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

Percentage Accurate: 93.0% → 98.1%

Time: 9.2s

Alternatives: 13

Speedup: 1.0×

• 25.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.5e+80)
   (+ x (* y (/ (- z t) a)))
   (if (<= y 7.5e-125) (+ x (/ (* (- z t) y) a)) (+ x (/ y (/ a (- z t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.5e+80) {
		tmp = x + (y * ((z - t) / a));
	} else if (y <= 7.5e-125) {
		tmp = x + (((z - t) * y) / a);
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.5d+80)) then
        tmp = x + (y * ((z - t) / a))
    else if (y <= 7.5d-125) then
        tmp = x + (((z - t) * y) / a)
    else
        tmp = x + (y / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.5e+80) {
		tmp = x + (y * ((z - t) / a));
	} else if (y <= 7.5e-125) {
		tmp = x + (((z - t) * y) / a);
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.5e+80:
		tmp = x + (y * ((z - t) / a))
	elif y <= 7.5e-125:
		tmp = x + (((z - t) * y) / a)
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.5e+80)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (y <= 7.5e-125)
		tmp = Float64(x + Float64(Float64(Float64(z - t) * y) / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.5e+80)
		tmp = x + (y * ((z - t) / a));
	elseif (y <= 7.5e-125)
		tmp = x + (((z - t) * y) / a);
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.5e+80], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e-125], N[(x + N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.49999999999999993e80

   1. Initial program 77.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -1.49999999999999993e80 < y < 7.5e-125

   1. Initial program 99.7%

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

   if 7.5e-125 < y

   1. Initial program 90.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-125}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{-a}\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+82}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a)))))
   (if (<= t -5.5e+82)
     t_1
     (if (<= t 1.25e-242)
       x
       (if (<= t 2.1e-150) (* y (/ z a)) (if (<= t 7.5e+25) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -a);
	double tmp;
	if (t <= -5.5e+82) {
		tmp = t_1;
	} else if (t <= 1.25e-242) {
		tmp = x;
	} else if (t <= 2.1e-150) {
		tmp = y * (z / a);
	} else if (t <= 7.5e+25) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / -a)
    if (t <= (-5.5d+82)) then
        tmp = t_1
    else if (t <= 1.25d-242) then
        tmp = x
    else if (t <= 2.1d-150) then
        tmp = y * (z / a)
    else if (t <= 7.5d+25) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -a);
	double tmp;
	if (t <= -5.5e+82) {
		tmp = t_1;
	} else if (t <= 1.25e-242) {
		tmp = x;
	} else if (t <= 2.1e-150) {
		tmp = y * (z / a);
	} else if (t <= 7.5e+25) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / -a)
	tmp = 0
	if t <= -5.5e+82:
		tmp = t_1
	elif t <= 1.25e-242:
		tmp = x
	elif t <= 2.1e-150:
		tmp = y * (z / a)
	elif t <= 7.5e+25:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / Float64(-a)))
	tmp = 0.0
	if (t <= -5.5e+82)
		tmp = t_1;
	elseif (t <= 1.25e-242)
		tmp = x;
	elseif (t <= 2.1e-150)
		tmp = Float64(y * Float64(z / a));
	elseif (t <= 7.5e+25)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / -a);
	tmp = 0.0;
	if (t <= -5.5e+82)
		tmp = t_1;
	elseif (t <= 1.25e-242)
		tmp = x;
	elseif (t <= 2.1e-150)
		tmp = y * (z / a);
	elseif (t <= 7.5e+25)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+82], t$95$1, If[LessEqual[t, 1.25e-242], x, If[LessEqual[t, 2.1e-150], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+25], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.49999999999999997e82 or 7.49999999999999993e25 < t

   1. Initial program 86.8%

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

      1. +-commutative 86.8%

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

      2. associate-/l* 90.3%

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

      3. fma-define 90.3%

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

   3. Simplified 90.3%

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

      1. fma-undefine 90.3%

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

      2. associate-*r/ 86.8%

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

      3. *-commutative 86.8%

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

      4. associate-/l* 98.1%

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

   6. Applied egg-rr 98.1%

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

   7. Taylor expanded in z around 0 76.6%

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

      1. associate-+r+ 76.6%

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

      2. mul-1-neg 76.6%

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

      3. associate-*l/ 77.5%

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

      4. *-commutative 77.5%

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

      5. sub-neg 77.5%

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

      6. associate-*l/ 79.1%

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

      7. *-commutative 79.1%

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

      8. *-commutative 79.1%

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

      9. associate-*l/ 74.7%

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

      10. associate-*r/ 86.1%

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

   9. Simplified 86.1%

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

   10. Taylor expanded in t around inf 60.2%

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

       1. associate-*r/ 67.7%

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

       2. associate-*r* 67.7%

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

       3. neg-mul-1 67.7%

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

       4. *-commutative 67.7%

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

   12. Simplified 67.7%

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

   if -5.49999999999999997e82 < t < 1.25e-242 or 2.1000000000000001e-150 < t < 7.49999999999999993e25

   1. Initial program 96.9%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 58.2%

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

   if 1.25e-242 < t < 2.1000000000000001e-150

   1. Initial program 84.5%

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

      1. +-commutative 84.5%

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

      2. associate-/l* 99.6%

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

      3. fma-define 99.6%

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

   3. Simplified 99.6%

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

      1. fma-undefine 99.6%

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

      2. associate-*r/ 84.5%

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

      3. *-commutative 84.5%

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

      4. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in z around 0 84.5%

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

      1. associate-+r+ 84.5%

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

      2. mul-1-neg 84.5%

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

      3. associate-*l/ 84.5%

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

      4. *-commutative 84.5%

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

      5. sub-neg 84.5%

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

      6. associate-*l/ 99.9%

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

      7. *-commutative 99.9%

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

      8. *-commutative 99.9%

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

      9. associate-*l/ 99.9%

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

      10. associate-*r/ 83.2%

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

   9. Simplified 83.2%

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

   10. Taylor expanded in z around inf 51.7%

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

       1. associate-*r/ 66.8%

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

   12. Simplified 66.8%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+82}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-150}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z - t \leq -1 \cdot 10^{+27} \lor \neg \left(z - t \leq 5 \cdot 10^{+82}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (- z t) -1e+27) (not (<= (- z t) 5e+82))) (* (- z t) (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z - t) <= -1e+27) || !((z - t) <= 5e+82)) {
		tmp = (z - 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 (((z - t) <= (-1d+27)) .or. (.not. ((z - t) <= 5d+82))) then
        tmp = (z - 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 (((z - t) <= -1e+27) || !((z - t) <= 5e+82)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((z - t) <= -1e+27) or not ((z - t) <= 5e+82):
		tmp = (z - t) * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z - t) <= -1e+27) || !(Float64(z - t) <= 5e+82))
		tmp = Float64(Float64(z - 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 (((z - t) <= -1e+27) || ~(((z - t) <= 5e+82)))
		tmp = (z - t) * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z - t), $MachinePrecision], -1e+27], N[Not[LessEqual[N[(z - t), $MachinePrecision], 5e+82]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (-.f64 z t) < -1e27 or 5.00000000000000015e82 < (-.f64 z t)

   1. Initial program 86.7%

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

      1. +-commutative 86.7%

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

      2. associate-/l* 92.6%

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

      3. fma-define 92.6%

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

   3. Simplified 92.6%

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

      1. fma-undefine 92.6%

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

      2. associate-*r/ 86.7%

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

      3. *-commutative 86.7%

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

      4. associate-/l* 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in z around 0 78.4%

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

      1. associate-+r+ 78.4%

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

      2. mul-1-neg 78.4%

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

      3. associate-*l/ 79.1%

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

      4. *-commutative 79.1%

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

      5. sub-neg 79.1%

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

      6. associate-*l/ 83.7%

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

      7. *-commutative 83.7%

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

      8. *-commutative 83.7%

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

      9. associate-*l/ 80.7%

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

      10. associate-*r/ 86.6%

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

   9. Simplified 86.6%

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

   10. Taylor expanded in x around 0 57.6%

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

       1. associate-*l/ 59.3%

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

       2. associate-*r/ 63.9%

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

       3. *-commutative 63.9%

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

       4. distribute-lft-out-- 75.4%

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

   12. Simplified 75.4%

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

   if -1e27 < (-.f64 z t) < 5.00000000000000015e82

   1. Initial program 99.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in x around inf 67.1%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z - t \leq -1 \cdot 10^{+27} \lor \neg \left(z - t \leq 5 \cdot 10^{+82}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-23} \lor \neg \left(t \leq 6.5 \cdot 10^{+62}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8e-23) (not (<= t 6.5e+62)))
   (- x (* t (/ y a)))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e-23) || !(t <= 6.5e+62)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8d-23)) .or. (.not. (t <= 6.5d+62))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8e-23) || !(t <= 6.5e+62)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8e-23) or not (t <= 6.5e+62):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8e-23) || !(t <= 6.5e+62))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8e-23) || ~((t <= 6.5e+62)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8e-23], N[Not[LessEqual[t, 6.5e+62]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.99999999999999968e-23 or 6.5000000000000003e62 < t

   1. Initial program 88.9%

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

      1. +-commutative 88.9%

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

      2. associate-/l* 92.0%

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

      3. fma-define 92.0%

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

   3. Simplified 92.0%

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

      1. fma-undefine 92.0%

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

      2. associate-*r/ 88.9%

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

      3. *-commutative 88.9%

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

      4. associate-/l* 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in z around 0 82.4%

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

      1. associate-*l/ 85.5%

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

      2. *-commutative 85.5%

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

      3. neg-mul-1 85.5%

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

      4. sub-neg 85.5%

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

      5. *-commutative 85.5%

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

      6. associate-*l/ 82.4%

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

      7. associate-*r/ 90.3%

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

   9. Simplified 90.3%

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

   if -7.99999999999999968e-23 < t < 6.5000000000000003e62

   1. Initial program 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-/l* 98.5%

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

      3. fma-define 98.5%

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

   3. Simplified 98.5%

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

      1. fma-undefine 98.5%

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

      2. associate-*r/ 94.3%

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

      3. *-commutative 94.3%

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

      4. associate-/l* 98.6%

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

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in z around inf 87.0%

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

      1. associate-*l/ 92.5%

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

      2. *-commutative 92.5%

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

   9. Simplified 92.5%

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

       1. clear-num 92.5%

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

       2. un-div-inv 92.5%

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

   11. Applied egg-rr 92.5%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-23} \lor \neg \left(t \leq 6.5 \cdot 10^{+62}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+109} \lor \neg \left(t \leq 1.85 \cdot 10^{+90}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -6.1e+109) (not (<= t 1.85e+90)))
   (* (- z t) (/ y a))
   (+ x (/ z (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.1e+109) || !(t <= 1.85e+90)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-6.1d+109)) .or. (.not. (t <= 1.85d+90))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x + (z / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -6.1e+109) || !(t <= 1.85e+90)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (z / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -6.1e+109) or not (t <= 1.85e+90):
		tmp = (z - t) * (y / a)
	else:
		tmp = x + (z / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -6.1e+109) || !(t <= 1.85e+90))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(z / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -6.1e+109) || ~((t <= 1.85e+90)))
		tmp = (z - t) * (y / a);
	else
		tmp = x + (z / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -6.1e+109], N[Not[LessEqual[t, 1.85e+90]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.10000000000000008e109 or 1.85e90 < t

   1. Initial program 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-/l* 88.9%

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

      3. fma-define 88.9%

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

   3. Simplified 88.9%

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

      1. fma-undefine 88.9%

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

      2. associate-*r/ 85.6%

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

      3. *-commutative 85.6%

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

      4. associate-/l* 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in z around 0 75.1%

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

      1. associate-+r+ 75.1%

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

      2. mul-1-neg 75.1%

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

      3. associate-*l/ 75.2%

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

      4. *-commutative 75.2%

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

      5. sub-neg 75.2%

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

      6. associate-*l/ 76.1%

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

      7. *-commutative 76.1%

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

      8. *-commutative 76.1%

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

      9. associate-*l/ 72.7%

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

      10. associate-*r/ 84.8%

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

   9. Simplified 84.8%

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

   10. Taylor expanded in x around 0 59.6%

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

       1. associate-*l/ 57.3%

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

       2. associate-*r/ 67.9%

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

       3. *-commutative 67.9%

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

       4. distribute-lft-out-- 80.6%

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

   12. Simplified 80.6%

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

   if -6.10000000000000008e109 < t < 1.85e90

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-/l* 98.7%

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

      3. fma-define 98.7%

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

   3. Simplified 98.7%

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

      1. fma-undefine 98.7%

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

      2. associate-*r/ 94.9%

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

      3. *-commutative 94.9%

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

      4. associate-/l* 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in z around inf 82.3%

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

      1. associate-*l/ 86.7%

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

      2. *-commutative 86.7%

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

   9. Simplified 86.7%

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

       1. clear-num 86.7%

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

       2. un-div-inv 86.7%

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

   11. Applied egg-rr 86.7%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+109} \lor \neg \left(t \leq 1.85 \cdot 10^{+90}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+109} \lor \neg \left(t \leq 7.1 \cdot 10^{+87}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.3e+109) (not (<= t 7.1e+87)))
   (* (- z t) (/ y a))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.3e+109) || !(t <= 7.1e+87)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.3d+109)) .or. (.not. (t <= 7.1d+87))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.3e+109) || !(t <= 7.1e+87)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.3e+109) or not (t <= 7.1e+87):
		tmp = (z - t) * (y / a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.3e+109) || !(t <= 7.1e+87))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.3e+109) || ~((t <= 7.1e+87)))
		tmp = (z - t) * (y / a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.3e+109], N[Not[LessEqual[t, 7.1e+87]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2999999999999999e109 or 7.0999999999999998e87 < t

   1. Initial program 85.6%

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

      1. +-commutative 85.6%

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

      2. associate-/l* 88.9%

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

      3. fma-define 88.9%

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

   3. Simplified 88.9%

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

      1. fma-undefine 88.9%

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

      2. associate-*r/ 85.6%

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

      3. *-commutative 85.6%

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

      4. associate-/l* 97.6%

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

   6. Applied egg-rr 97.6%

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

   7. Taylor expanded in z around 0 75.1%

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

      1. associate-+r+ 75.1%

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

      2. mul-1-neg 75.1%

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

      3. associate-*l/ 75.2%

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

      4. *-commutative 75.2%

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

      5. sub-neg 75.2%

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

      6. associate-*l/ 76.1%

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

      7. *-commutative 76.1%

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

      8. *-commutative 76.1%

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

      9. associate-*l/ 72.7%

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

      10. associate-*r/ 84.8%

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

   9. Simplified 84.8%

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

   10. Taylor expanded in x around 0 59.6%

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

       1. associate-*l/ 57.3%

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

       2. associate-*r/ 67.9%

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

       3. *-commutative 67.9%

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

       4. distribute-lft-out-- 80.6%

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

   12. Simplified 80.6%

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

   if -3.2999999999999999e109 < t < 7.0999999999999998e87

   1. Initial program 94.9%

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

      1. +-commutative 94.9%

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

      2. associate-/l* 98.7%

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

      3. fma-define 98.7%

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

   3. Simplified 98.7%

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

      1. fma-undefine 98.7%

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

      2. associate-*r/ 94.9%

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

      3. *-commutative 94.9%

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

      4. associate-/l* 98.3%

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

   6. Applied egg-rr 98.3%

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

   7. Taylor expanded in z around inf 82.3%

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

      1. associate-*l/ 86.7%

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

      2. *-commutative 86.7%

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

   9. Simplified 86.7%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+109} \lor \neg \left(t \leq 7.1 \cdot 10^{+87}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+109} \lor \neg \left(t \leq 3.8 \cdot 10^{+26}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.4e+109) (not (<= t 3.8e+26)))
   (* (- z t) (/ y a))
   (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.4e+109) || !(t <= 3.8e+26)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.4d+109)) .or. (.not. (t <= 3.8d+26))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.4e+109) || !(t <= 3.8e+26)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.4e+109) or not (t <= 3.8e+26):
		tmp = (z - t) * (y / a)
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.4e+109) || !(t <= 3.8e+26))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.4e+109) || ~((t <= 3.8e+26)))
		tmp = (z - t) * (y / a);
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.4e+109], N[Not[LessEqual[t, 3.8e+26]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.40000000000000006e109 or 3.8000000000000002e26 < t

   1. Initial program 86.4%

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

      1. +-commutative 86.4%

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

      2. associate-/l* 89.3%

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

      3. fma-define 89.3%

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

   3. Simplified 89.3%

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

      1. fma-undefine 89.3%

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

      2. associate-*r/ 86.4%

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

      3. *-commutative 86.4%

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

      4. associate-/l* 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in z around 0 77.1%

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

      1. associate-+r+ 77.1%

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

      2. mul-1-neg 77.1%

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

      3. associate-*l/ 77.3%

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

      4. *-commutative 77.3%

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

      5. sub-neg 77.3%

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

      6. associate-*l/ 79.0%

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

      7. *-commutative 79.0%

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

      8. *-commutative 79.0%

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

      9. associate-*l/ 75.1%

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

      10. associate-*r/ 86.7%

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

   9. Simplified 86.7%

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

   10. Taylor expanded in x around 0 60.7%

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

       1. associate-*l/ 58.6%

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

       2. associate-*r/ 68.2%

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

       3. *-commutative 68.2%

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

       4. distribute-lft-out-- 79.4%

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

   12. Simplified 79.4%

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

   if -3.40000000000000006e109 < t < 3.8000000000000002e26

   1. Initial program 95.1%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 83.3%

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

      1. +-commutative 83.3%

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

      2. associate-/l* 86.8%

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

   7. Simplified 86.8%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+109} \lor \neg \left(t \leq 3.8 \cdot 10^{+26}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 78.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+109} \lor \neg \left(t \leq 6 \cdot 10^{+25}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.5e+109) (not (<= t 6e+25)))
   (* (- z t) (/ y a))
   (+ x (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.5e+109) || !(t <= 6e+25)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.5d+109)) .or. (.not. (t <= 6d+25))) then
        tmp = (z - t) * (y / a)
    else
        tmp = x + ((z * y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.5e+109) || !(t <= 6e+25)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.5e+109) or not (t <= 6e+25):
		tmp = (z - t) * (y / a)
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.5e+109) || !(t <= 6e+25))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.5e+109) || ~((t <= 6e+25)))
		tmp = (z - t) * (y / a);
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.5e+109], N[Not[LessEqual[t, 6e+25]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.4999999999999998e109 or 6.00000000000000011e25 < t

   1. Initial program 86.4%

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

      1. +-commutative 86.4%

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

      2. associate-/l* 89.3%

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

      3. fma-define 89.3%

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

   3. Simplified 89.3%

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

      1. fma-undefine 89.3%

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

      2. associate-*r/ 86.4%

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

      3. *-commutative 86.4%

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

      4. associate-/l* 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in z around 0 77.1%

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

      1. associate-+r+ 77.1%

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

      2. mul-1-neg 77.1%

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

      3. associate-*l/ 77.3%

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

      4. *-commutative 77.3%

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

      5. sub-neg 77.3%

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

      6. associate-*l/ 79.0%

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

      7. *-commutative 79.0%

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

      8. *-commutative 79.0%

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

      9. associate-*l/ 75.1%

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

      10. associate-*r/ 86.7%

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

   9. Simplified 86.7%

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

   10. Taylor expanded in x around 0 60.7%

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

       1. associate-*l/ 58.6%

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

       2. associate-*r/ 68.2%

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

       3. *-commutative 68.2%

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

       4. distribute-lft-out-- 79.4%

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

   12. Simplified 79.4%

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

   if -5.4999999999999998e109 < t < 6.00000000000000011e25

   1. Initial program 95.1%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in z around inf 83.3%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+109} \lor \neg \left(t \leq 6 \cdot 10^{+25}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+113} \lor \neg \left(y \leq 1.45 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.2e+113) (not (<= y 1.45e+45))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.2e+113) || !(y <= 1.45e+45)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.2d+113)) .or. (.not. (y <= 1.45d+45))) then
        tmp = y * (z / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.2e+113) || !(y <= 1.45e+45)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.2e+113) or not (y <= 1.45e+45):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.2e+113) || !(y <= 1.45e+45))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.2e+113) || ~((y <= 1.45e+45)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.2e+113], N[Not[LessEqual[y, 1.45e+45]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.1999999999999998e113 or 1.4499999999999999e45 < y

   1. Initial program 81.6%

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

      1. +-commutative 81.6%

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

      2. associate-/l* 99.8%

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

      3. fma-define 99.8%

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

   3. Simplified 99.8%

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

      1. fma-undefine 99.8%

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

      2. associate-*r/ 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-/l* 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in z around 0 71.7%

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

      1. associate-+r+ 71.7%

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

      2. mul-1-neg 71.7%

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

      3. associate-*l/ 80.0%

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

      4. *-commutative 80.0%

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

      5. sub-neg 80.0%

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

      6. associate-*l/ 87.2%

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

      7. *-commutative 87.2%

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

      8. *-commutative 87.2%

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

      9. associate-*l/ 75.3%

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

      10. associate-*r/ 80.3%

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

   9. Simplified 80.3%

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

   10. Taylor expanded in z around inf 42.2%

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

       1. associate-*r/ 49.6%

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

   12. Simplified 49.6%

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

   if -3.1999999999999998e113 < y < 1.4499999999999999e45

   1. Initial program 98.5%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf 56.4%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+113} \lor \neg \left(y \leq 1.45 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. +-commutative 91.8%

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

   2. associate-/l* 95.4%

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

   3. fma-define 95.4%

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

3. Simplified 95.4%

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

   1. fma-undefine 95.4%

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

   2. associate-*r/ 91.8%

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

   3. *-commutative 91.8%

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

   4. associate-/l* 98.0%

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

6. Applied egg-rr 98.0%

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

7. Final simplification 98.0%

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

Alternative 11: 93.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-/l* 95.4%

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

3. Simplified 95.4%

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

   1. clear-num 95.4%

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

   2. un-div-inv 95.5%

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

6. Applied egg-rr 95.5%

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

Alternative 12: 93.0% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 91.8%

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

   1. associate-/l* 95.4%

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

3. Simplified 95.4%

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

Alternative 13: 38.7% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 91.8%

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

   1. associate-/l* 95.4%

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

3. Simplified 95.4%

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

5. Taylor expanded in x around inf 40.4%

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

Developer target: 99.0% 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 2024100 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))