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

Percentage Accurate: 93.3% → 99.2%

Time: 11.8s

Alternatives: 15

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: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+167} \lor \neg \left(t\_1 \leq 10^{+156}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -2e+167) (not (<= t_1 1e+156)))
     (+ x (/ y (/ a (- t z))))
     (+ 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 <= -2e+167) || !(t_1 <= 1e+156)) {
		tmp = x + (y / (a / (t - z)));
	} 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 <= (-2d+167)) .or. (.not. (t_1 <= 1d+156))) then
        tmp = x + (y / (a / (t - z)))
    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 <= -2e+167) || !(t_1 <= 1e+156)) {
		tmp = x + (y / (a / (t - z)));
	} 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 <= -2e+167) or not (t_1 <= 1e+156):
		tmp = x + (y / (a / (t - z)))
	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 <= -2e+167) || !(t_1 <= 1e+156))
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - z))));
	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 <= -2e+167) || ~((t_1 <= 1e+156)))
		tmp = x + (y / (a / (t - z)));
	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, -2e+167], N[Not[LessEqual[t$95$1, 1e+156]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(t - z), $MachinePrecision]), $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)) < -2.0000000000000001e167 or 9.9999999999999998e155 < (*.f64 y (-.f64 z t))

   1. Initial program 85.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.8%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -2.0000000000000001e167 < (*.f64 y (-.f64 z t)) < 9.9999999999999998e155

   1. Initial program 99.4%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2 \cdot 10^{+167} \lor \neg \left(y \cdot \left(z - t\right) \leq 10^{+156}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{-a}\\ t_2 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -1700:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-117}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a)))) (t_2 (* t (/ y a))))
   (if (<= y -1700.0)
     t_2
     (if (<= y -1e-24)
       t_1
       (if (<= y -6.2e-52)
         t_2
         (if (<= y -5.2e-87)
           x
           (if (<= y -2.85e-117)
             (/ (* y t) a)
             (if (<= y 2.75e-14)
               x
               (if (<= y 6.9e+198) (* y (/ t a)) t_1)))))))))

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 (y <= -1700.0) {
		tmp = t_2;
	} else if (y <= -1e-24) {
		tmp = t_1;
	} else if (y <= -6.2e-52) {
		tmp = t_2;
	} else if (y <= -5.2e-87) {
		tmp = x;
	} else if (y <= -2.85e-117) {
		tmp = (y * t) / a;
	} else if (y <= 2.75e-14) {
		tmp = x;
	} else if (y <= 6.9e+198) {
		tmp = y * (t / 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) :: t_2
    real(8) :: tmp
    t_1 = y * (z / -a)
    t_2 = t * (y / a)
    if (y <= (-1700.0d0)) then
        tmp = t_2
    else if (y <= (-1d-24)) then
        tmp = t_1
    else if (y <= (-6.2d-52)) then
        tmp = t_2
    else if (y <= (-5.2d-87)) then
        tmp = x
    else if (y <= (-2.85d-117)) then
        tmp = (y * t) / a
    else if (y <= 2.75d-14) then
        tmp = x
    else if (y <= 6.9d+198) then
        tmp = y * (t / 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 = y * (z / -a);
	double t_2 = t * (y / a);
	double tmp;
	if (y <= -1700.0) {
		tmp = t_2;
	} else if (y <= -1e-24) {
		tmp = t_1;
	} else if (y <= -6.2e-52) {
		tmp = t_2;
	} else if (y <= -5.2e-87) {
		tmp = x;
	} else if (y <= -2.85e-117) {
		tmp = (y * t) / a;
	} else if (y <= 2.75e-14) {
		tmp = x;
	} else if (y <= 6.9e+198) {
		tmp = y * (t / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / -a)
	t_2 = t * (y / a)
	tmp = 0
	if y <= -1700.0:
		tmp = t_2
	elif y <= -1e-24:
		tmp = t_1
	elif y <= -6.2e-52:
		tmp = t_2
	elif y <= -5.2e-87:
		tmp = x
	elif y <= -2.85e-117:
		tmp = (y * t) / a
	elif y <= 2.75e-14:
		tmp = x
	elif y <= 6.9e+198:
		tmp = y * (t / a)
	else:
		tmp = t_1
	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 (y <= -1700.0)
		tmp = t_2;
	elseif (y <= -1e-24)
		tmp = t_1;
	elseif (y <= -6.2e-52)
		tmp = t_2;
	elseif (y <= -5.2e-87)
		tmp = x;
	elseif (y <= -2.85e-117)
		tmp = Float64(Float64(y * t) / a);
	elseif (y <= 2.75e-14)
		tmp = x;
	elseif (y <= 6.9e+198)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = t_1;
	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 (y <= -1700.0)
		tmp = t_2;
	elseif (y <= -1e-24)
		tmp = t_1;
	elseif (y <= -6.2e-52)
		tmp = t_2;
	elseif (y <= -5.2e-87)
		tmp = x;
	elseif (y <= -2.85e-117)
		tmp = (y * t) / a;
	elseif (y <= 2.75e-14)
		tmp = x;
	elseif (y <= 6.9e+198)
		tmp = y * (t / a);
	else
		tmp = t_1;
	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[y, -1700.0], t$95$2, If[LessEqual[y, -1e-24], t$95$1, If[LessEqual[y, -6.2e-52], t$95$2, If[LessEqual[y, -5.2e-87], x, If[LessEqual[y, -2.85e-117], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2.75e-14], x, If[LessEqual[y, 6.9e+198], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1700 or -9.99999999999999924e-25 < y < -6.1999999999999998e-52

   1. Initial program 88.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 88.8%

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

      2. clear-num 88.8%

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

   6. Applied egg-rr 88.8%

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

   7. Taylor expanded in t around inf 49.2%

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

      1. associate-*r/ 60.5%

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

   9. Simplified 60.5%

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

   if -1700 < y < -9.99999999999999924e-25 or 6.89999999999999963e198 < y

   1. Initial program 89.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 64.6%

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

      1. mul-1-neg 64.6%

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

      2. associate-/l* 71.2%

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

      3. distribute-rgt-neg-in 71.2%

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

      4. distribute-frac-neg2 71.2%

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

   7. Simplified 71.2%

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

   if -6.1999999999999998e-52 < y < -5.20000000000000005e-87 or -2.85e-117 < y < 2.74999999999999996e-14

   1. Initial program 99.2%

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

      1. associate-/l* 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in x around inf 69.2%

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

   if -5.20000000000000005e-87 < y < -2.85e-117

   1. Initial program 99.5%

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

      1. associate-/l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around inf 67.4%

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

      1. *-commutative 67.4%

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

   7. Simplified 67.4%

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

   if 2.74999999999999996e-14 < y < 6.89999999999999963e198

   1. Initial program 91.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-/l* 58.1%

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

   7. Simplified 58.1%

      \[\leadsto \color{blue}{y \cdot \frac{t}{a}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1700:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-24}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.85 \cdot 10^{-117}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.9 \cdot 10^{+198}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -1920:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-38}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-53}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-117}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+199}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= y -1920.0)
     t_1
     (if (<= y -1.3e-38)
       (/ (* y (- z)) a)
       (if (<= y -3.9e-53)
         t_1
         (if (<= y -4.2e-85)
           x
           (if (<= y -2.15e-117)
             (/ (* y t) a)
             (if (<= y 2.35e-14)
               x
               (if (<= y 1.26e+199) (* y (/ t a)) (* y (/ z (- a))))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -1920.0) {
		tmp = t_1;
	} else if (y <= -1.3e-38) {
		tmp = (y * -z) / a;
	} else if (y <= -3.9e-53) {
		tmp = t_1;
	} else if (y <= -4.2e-85) {
		tmp = x;
	} else if (y <= -2.15e-117) {
		tmp = (y * t) / a;
	} else if (y <= 2.35e-14) {
		tmp = x;
	} else if (y <= 1.26e+199) {
		tmp = y * (t / a);
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (y <= (-1920.0d0)) then
        tmp = t_1
    else if (y <= (-1.3d-38)) then
        tmp = (y * -z) / a
    else if (y <= (-3.9d-53)) then
        tmp = t_1
    else if (y <= (-4.2d-85)) then
        tmp = x
    else if (y <= (-2.15d-117)) then
        tmp = (y * t) / a
    else if (y <= 2.35d-14) then
        tmp = x
    else if (y <= 1.26d+199) then
        tmp = y * (t / a)
    else
        tmp = 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 t_1 = t * (y / a);
	double tmp;
	if (y <= -1920.0) {
		tmp = t_1;
	} else if (y <= -1.3e-38) {
		tmp = (y * -z) / a;
	} else if (y <= -3.9e-53) {
		tmp = t_1;
	} else if (y <= -4.2e-85) {
		tmp = x;
	} else if (y <= -2.15e-117) {
		tmp = (y * t) / a;
	} else if (y <= 2.35e-14) {
		tmp = x;
	} else if (y <= 1.26e+199) {
		tmp = y * (t / a);
	} else {
		tmp = y * (z / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if y <= -1920.0:
		tmp = t_1
	elif y <= -1.3e-38:
		tmp = (y * -z) / a
	elif y <= -3.9e-53:
		tmp = t_1
	elif y <= -4.2e-85:
		tmp = x
	elif y <= -2.15e-117:
		tmp = (y * t) / a
	elif y <= 2.35e-14:
		tmp = x
	elif y <= 1.26e+199:
		tmp = y * (t / a)
	else:
		tmp = y * (z / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (y <= -1920.0)
		tmp = t_1;
	elseif (y <= -1.3e-38)
		tmp = Float64(Float64(y * Float64(-z)) / a);
	elseif (y <= -3.9e-53)
		tmp = t_1;
	elseif (y <= -4.2e-85)
		tmp = x;
	elseif (y <= -2.15e-117)
		tmp = Float64(Float64(y * t) / a);
	elseif (y <= 2.35e-14)
		tmp = x;
	elseif (y <= 1.26e+199)
		tmp = Float64(y * Float64(t / a));
	else
		tmp = Float64(y * Float64(z / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (y <= -1920.0)
		tmp = t_1;
	elseif (y <= -1.3e-38)
		tmp = (y * -z) / a;
	elseif (y <= -3.9e-53)
		tmp = t_1;
	elseif (y <= -4.2e-85)
		tmp = x;
	elseif (y <= -2.15e-117)
		tmp = (y * t) / a;
	elseif (y <= 2.35e-14)
		tmp = x;
	elseif (y <= 1.26e+199)
		tmp = y * (t / a);
	else
		tmp = y * (z / -a);
	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[y, -1920.0], t$95$1, If[LessEqual[y, -1.3e-38], N[(N[(y * (-z)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -3.9e-53], t$95$1, If[LessEqual[y, -4.2e-85], x, If[LessEqual[y, -2.15e-117], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 2.35e-14], x, If[LessEqual[y, 1.26e+199], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1920 or -1.30000000000000005e-38 < y < -3.9000000000000002e-53

   1. Initial program 88.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 88.8%

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

      2. clear-num 88.8%

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

   6. Applied egg-rr 88.8%

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

   7. Taylor expanded in t around inf 49.2%

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

      1. associate-*r/ 60.5%

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

   9. Simplified 60.5%

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

   if -1920 < y < -1.30000000000000005e-38

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 83.8%

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

      1. mul-1-neg 83.8%

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

      2. associate-/l* 83.5%

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

      3. distribute-rgt-neg-in 83.5%

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

      4. distribute-frac-neg2 83.5%

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

   7. Simplified 83.5%

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

      1. *-commutative 83.5%

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

      2. distribute-frac-neg2 83.5%

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

      3. distribute-frac-neg 83.5%

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

      4. associate-*l/ 83.8%

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

   9. Applied egg-rr 83.8%

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

   if -3.9000000000000002e-53 < y < -4.2e-85 or -2.15e-117 < y < 2.3500000000000001e-14

   1. Initial program 99.2%

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

      1. associate-/l* 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in x around inf 69.2%

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

   if -4.2e-85 < y < -2.15e-117

   1. Initial program 99.5%

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

      1. associate-/l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around inf 67.4%

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

      1. *-commutative 67.4%

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

   7. Simplified 67.4%

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

   if 2.3500000000000001e-14 < y < 1.26000000000000002e199

   1. Initial program 91.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around inf 50.1%

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

      1. *-commutative 50.1%

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

      2. associate-/l* 58.1%

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

   7. Simplified 58.1%

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

   if 1.26000000000000002e199 < y

   1. Initial program 86.4%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in z around inf 59.1%

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

      1. mul-1-neg 59.1%

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

      2. associate-/l* 67.6%

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

      3. distribute-rgt-neg-in 67.6%

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

      4. distribute-frac-neg2 67.6%

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

   7. Simplified 67.6%

      \[\leadsto \color{blue}{y \cdot \frac{z}{-a}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1920:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-38}:\\ \;\;\;\;\frac{y \cdot \left(-z\right)}{a}\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-53}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-85}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-117}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{+199}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 68.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-56} \lor \neg \left(y \leq -6 \cdot 10^{-80} \lor \neg \left(y \leq -3.8 \cdot 10^{-118}\right) \land y \leq 2.15 \cdot 10^{-14}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.4e-56)
         (not (or (<= y -6e-80) (and (not (<= y -3.8e-118)) (<= y 2.15e-14)))))
   (* y (/ (- t z) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.4e-56) || !((y <= -6e-80) || (!(y <= -3.8e-118) && (y <= 2.15e-14)))) {
		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 <= (-1.4d-56)) .or. (.not. (y <= (-6d-80)) .or. (.not. (y <= (-3.8d-118))) .and. (y <= 2.15d-14))) 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 <= -1.4e-56) || !((y <= -6e-80) || (!(y <= -3.8e-118) && (y <= 2.15e-14)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.4e-56) or not ((y <= -6e-80) or (not (y <= -3.8e-118) and (y <= 2.15e-14))):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.4e-56) || !((y <= -6e-80) || (!(y <= -3.8e-118) && (y <= 2.15e-14))))
		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 <= -1.4e-56) || ~(((y <= -6e-80) || (~((y <= -3.8e-118)) && (y <= 2.15e-14)))))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.4e-56], N[Not[Or[LessEqual[y, -6e-80], And[N[Not[LessEqual[y, -3.8e-118]], $MachinePrecision], LessEqual[y, 2.15e-14]]]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999997e-56 or -6.00000000000000014e-80 < y < -3.8000000000000001e-118 or 2.14999999999999999e-14 < y

   1. Initial program 90.5%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in x around 0 77.5%

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

      1. mul-1-neg 77.5%

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

      2. distribute-frac-neg2 77.5%

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

      3. associate-*r/ 84.3%

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

   7. Simplified 84.3%

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

      1. frac-2neg 84.3%

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

      2. div-inv 84.3%

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

      3. sub-neg 84.3%

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

      4. distribute-neg-in 84.3%

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

      5. add-sqr-sqrt 44.7%

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

      6. sqrt-unprod 56.2%

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

      7. sqr-neg 56.2%

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

      8. sqrt-unprod 18.9%

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

      9. add-sqr-sqrt 38.0%

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

      10. add-sqr-sqrt 19.0%

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

      11. sqrt-unprod 52.2%

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

      12. sqr-neg 52.2%

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

      13. sqrt-unprod 39.5%

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

      14. add-sqr-sqrt 84.3%

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

      15. remove-double-neg 84.3%

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

   9. Applied egg-rr 84.3%

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

       1. associate-*r/ 84.3%

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

       2. *-rgt-identity 84.3%

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

       3. +-commutative 84.3%

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

       4. unsub-neg 84.3%

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

   11. Simplified 84.3%

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

   if -1.39999999999999997e-56 < y < -6.00000000000000014e-80 or -3.8000000000000001e-118 < y < 2.14999999999999999e-14

   1. Initial program 99.2%

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

      1. associate-/l* 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in x around inf 69.2%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-56} \lor \neg \left(y \leq -6 \cdot 10^{-80} \lor \neg \left(y \leq -3.8 \cdot 10^{-118}\right) \land y \leq 2.15 \cdot 10^{-14}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 68.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-132}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t z))))
   (if (<= y -1.05e-55)
     t_1
     (if (<= y -1.5e-81)
       x
       (if (<= y -4e-132) t_1 (if (<= y 1.95e-14) x (* y (/ (- t z) a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (t - z);
	double tmp;
	if (y <= -1.05e-55) {
		tmp = t_1;
	} else if (y <= -1.5e-81) {
		tmp = x;
	} else if (y <= -4e-132) {
		tmp = t_1;
	} else if (y <= 1.95e-14) {
		tmp = x;
	} else {
		tmp = 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 / a) * (t - z)
    if (y <= (-1.05d-55)) then
        tmp = t_1
    else if (y <= (-1.5d-81)) then
        tmp = x
    else if (y <= (-4d-132)) then
        tmp = t_1
    else if (y <= 1.95d-14) then
        tmp = x
    else
        tmp = 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 / a) * (t - z);
	double tmp;
	if (y <= -1.05e-55) {
		tmp = t_1;
	} else if (y <= -1.5e-81) {
		tmp = x;
	} else if (y <= -4e-132) {
		tmp = t_1;
	} else if (y <= 1.95e-14) {
		tmp = x;
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (t - z)
	tmp = 0
	if y <= -1.05e-55:
		tmp = t_1
	elif y <= -1.5e-81:
		tmp = x
	elif y <= -4e-132:
		tmp = t_1
	elif y <= 1.95e-14:
		tmp = x
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(t - z))
	tmp = 0.0
	if (y <= -1.05e-55)
		tmp = t_1;
	elseif (y <= -1.5e-81)
		tmp = x;
	elseif (y <= -4e-132)
		tmp = t_1;
	elseif (y <= 1.95e-14)
		tmp = x;
	else
		tmp = Float64(y * Float64(Float64(t - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * (t - z);
	tmp = 0.0;
	if (y <= -1.05e-55)
		tmp = t_1;
	elseif (y <= -1.5e-81)
		tmp = x;
	elseif (y <= -4e-132)
		tmp = t_1;
	elseif (y <= 1.95e-14)
		tmp = x;
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e-55], t$95$1, If[LessEqual[y, -1.5e-81], x, If[LessEqual[y, -4e-132], t$95$1, If[LessEqual[y, 1.95e-14], x, N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0500000000000001e-55 or -1.4999999999999999e-81 < y < -3.9999999999999999e-132

   1. Initial program 91.0%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. associate-*r/ 91.0%

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

      2. clear-num 91.0%

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

   6. Applied egg-rr 91.0%

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

   7. Taylor expanded in x around 0 77.2%

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

      1. associate-/l* 81.6%

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

      2. associate-*r* 81.6%

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

      3. neg-mul-1 81.6%

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

      4. div-sub 79.2%

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

      5. distribute-lft-out-- 78.0%

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

      6. distribute-lft-neg-in 78.0%

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

      7. associate-*r/ 73.6%

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

      8. mul-1-neg 73.6%

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

      9. cancel-sign-sub 73.6%

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

      10. *-commutative 73.6%

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

      11. associate-*l/ 72.3%

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

      12. +-commutative 72.3%

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

      13. associate-*r/ 74.3%

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

      14. mul-1-neg 74.3%

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

      15. distribute-frac-neg 74.3%

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

      16. distribute-rgt-neg-in 74.3%

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

      17. *-commutative 74.3%

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

      18. associate-/l* 76.3%

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

      19. distribute-rgt-out 84.6%

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

      20. unsub-neg 84.6%

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

   9. Simplified 84.6%

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

   if -1.0500000000000001e-55 < y < -1.4999999999999999e-81 or -3.9999999999999999e-132 < y < 1.9499999999999999e-14

   1. Initial program 99.2%

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

      1. associate-/l* 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in x around inf 69.6%

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

   if 1.9499999999999999e-14 < y

   1. Initial program 90.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 77.2%

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

      1. mul-1-neg 77.2%

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

      2. distribute-frac-neg2 77.2%

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

      3. associate-*r/ 85.4%

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

   7. Simplified 85.4%

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

      1. frac-2neg 85.4%

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

      2. div-inv 85.4%

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

      3. sub-neg 85.4%

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

      4. distribute-neg-in 85.4%

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

      5. add-sqr-sqrt 44.1%

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

      6. sqrt-unprod 52.5%

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

      7. sqr-neg 52.5%

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

      8. sqrt-unprod 16.6%

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

      9. add-sqr-sqrt 36.1%

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

      10. add-sqr-sqrt 19.5%

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

      11. sqrt-unprod 53.8%

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

      12. sqr-neg 53.8%

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

      13. sqrt-unprod 41.2%

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

      14. add-sqr-sqrt 85.4%

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

      15. remove-double-neg 85.4%

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

   9. Applied egg-rr 85.4%

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

       1. associate-*r/ 85.4%

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

       2. *-rgt-identity 85.4%

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

       3. +-commutative 85.4%

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

       4. unsub-neg 85.4%

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

   11. Simplified 85.4%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-81}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-132}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-55} \lor \neg \left(y \leq -1.95 \cdot 10^{-86}\right) \land \left(y \leq -3 \cdot 10^{-117} \lor \neg \left(y \leq 4.2 \cdot 10^{-14}\right)\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.15e-55)
         (and (not (<= y -1.95e-86)) (or (<= y -3e-117) (not (<= y 4.2e-14)))))
   (* t (/ y a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.15e-55) || (!(y <= -1.95e-86) && ((y <= -3e-117) || !(y <= 4.2e-14)))) {
		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 <= (-2.15d-55)) .or. (.not. (y <= (-1.95d-86))) .and. (y <= (-3d-117)) .or. (.not. (y <= 4.2d-14))) 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 <= -2.15e-55) || (!(y <= -1.95e-86) && ((y <= -3e-117) || !(y <= 4.2e-14)))) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.15e-55) or (not (y <= -1.95e-86) and ((y <= -3e-117) or not (y <= 4.2e-14))):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.15e-55) || (!(y <= -1.95e-86) && ((y <= -3e-117) || !(y <= 4.2e-14))))
		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 <= -2.15e-55) || (~((y <= -1.95e-86)) && ((y <= -3e-117) || ~((y <= 4.2e-14)))))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.15e-55], And[N[Not[LessEqual[y, -1.95e-86]], $MachinePrecision], Or[LessEqual[y, -3e-117], N[Not[LessEqual[y, 4.2e-14]], $MachinePrecision]]]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.15000000000000005e-55 or -1.9500000000000001e-86 < y < -2.99999999999999991e-117 or 4.1999999999999998e-14 < y

   1. Initial program 90.5%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

      1. associate-*r/ 90.5%

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

      2. clear-num 90.5%

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

   6. Applied egg-rr 90.5%

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

   7. Taylor expanded in t around inf 46.4%

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

      1. associate-*r/ 51.9%

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

   9. Simplified 51.9%

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

   if -2.15000000000000005e-55 < y < -1.9500000000000001e-86 or -2.99999999999999991e-117 < y < 4.1999999999999998e-14

   1. Initial program 99.2%

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

      1. associate-/l* 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in x around inf 69.2%

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

4. Final simplification 59.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-55} \lor \neg \left(y \leq -1.95 \cdot 10^{-86}\right) \land \left(y \leq -3 \cdot 10^{-117} \lor \neg \left(y \leq 4.2 \cdot 10^{-14}\right)\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;y \leq -2.55 \cdot 10^{-54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= y -2.55e-54)
     t_1
     (if (<= y -5e-87)
       x
       (if (<= y -2.95e-117) t_1 (if (<= y 2e-14) x (* y (/ t a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (y <= -2.55e-54) {
		tmp = t_1;
	} else if (y <= -5e-87) {
		tmp = x;
	} else if (y <= -2.95e-117) {
		tmp = t_1;
	} else if (y <= 2e-14) {
		tmp = x;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (y <= (-2.55d-54)) then
        tmp = t_1
    else if (y <= (-5d-87)) then
        tmp = x
    else if (y <= (-2.95d-117)) then
        tmp = t_1
    else if (y <= 2d-14) then
        tmp = x
    else
        tmp = 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 t_1 = t * (y / a);
	double tmp;
	if (y <= -2.55e-54) {
		tmp = t_1;
	} else if (y <= -5e-87) {
		tmp = x;
	} else if (y <= -2.95e-117) {
		tmp = t_1;
	} else if (y <= 2e-14) {
		tmp = x;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if y <= -2.55e-54:
		tmp = t_1
	elif y <= -5e-87:
		tmp = x
	elif y <= -2.95e-117:
		tmp = t_1
	elif y <= 2e-14:
		tmp = x
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (y <= -2.55e-54)
		tmp = t_1;
	elseif (y <= -5e-87)
		tmp = x;
	elseif (y <= -2.95e-117)
		tmp = t_1;
	elseif (y <= 2e-14)
		tmp = x;
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (y <= -2.55e-54)
		tmp = t_1;
	elseif (y <= -5e-87)
		tmp = x;
	elseif (y <= -2.95e-117)
		tmp = t_1;
	elseif (y <= 2e-14)
		tmp = x;
	else
		tmp = y * (t / a);
	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[y, -2.55e-54], t$95$1, If[LessEqual[y, -5e-87], x, If[LessEqual[y, -2.95e-117], t$95$1, If[LessEqual[y, 2e-14], x, N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.55000000000000005e-54 or -5.00000000000000042e-87 < y < -2.9500000000000002e-117

   1. Initial program 90.8%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

      1. associate-*r/ 90.8%

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

      2. clear-num 90.8%

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

   6. Applied egg-rr 90.8%

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

   7. Taylor expanded in t around inf 47.9%

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

      1. associate-*r/ 56.9%

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

   9. Simplified 56.9%

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

   if -2.55000000000000005e-54 < y < -5.00000000000000042e-87 or -2.9500000000000002e-117 < y < 2e-14

   1. Initial program 99.2%

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

      1. associate-/l* 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in x around inf 69.2%

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

   if 2e-14 < y

   1. Initial program 90.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 44.5%

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

      1. *-commutative 44.5%

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

      2. associate-/l* 50.1%

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

   7. Simplified 50.1%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.55 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-87}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.95 \cdot 10^{-117}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-117}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.3e-51)
   (* t (/ y a))
   (if (<= y -1.2e-86)
     x
     (if (<= y -2.9e-117) (/ (* y t) a) (if (<= y 3.1e-14) x (* y (/ t a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.3e-51) {
		tmp = t * (y / a);
	} else if (y <= -1.2e-86) {
		tmp = x;
	} else if (y <= -2.9e-117) {
		tmp = (y * t) / a;
	} else if (y <= 3.1e-14) {
		tmp = x;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.3d-51)) then
        tmp = t * (y / a)
    else if (y <= (-1.2d-86)) then
        tmp = x
    else if (y <= (-2.9d-117)) then
        tmp = (y * t) / a
    else if (y <= 3.1d-14) then
        tmp = x
    else
        tmp = y * (t / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.3e-51) {
		tmp = t * (y / a);
	} else if (y <= -1.2e-86) {
		tmp = x;
	} else if (y <= -2.9e-117) {
		tmp = (y * t) / a;
	} else if (y <= 3.1e-14) {
		tmp = x;
	} else {
		tmp = y * (t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.3e-51:
		tmp = t * (y / a)
	elif y <= -1.2e-86:
		tmp = x
	elif y <= -2.9e-117:
		tmp = (y * t) / a
	elif y <= 3.1e-14:
		tmp = x
	else:
		tmp = y * (t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.3e-51)
		tmp = Float64(t * Float64(y / a));
	elseif (y <= -1.2e-86)
		tmp = x;
	elseif (y <= -2.9e-117)
		tmp = Float64(Float64(y * t) / a);
	elseif (y <= 3.1e-14)
		tmp = x;
	else
		tmp = Float64(y * Float64(t / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.3e-51)
		tmp = t * (y / a);
	elseif (y <= -1.2e-86)
		tmp = x;
	elseif (y <= -2.9e-117)
		tmp = (y * t) / a;
	elseif (y <= 3.1e-14)
		tmp = x;
	else
		tmp = y * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.3e-51], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-86], x, If[LessEqual[y, -2.9e-117], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 3.1e-14], x, N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.30000000000000002e-51

   1. Initial program 89.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 89.8%

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

      2. clear-num 89.7%

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

   6. Applied egg-rr 89.7%

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

   7. Taylor expanded in t around inf 45.5%

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

      1. associate-*r/ 55.9%

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

   9. Simplified 55.9%

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

   if -2.30000000000000002e-51 < y < -1.20000000000000007e-86 or -2.9000000000000001e-117 < y < 3.10000000000000004e-14

   1. Initial program 99.2%

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

      1. associate-/l* 82.1%

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

   3. Simplified 82.1%

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

   5. Taylor expanded in x around inf 69.2%

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

   if -1.20000000000000007e-86 < y < -2.9000000000000001e-117

   1. Initial program 99.5%

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

      1. associate-/l* 79.3%

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

   3. Simplified 79.3%

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

   5. Taylor expanded in t around inf 67.4%

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

      1. *-commutative 67.4%

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

   7. Simplified 67.4%

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

   if 3.10000000000000004e-14 < y

   1. Initial program 90.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 44.5%

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

      1. *-commutative 44.5%

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

      2. associate-/l* 50.1%

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

   7. Simplified 50.1%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-51}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-117}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 82.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-6} \lor \neg \left(z \leq 5.8 \cdot 10^{+54}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.2e-6) (not (<= z 5.8e+54)))
   (- x (* y (/ z a)))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.2e-6) || !(z <= 5.8e+54)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.2d-6)) .or. (.not. (z <= 5.8d+54))) then
        tmp = x - (y * (z / a))
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.2e-6) || !(z <= 5.8e+54)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.2e-6) or not (z <= 5.8e+54):
		tmp = x - (y * (z / a))
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.2e-6) || !(z <= 5.8e+54))
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.2e-6) || ~((z <= 5.8e+54)))
		tmp = x - (y * (z / a));
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.2e-6], N[Not[LessEqual[z, 5.8e+54]], $MachinePrecision]], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999999e-6 or 5.7999999999999997e54 < z

   1. Initial program 92.5%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in z around inf 86.2%

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

      1. associate-/l* 80.2%

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

   7. Simplified 80.2%

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

   if -6.1999999999999999e-6 < z < 5.7999999999999997e54

   1. Initial program 95.7%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around 0 90.3%

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

      1. associate-*r/ 90.3%

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

      2. mul-1-neg 90.3%

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

      3. distribute-lft-neg-out 90.3%

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

      4. *-commutative 90.3%

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

   7. Simplified 90.3%

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

      1. sub-neg 90.3%

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

      2. +-commutative 90.3%

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

      3. distribute-neg-frac2 90.3%

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

      4. add-sqr-sqrt 50.0%

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

      5. sqrt-unprod 57.1%

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

      6. sqr-neg 57.1%

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

      7. sqrt-unprod 19.3%

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

      8. add-sqr-sqrt 41.6%

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

      9. associate-/l* 41.6%

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

      10. add-sqr-sqrt 25.4%

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

      11. sqrt-unprod 58.0%

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

      12. sqr-neg 58.0%

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

      13. sqrt-unprod 38.1%

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

      14. add-sqr-sqrt 90.9%

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

   9. Applied egg-rr 90.9%

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

       1. clear-num 90.9%

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

       2. un-div-inv 91.8%

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

   11. Applied egg-rr 91.8%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-6} \lor \neg \left(z \leq 5.8 \cdot 10^{+54}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 81.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{-17} \lor \neg \left(z \leq 7.6 \cdot 10^{+80}\right):\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.4e-17) (not (<= z 7.6e+80)))
   (- x (/ (* y z) a))
   (+ x (/ y (/ a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.4e-17) || !(z <= 7.6e+80)) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.4d-17)) .or. (.not. (z <= 7.6d+80))) then
        tmp = x - ((y * z) / a)
    else
        tmp = x + (y / (a / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.4e-17) || !(z <= 7.6e+80)) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (y / (a / t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.4e-17) or not (z <= 7.6e+80):
		tmp = x - ((y * z) / a)
	else:
		tmp = x + (y / (a / t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.4e-17) || !(z <= 7.6e+80))
		tmp = Float64(x - Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.4e-17) || ~((z <= 7.6e+80)))
		tmp = x - ((y * z) / a);
	else
		tmp = x + (y / (a / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.4e-17], N[Not[LessEqual[z, 7.6e+80]], $MachinePrecision]], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.3999999999999999e-17 or 7.59999999999999995e80 < z

   1. Initial program 93.1%

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

      1. associate-/l* 86.8%

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

   3. Simplified 86.8%

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

   5. Taylor expanded in z around inf 87.5%

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

   if -9.3999999999999999e-17 < z < 7.59999999999999995e80

   1. Initial program 95.0%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in z around 0 89.7%

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

      1. associate-*r/ 89.7%

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

      2. mul-1-neg 89.7%

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

      3. distribute-lft-neg-out 89.7%

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

      4. *-commutative 89.7%

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

   7. Simplified 89.7%

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

      1. sub-neg 89.7%

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

      2. +-commutative 89.7%

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

      3. distribute-neg-frac2 89.7%

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

      4. add-sqr-sqrt 48.8%

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

      5. sqrt-unprod 56.4%

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

      6. sqr-neg 56.4%

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

      7. sqrt-unprod 19.5%

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

      8. add-sqr-sqrt 41.3%

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

      9. associate-/l* 41.3%

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

      10. add-sqr-sqrt 24.9%

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

      11. sqrt-unprod 58.1%

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

      12. sqr-neg 58.1%

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

      13. sqrt-unprod 38.6%

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

      14. add-sqr-sqrt 90.3%

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

   9. Applied egg-rr 90.3%

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

       1. clear-num 90.2%

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

       2. un-div-inv 91.1%

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

   11. Applied egg-rr 91.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{-17} \lor \neg \left(z \leq 7.6 \cdot 10^{+80}\right):\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+68} \lor \neg \left(z \leq 1.14 \cdot 10^{+83}\right):\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.25e+68) (not (<= z 1.14e+83)))
   (- x (/ (* y z) a))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+68) || !(z <= 1.14e+83)) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.25d+68)) .or. (.not. (z <= 1.14d+83))) then
        tmp = x - ((y * z) / a)
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.25e+68) || !(z <= 1.14e+83)) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.25e+68) or not (z <= 1.14e+83):
		tmp = x - ((y * z) / a)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.25e+68) || !(z <= 1.14e+83))
		tmp = Float64(x - Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.25e+68) || ~((z <= 1.14e+83)))
		tmp = x - ((y * z) / a);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.25e+68], N[Not[LessEqual[z, 1.14e+83]], $MachinePrecision]], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2500000000000001e68 or 1.14000000000000003e83 < z

   1. Initial program 92.9%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

   5. Taylor expanded in z around inf 90.0%

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

   if -1.2500000000000001e68 < z < 1.14000000000000003e83

   1. Initial program 94.9%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in z around 0 87.3%

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

      1. mul-1-neg 87.3%

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

      2. associate-/l* 90.3%

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

      3. distribute-rgt-neg-in 90.3%

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

      4. distribute-neg-frac2 90.3%

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

   7. Simplified 90.3%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{+68} \lor \neg \left(z \leq 1.14 \cdot 10^{+83}\right):\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-42}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.85e-42)
   (* (/ y a) (- t z))
   (if (<= y 4.3e+26) (+ x (/ (* y t) a)) (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.85e-42) {
		tmp = (y / a) * (t - z);
	} else if (y <= 4.3e+26) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.85d-42)) then
        tmp = (y / a) * (t - z)
    else if (y <= 4.3d+26) then
        tmp = x + ((y * t) / a)
    else
        tmp = y * ((t - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.85e-42) {
		tmp = (y / a) * (t - z);
	} else if (y <= 4.3e+26) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.85e-42:
		tmp = (y / a) * (t - z)
	elif y <= 4.3e+26:
		tmp = x + ((y * t) / a)
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.85e-42)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (y <= 4.3e+26)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(y * Float64(Float64(t - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.85e-42)
		tmp = (y / a) * (t - z);
	elseif (y <= 4.3e+26)
		tmp = x + ((y * t) / a);
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.85e-42], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+26], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.85e-42

   1. Initial program 89.5%

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

      1. associate-*r/ 89.5%

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

      2. clear-num 89.4%

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

   6. Applied egg-rr 89.4%

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

   7. Taylor expanded in x around 0 75.9%

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

      1. associate-/l* 84.9%

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

      2. associate-*r* 84.9%

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

      3. neg-mul-1 84.9%

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

      4. div-sub 82.1%

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

      5. distribute-lft-out-- 80.6%

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

      6. distribute-lft-neg-in 80.6%

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

      7. associate-*r/ 74.1%

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

      8. mul-1-neg 74.1%

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

      9. cancel-sign-sub 74.1%

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

      10. *-commutative 74.1%

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

      11. associate-*l/ 70.0%

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

      12. +-commutative 70.0%

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

      13. associate-*r/ 72.8%

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

      14. mul-1-neg 72.8%

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

      15. distribute-frac-neg 72.8%

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

      16. distribute-rgt-neg-in 72.8%

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

      17. *-commutative 72.8%

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

      18. associate-/l* 75.0%

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

      19. distribute-rgt-out 84.9%

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

      20. unsub-neg 84.9%

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

   9. Simplified 84.9%

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

   if -2.85e-42 < y < 4.2999999999999998e26

   1. Initial program 99.3%

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

      1. associate-/l* 83.3%

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

   3. Simplified 83.3%

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

   5. Taylor expanded in z around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. mul-1-neg 84.3%

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

      3. distribute-lft-neg-out 84.3%

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

      4. *-commutative 84.3%

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

   7. Simplified 84.3%

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

   8. Taylor expanded in y around 0 84.3%

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

   if 4.2999999999999998e26 < y

   1. Initial program 88.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. distribute-frac-neg2 80.7%

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

      3. associate-*r/ 90.0%

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

   7. Simplified 90.0%

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

      1. frac-2neg 90.0%

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

      2. div-inv 90.0%

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

      3. sub-neg 90.0%

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

      4. distribute-neg-in 90.0%

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

      5. add-sqr-sqrt 49.9%

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

      6. sqrt-unprod 59.1%

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

      7. sqr-neg 59.1%

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

      8. sqrt-unprod 18.5%

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

      9. add-sqr-sqrt 40.5%

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

      10. add-sqr-sqrt 22.0%

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

      11. sqrt-unprod 54.2%

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

      12. sqr-neg 54.2%

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

      13. sqrt-unprod 40.0%

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

      14. add-sqr-sqrt 90.0%

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

      15. remove-double-neg 90.0%

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

   9. Applied egg-rr 90.0%

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

       1. associate-*r/ 90.0%

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

       2. *-rgt-identity 90.0%

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

       3. +-commutative 90.0%

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

       4. unsub-neg 90.0%

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

   11. Simplified 90.0%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.85 \cdot 10^{-42}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+26}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 92.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+196}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.3e+196) (- x (/ (* y z) a)) (+ x (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+196) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.3d+196)) then
        tmp = x - ((y * z) / a)
    else
        tmp = x + (y * ((t - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.3e+196) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.3e+196:
		tmp = x - ((y * z) / a)
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.3e+196)
		tmp = Float64(x - Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.3e+196)
		tmp = x - ((y * z) / a);
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.3e+196], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.30000000000000006e196

   1. Initial program 99.9%

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

      1. associate-/l* 75.9%

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

   3. Simplified 75.9%

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

   5. Taylor expanded in z around inf 96.4%

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

   if -1.30000000000000006e196 < z

   1. Initial program 93.4%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+196}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 93.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+197}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.4e+197) (- x (/ (* y z) a)) (+ x (/ y (/ a (- t z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.4e+197) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (y / (a / (t - z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-9.4d+197)) then
        tmp = x - ((y * z) / a)
    else
        tmp = x + (y / (a / (t - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.4e+197) {
		tmp = x - ((y * z) / a);
	} else {
		tmp = x + (y / (a / (t - z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.4e+197:
		tmp = x - ((y * z) / a)
	else:
		tmp = x + (y / (a / (t - z)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.4e+197)
		tmp = Float64(x - Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -9.4e+197)
		tmp = x - ((y * z) / a);
	else
		tmp = x + (y / (a / (t - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.4e+197], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.3999999999999999e197

   1. Initial program 99.9%

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

      1. associate-/l* 75.1%

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

   3. Simplified 75.1%

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

   5. Taylor expanded in z around inf 96.2%

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

   if -9.3999999999999999e197 < z

   1. Initial program 93.4%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 93.7%

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

      2. un-div-inv 94.7%

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

   6. Applied egg-rr 94.7%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.4 \cdot 10^{+197}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.8% 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 94.1%

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

   1. associate-/l* 91.8%

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

3. Simplified 91.8%

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

5. Taylor expanded in x around inf 38.0%

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

6. Final simplification 38.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024077 
(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)))