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

Percentage Accurate: 92.9% → 98.8%

Time: 9.6s

Alternatives: 10

Speedup: 1.0×

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% 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: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.3e+102)
   (+ x (/ y (/ a (- z t))))
   (if (<= a 2e+35) (+ x (/ (* (- z t) y) a)) (+ x (* y (/ (- z t) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e+102) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 2e+35) {
		tmp = x + (((z - t) * y) / a);
	} else {
		tmp = x + (y * ((z - 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 (a <= (-4.3d+102)) then
        tmp = x + (y / (a / (z - t)))
    else if (a <= 2d+35) then
        tmp = x + (((z - t) * y) / a)
    else
        tmp = x + (y * ((z - 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 (a <= -4.3e+102) {
		tmp = x + (y / (a / (z - t)));
	} else if (a <= 2e+35) {
		tmp = x + (((z - t) * y) / a);
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.3e+102:
		tmp = x + (y / (a / (z - t)))
	elif a <= 2e+35:
		tmp = x + (((z - t) * y) / a)
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.3e+102)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= 2e+35)
		tmp = Float64(x + Float64(Float64(Float64(z - t) * y) / a));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.3e+102)
		tmp = x + (y / (a / (z - t)));
	elseif (a <= 2e+35)
		tmp = x + (((z - t) * y) / a);
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.3e+102], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+35], N[(x + N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.3000000000000001e102

   1. Initial program 87.8%

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

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

   if -4.3000000000000001e102 < a < 1.9999999999999999e35

   1. Initial program 99.8%

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

   if 1.9999999999999999e35 < a

   1. Initial program 80.1%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+35}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot y}{a}\\ t_2 := t \cdot \frac{y}{-a}\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+158}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+103}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z y) a))) (t_2 (* t (/ y (- a)))))
   (if (<= t -5.8e+158)
     t_2
     (if (<= t -4.5e+96)
       t_1
       (if (<= t -2.1e+73) (* y (/ t (- a))) (if (<= t 2.55e+103) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z * y) / a);
	double t_2 = t * (y / -a);
	double tmp;
	if (t <= -5.8e+158) {
		tmp = t_2;
	} else if (t <= -4.5e+96) {
		tmp = t_1;
	} else if (t <= -2.1e+73) {
		tmp = y * (t / -a);
	} else if (t <= 2.55e+103) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z * y) / a)
    t_2 = t * (y / -a)
    if (t <= (-5.8d+158)) then
        tmp = t_2
    else if (t <= (-4.5d+96)) then
        tmp = t_1
    else if (t <= (-2.1d+73)) then
        tmp = y * (t / -a)
    else if (t <= 2.55d+103) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z * y) / a);
	double t_2 = t * (y / -a);
	double tmp;
	if (t <= -5.8e+158) {
		tmp = t_2;
	} else if (t <= -4.5e+96) {
		tmp = t_1;
	} else if (t <= -2.1e+73) {
		tmp = y * (t / -a);
	} else if (t <= 2.55e+103) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z * y) / a)
	t_2 = t * (y / -a)
	tmp = 0
	if t <= -5.8e+158:
		tmp = t_2
	elif t <= -4.5e+96:
		tmp = t_1
	elif t <= -2.1e+73:
		tmp = y * (t / -a)
	elif t <= 2.55e+103:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z * y) / a))
	t_2 = Float64(t * Float64(y / Float64(-a)))
	tmp = 0.0
	if (t <= -5.8e+158)
		tmp = t_2;
	elseif (t <= -4.5e+96)
		tmp = t_1;
	elseif (t <= -2.1e+73)
		tmp = Float64(y * Float64(t / Float64(-a)));
	elseif (t <= 2.55e+103)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z * y) / a);
	t_2 = t * (y / -a);
	tmp = 0.0;
	if (t <= -5.8e+158)
		tmp = t_2;
	elseif (t <= -4.5e+96)
		tmp = t_1;
	elseif (t <= -2.1e+73)
		tmp = y * (t / -a);
	elseif (t <= 2.55e+103)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+158], t$95$2, If[LessEqual[t, -4.5e+96], t$95$1, If[LessEqual[t, -2.1e+73], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.55e+103], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.80000000000000048e158 or 2.5500000000000001e103 < t

   1. Initial program 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-/l* 89.6%

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

      3. fma-define 89.6%

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

   3. Simplified 89.6%

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

      1. fma-undefine 89.6%

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

      2. associate-*r/ 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-/l* 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in z around 0 78.5%

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

      1. associate-*l/ 82.3%

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

      2. *-commutative 82.3%

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

      3. neg-mul-1 82.3%

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

      4. sub-neg 82.3%

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

      5. *-commutative 82.3%

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

      6. associate-*l/ 78.5%

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

      7. associate-*r/ 88.2%

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

   9. Simplified 88.2%

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

   10. Taylor expanded in x around 0 61.8%

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

       1. mul-1-neg 61.8%

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

       2. associate-*r/ 70.2%

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

       3. distribute-rgt-neg-in 70.2%

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

       4. distribute-neg-frac 70.2%

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

   12. Simplified 70.2%

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

   if -5.80000000000000048e158 < t < -4.49999999999999957e96 or -2.1000000000000001e73 < t < 2.5500000000000001e103

   1. Initial program 95.4%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around inf 87.1%

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

   if -4.49999999999999957e96 < t < -2.1000000000000001e73

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 99.7%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. sub-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-*l/ 99.7%

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

      7. associate-*r/ 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in x around 0 99.7%

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

       1. mul-1-neg 99.7%

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

       2. associate-*l/ 100.0%

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

       3. distribute-rgt-neg-in 100.0%

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

   12. Simplified 100.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+158}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{+96}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq -2.1 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq 2.55 \cdot 10^{+103}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{-a}\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+102}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a)))))
   (if (<= t -4.5e+159)
     t_1
     (if (<= t -2.8e+95)
       (+ x (* y (/ z a)))
       (if (<= t -1.65e+72)
         (* y (/ t (- a)))
         (if (<= t 3.4e+102) (+ x (/ (* z y) a)) 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 <= -4.5e+159) {
		tmp = t_1;
	} else if (t <= -2.8e+95) {
		tmp = x + (y * (z / a));
	} else if (t <= -1.65e+72) {
		tmp = y * (t / -a);
	} else if (t <= 3.4e+102) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / -a)
    if (t <= (-4.5d+159)) then
        tmp = t_1
    else if (t <= (-2.8d+95)) then
        tmp = x + (y * (z / a))
    else if (t <= (-1.65d+72)) then
        tmp = y * (t / -a)
    else if (t <= 3.4d+102) then
        tmp = x + ((z * y) / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -a);
	double tmp;
	if (t <= -4.5e+159) {
		tmp = t_1;
	} else if (t <= -2.8e+95) {
		tmp = x + (y * (z / a));
	} else if (t <= -1.65e+72) {
		tmp = y * (t / -a);
	} else if (t <= 3.4e+102) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / -a)
	tmp = 0
	if t <= -4.5e+159:
		tmp = t_1
	elif t <= -2.8e+95:
		tmp = x + (y * (z / a))
	elif t <= -1.65e+72:
		tmp = y * (t / -a)
	elif t <= 3.4e+102:
		tmp = x + ((z * y) / a)
	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 <= -4.5e+159)
		tmp = t_1;
	elseif (t <= -2.8e+95)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= -1.65e+72)
		tmp = Float64(y * Float64(t / Float64(-a)));
	elseif (t <= 3.4e+102)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	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 <= -4.5e+159)
		tmp = t_1;
	elseif (t <= -2.8e+95)
		tmp = x + (y * (z / a));
	elseif (t <= -1.65e+72)
		tmp = y * (t / -a);
	elseif (t <= 3.4e+102)
		tmp = x + ((z * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+159], t$95$1, If[LessEqual[t, -2.8e+95], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.65e+72], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.4e+102], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.50000000000000026e159 or 3.4e102 < t

   1. Initial program 85.9%

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

      1. +-commutative 85.9%

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

      2. associate-/l* 89.6%

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

      3. fma-define 89.6%

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

   3. Simplified 89.6%

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

      1. fma-undefine 89.6%

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

      2. associate-*r/ 85.9%

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

      3. *-commutative 85.9%

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

      4. associate-/l* 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in z around 0 78.5%

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

      1. associate-*l/ 82.3%

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

      2. *-commutative 82.3%

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

      3. neg-mul-1 82.3%

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

      4. sub-neg 82.3%

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

      5. *-commutative 82.3%

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

      6. associate-*l/ 78.5%

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

      7. associate-*r/ 88.2%

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

   9. Simplified 88.2%

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

   10. Taylor expanded in x around 0 61.8%

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

       1. mul-1-neg 61.8%

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

       2. associate-*r/ 70.2%

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

       3. distribute-rgt-neg-in 70.2%

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

       4. distribute-neg-frac 70.2%

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

   12. Simplified 70.2%

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

   if -4.50000000000000026e159 < t < -2.7999999999999998e95

   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 t around 0 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-/l* 75.3%

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

   7. Simplified 75.3%

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

   if -2.7999999999999998e95 < t < -1.65e72

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 99.7%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. sub-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-*l/ 99.7%

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

      7. associate-*r/ 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in x around 0 99.7%

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

       1. mul-1-neg 99.7%

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

       2. associate-*l/ 100.0%

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

       3. distribute-rgt-neg-in 100.0%

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

   12. Simplified 100.0%

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

   if -1.65e72 < t < 3.4e102

   1. Initial program 96.2%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in z around inf 88.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+159}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -1.65 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+102}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{-a}\\ \mathbf{if}\;t \leq -5.3 \cdot 10^{+157}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+99}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq 7.1 \cdot 10^{+121}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y (- a)))))
   (if (<= t -5.3e+157)
     t_1
     (if (<= t -1.1e+99)
       (+ x (* y (/ z a)))
       (if (<= t -2.15e+73)
         (* y (/ t (- a)))
         (if (<= t 7.1e+121) (+ x (* z (/ y a))) 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 <= -5.3e+157) {
		tmp = t_1;
	} else if (t <= -1.1e+99) {
		tmp = x + (y * (z / a));
	} else if (t <= -2.15e+73) {
		tmp = y * (t / -a);
	} else if (t <= 7.1e+121) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / -a)
    if (t <= (-5.3d+157)) then
        tmp = t_1
    else if (t <= (-1.1d+99)) then
        tmp = x + (y * (z / a))
    else if (t <= (-2.15d+73)) then
        tmp = y * (t / -a)
    else if (t <= 7.1d+121) then
        tmp = x + (z * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / -a);
	double tmp;
	if (t <= -5.3e+157) {
		tmp = t_1;
	} else if (t <= -1.1e+99) {
		tmp = x + (y * (z / a));
	} else if (t <= -2.15e+73) {
		tmp = y * (t / -a);
	} else if (t <= 7.1e+121) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / -a)
	tmp = 0
	if t <= -5.3e+157:
		tmp = t_1
	elif t <= -1.1e+99:
		tmp = x + (y * (z / a))
	elif t <= -2.15e+73:
		tmp = y * (t / -a)
	elif t <= 7.1e+121:
		tmp = x + (z * (y / a))
	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 <= -5.3e+157)
		tmp = t_1;
	elseif (t <= -1.1e+99)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= -2.15e+73)
		tmp = Float64(y * Float64(t / Float64(-a)));
	elseif (t <= 7.1e+121)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	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 <= -5.3e+157)
		tmp = t_1;
	elseif (t <= -1.1e+99)
		tmp = x + (y * (z / a));
	elseif (t <= -2.15e+73)
		tmp = y * (t / -a);
	elseif (t <= 7.1e+121)
		tmp = x + (z * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.3e+157], t$95$1, If[LessEqual[t, -1.1e+99], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.15e+73], N[(y * N[(t / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.1e+121], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.2999999999999998e157 or 7.10000000000000023e121 < t

   1. Initial program 87.6%

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

      1. +-commutative 87.6%

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

      2. associate-/l* 89.1%

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

      3. fma-define 89.1%

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

   3. Simplified 89.1%

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

      1. fma-undefine 89.1%

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

      2. associate-*r/ 87.6%

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

      3. *-commutative 87.6%

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

      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 79.8%

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

      1. associate-*l/ 82.6%

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

      2. *-commutative 82.6%

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

      3. neg-mul-1 82.6%

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

      4. sub-neg 82.6%

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

      5. *-commutative 82.6%

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

      6. associate-*l/ 79.8%

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

      7. associate-*r/ 88.8%

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

   9. Simplified 88.8%

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

   10. Taylor expanded in x around 0 63.5%

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

       1. mul-1-neg 63.5%

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

       2. associate-*r/ 71.1%

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

       3. distribute-rgt-neg-in 71.1%

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

       4. distribute-neg-frac 71.1%

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

   12. Simplified 71.1%

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

   if -5.2999999999999998e157 < t < -1.09999999999999989e99

   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 t around 0 68.7%

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

      1. +-commutative 68.7%

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

      2. associate-/l* 75.3%

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

   7. Simplified 75.3%

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

   if -1.09999999999999989e99 < t < -2.15000000000000007e73

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-/l* 100.0%

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

      3. fma-define 100.0%

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

   3. Simplified 100.0%

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

      1. fma-undefine 100.0%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 99.7%

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

      1. associate-*l/ 100.0%

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

      2. *-commutative 100.0%

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

      3. neg-mul-1 100.0%

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

      4. sub-neg 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-*l/ 99.7%

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

      7. associate-*r/ 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in x around 0 99.7%

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

       1. mul-1-neg 99.7%

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

       2. associate-*l/ 100.0%

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

       3. distribute-rgt-neg-in 100.0%

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

   12. Simplified 100.0%

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

   if -2.15000000000000007e73 < t < 7.10000000000000023e121

   1. Initial program 95.1%

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

      1. +-commutative 95.1%

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

      2. associate-/l* 94.2%

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

      3. fma-define 94.2%

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

   3. Simplified 94.2%

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

      1. fma-undefine 94.2%

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

      2. associate-*r/ 95.1%

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

      3. *-commutative 95.1%

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

      4. associate-/l* 97.5%

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

   6. Applied egg-rr 97.5%

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

   7. Taylor expanded in z around inf 87.8%

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

      1. associate-*l/ 89.6%

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

      2. *-commutative 89.6%

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

   9. Simplified 89.6%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.3 \cdot 10^{+157}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+99}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{+73}:\\ \;\;\;\;y \cdot \frac{t}{-a}\\ \mathbf{elif}\;t \leq 7.1 \cdot 10^{+121}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+39} \lor \neg \left(t \leq 3.4 \cdot 10^{+31}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.7e+39) (not (<= t 3.4e+31)))
   (- 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 <= -3.7e+39) || !(t <= 3.4e+31)) {
		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 <= (-3.7d+39)) .or. (.not. (t <= 3.4d+31))) 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 <= -3.7e+39) || !(t <= 3.4e+31)) {
		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 <= -3.7e+39) or not (t <= 3.4e+31):
		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 <= -3.7e+39) || !(t <= 3.4e+31))
		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 <= -3.7e+39) || ~((t <= 3.4e+31)))
		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, -3.7e+39], N[Not[LessEqual[t, 3.4e+31]], $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 < -3.70000000000000012e39 or 3.3999999999999998e31 < t

   1. Initial program 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-/l* 92.5%

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

      3. fma-define 92.5%

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

   3. Simplified 92.5%

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

      1. fma-undefine 92.5%

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

      2. associate-*r/ 87.7%

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

      3. *-commutative 87.7%

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

      4. associate-/l* 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in z around 0 78.5%

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

      1. associate-*l/ 81.7%

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

      2. *-commutative 81.7%

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

      3. neg-mul-1 81.7%

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

      4. sub-neg 81.7%

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

      5. *-commutative 81.7%

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

      6. associate-*l/ 78.5%

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

      7. associate-*r/ 86.2%

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

   9. Simplified 86.2%

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

   if -3.70000000000000012e39 < t < 3.3999999999999998e31

   1. Initial program 97.0%

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

      1. +-commutative 97.0%

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

      2. associate-/l* 93.7%

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

      3. fma-define 93.7%

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

   3. Simplified 93.7%

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

      1. fma-undefine 93.7%

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

      2. associate-*r/ 97.0%

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

      3. *-commutative 97.0%

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

      4. associate-/l* 97.0%

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

   6. Applied egg-rr 97.0%

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

   7. Taylor expanded in z around inf 92.0%

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

      1. associate-*l/ 92.7%

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

      2. *-commutative 92.7%

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

   9. Simplified 92.7%

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

       1. clear-num 92.6%

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

       2. un-div-inv 92.7%

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

   11. Applied egg-rr 92.7%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+39} \lor \neg \left(t \leq 3.4 \cdot 10^{+31}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+67} \lor \neg \left(t \leq 1.04 \cdot 10^{+102}\right):\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.8e+67) (not (<= t 1.04e+102))) (* t (/ y (- a))) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+67) || !(t <= 1.04e+102)) {
		tmp = t * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.8d+67)) .or. (.not. (t <= 1.04d+102))) then
        tmp = t * (y / -a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.8e+67) || !(t <= 1.04e+102)) {
		tmp = t * (y / -a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.8e+67) or not (t <= 1.04e+102):
		tmp = t * (y / -a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.8e+67) || !(t <= 1.04e+102))
		tmp = Float64(t * Float64(y / Float64(-a)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.8e+67) || ~((t <= 1.04e+102)))
		tmp = t * (y / -a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.8e+67], N[Not[LessEqual[t, 1.04e+102]], $MachinePrecision]], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.7999999999999998e67 or 1.04e102 < 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* 91.7%

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

      3. fma-define 91.7%

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

   3. Simplified 91.7%

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

      1. fma-undefine 91.7%

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

      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* 97.2%

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

   6. Applied egg-rr 97.2%

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

   7. Taylor expanded in z around 0 79.1%

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

      1. associate-*l/ 83.1%

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

      2. *-commutative 83.1%

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

      3. neg-mul-1 83.1%

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

      4. sub-neg 83.1%

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

      5. *-commutative 83.1%

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

      6. associate-*l/ 79.1%

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

      7. associate-*r/ 87.8%

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

   9. Simplified 87.8%

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

   10. Taylor expanded in x around 0 59.9%

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

       1. mul-1-neg 59.9%

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

       2. associate-*r/ 66.6%

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

       3. distribute-rgt-neg-in 66.6%

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

       4. distribute-neg-frac 66.6%

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

   12. Simplified 66.6%

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

   if -2.7999999999999998e67 < t < 1.04e102

   1. Initial program 96.2%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in x around inf 54.5%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+67} \lor \neg \left(t \leq 1.04 \cdot 10^{+102}\right):\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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 92.5%

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

   1. associate-/l* 93.1%

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

3. Simplified 93.1%

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

5. Final simplification 93.1%

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

Alternative 8: 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 92.5%

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

   1. associate-/l* 93.1%

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

3. Simplified 93.1%

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

   1. clear-num 92.9%

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

   2. un-div-inv 93.5%

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

6. Applied egg-rr 93.5%

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

7. Final simplification 93.5%

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

Alternative 9: 97.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

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

   1. +-commutative 92.5%

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

   2. associate-/l* 93.1%

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

   3. fma-define 93.1%

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

3. Simplified 93.1%

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

   1. fma-undefine 93.1%

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

   2. associate-*r/ 92.5%

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

   3. *-commutative 92.5%

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

   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. Final simplification 97.4%

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

Alternative 10: 39.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

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

   1. associate-/l* 93.1%

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

3. Simplified 93.1%

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

5. Taylor expanded in x around inf 42.2%

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

6. Final simplification 42.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024079 
(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)))