
    else if (z <= 1.35d-10) 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 (z <= -0.0064) {
		tmp = x - (z / (a / y));
	} else if (z <= 1.35e-10) {
		tmp = x + (y * (t / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -0.0064:
		tmp = x - (z / (a / y))
	elif z <= 1.35e-10:
		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 (z <= -0.0064)
		tmp = Float64(x - Float64(z / Float64(a / y)));
	elseif (z <= 1.35e-10)
		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 (z <= -0.0064)
		tmp = x - (z / (a / y));
	elseif (z <= 1.35e-10)
		tmp = x + (y * (t / a));
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -0.0064], N[(x - N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e-10], 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 3 regimes

2. if z < -0.00640000000000000031

   1. Initial program 93.3%

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

      1. associate-/l* 89.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in z around inf 85.4%

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

      1. div-inv 85.4%

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

      2. *-commutative 85.4%

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

   7. Applied egg-rr 85.4%

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

      1. associate-*l* 89.1%

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

      2. div-inv 89.1%

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

      3. clear-num 87.9%

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

      4. un-div-inv 87.9%

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

   9. Applied egg-rr 87.9%

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

   if -0.00640000000000000031 < z < 1.35e-10

   1. Initial program 91.8%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

      1. clear-num 94.3%

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

      2. un-div-inv 94.3%

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

   6. Applied egg-rr 94.3%

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

   7. Taylor expanded in z around 0 84.9%

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

      1. cancel-sign-sub-inv 84.9%

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

      2. metadata-eval 84.9%

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

      3. associate-*l/ 88.3%

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

      4. *-commutative 88.3%

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

      5. *-lft-identity 88.3%

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

   9. Simplified 88.3%

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

   if 1.35e-10 < z

   1. Initial program 88.7%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around inf 78.3%

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

      1. associate-/l* 82.5%

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

   7. Simplified 82.5%

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

      1. clear-num 82.5%

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

      2. un-div-inv 82.9%

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

   9. Applied egg-rr 82.9%

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

Alternative 10: 67.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -3.6e+143) x (if (<= x 2.4e-14) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -3.6e+143) {
		tmp = x;
	} else if (x <= 2.4e-14) {
		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 (x <= (-3.6d+143)) then
        tmp = x
    else if (x <= 2.4d-14) 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 (x <= -3.6e+143) {
		tmp = x;
	} else if (x <= 2.4e-14) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -3.6e+143:
		tmp = x
	elif x <= 2.4e-14:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -3.6e+143)
		tmp = x;
	elseif (x <= 2.4e-14)
		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 (x <= -3.6e+143)
		tmp = x;
	elseif (x <= 2.4e-14)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -3.6e+143], x, If[LessEqual[x, 2.4e-14], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5999999999999999e143 or 2.4e-14 < x

   1. Initial program 92.7%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf 63.7%

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

   if -3.5999999999999999e143 < x < 2.4e-14

   1. Initial program 90.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 91.2%

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

      2. un-div-inv 91.4%

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

   6. Applied egg-rr 91.4%

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

   7. Taylor expanded in x around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. associate-*r/ 76.0%

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

      3. distribute-rgt-neg-in 76.0%

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

      4. neg-sub0 76.0%

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

      5. div-sub 74.7%

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

      6. associate--r- 74.7%

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

      7. neg-sub0 74.7%

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

      8. mul-1-neg 74.7%

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

      9. +-commutative 74.7%

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

      10. mul-1-neg 74.7%

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

      11. sub-neg 74.7%

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

      12. distribute-rgt-out-- 73.4%

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

      13. associate-*l/ 70.2%

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

      14. *-commutative 70.2%

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

      15. associate-*r/ 72.5%

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

      16. associate-*r/ 73.7%

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

      17. associate-*l/ 74.1%

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

      18. *-commutative 74.1%

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

      19. distribute-rgt-out-- 81.4%

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

   9. Simplified 81.4%

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

Alternative 11: 48.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{+143}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-24}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.4e+143) x (if (<= x 1.25e-24) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.4e+143) {
		tmp = x;
	} else if (x <= 1.25e-24) {
		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 (x <= (-6.4d+143)) then
        tmp = x
    else if (x <= 1.25d-24) 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 (x <= -6.4e+143) {
		tmp = x;
	} else if (x <= 1.25e-24) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.4e+143:
		tmp = x
	elif x <= 1.25e-24:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.4e+143)
		tmp = x;
	elseif (x <= 1.25e-24)
		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 (x <= -6.4e+143)
		tmp = x;
	elseif (x <= 1.25e-24)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.4e+143], x, If[LessEqual[x, 1.25e-24], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.40000000000000033e143 or 1.24999999999999995e-24 < x

   1. Initial program 92.7%

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

      1. associate-/l* 97.2%

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

   3. Simplified 97.2%

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

   5. Taylor expanded in x around inf 63.7%

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

   if -6.40000000000000033e143 < x < 1.24999999999999995e-24

   1. Initial program 90.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around inf 40.1%

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

      1. *-commutative 40.1%

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

   7. Simplified 40.1%

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

      1. *-commutative 40.1%

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

      2. associate-/l* 46.0%

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

   9. Applied egg-rr 46.0%

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

Alternative 12: 93.7% 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 91.5%

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

   1. associate-/l* 93.7%

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

3. Simplified 93.7%

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

   1. clear-num 93.6%

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

   2. un-div-inv 93.7%

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

6. Applied egg-rr 93.7%

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

7. Final simplification 93.7%

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

Alternative 13: 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 91.5%

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

   1. associate-/l* 93.7%

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

3. Simplified 93.7%

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

5. Final simplification 93.7%

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

Alternative 14: 40.6% 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 91.5%

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

   1. associate-/l* 93.7%

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

3. Simplified 93.7%

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

5. Taylor expanded in x around inf 36.3%

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

Developer target: 99.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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