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

Percentage Accurate: 93.4% → 95.8%

Time: 8.4s

Alternatives: 13

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: 93.4% 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: 95.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 8.5e-135) (+ 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 <= 8.5e-135) {
		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 <= 8.5d-135) 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 <= 8.5e-135) {
		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 <= 8.5e-135:
		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 <= 8.5e-135)
		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 <= 8.5e-135)
		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, 8.5e-135], 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 2 regimes

2. if y < 8.49999999999999942e-135

   1. Initial program 97.8%

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

   if 8.49999999999999942e-135 < y

   1. Initial program 87.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-135}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 47.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-275}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;a \leq 10^{+15}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.1e-80)
   x
   (if (<= a 1.75e-275)
     (/ (* z y) a)
     (if (<= a 1e+15)
       (* t (/ y (- a)))
       (if (<= a 3.6e+132) x (if (<= a 2.1e+214) (* y (/ z a)) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.1e-80) {
		tmp = x;
	} else if (a <= 1.75e-275) {
		tmp = (z * y) / a;
	} else if (a <= 1e+15) {
		tmp = t * (y / -a);
	} else if (a <= 3.6e+132) {
		tmp = x;
	} else if (a <= 2.1e+214) {
		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 (a <= (-1.1d-80)) then
        tmp = x
    else if (a <= 1.75d-275) then
        tmp = (z * y) / a
    else if (a <= 1d+15) then
        tmp = t * (y / -a)
    else if (a <= 3.6d+132) then
        tmp = x
    else if (a <= 2.1d+214) 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 (a <= -1.1e-80) {
		tmp = x;
	} else if (a <= 1.75e-275) {
		tmp = (z * y) / a;
	} else if (a <= 1e+15) {
		tmp = t * (y / -a);
	} else if (a <= 3.6e+132) {
		tmp = x;
	} else if (a <= 2.1e+214) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.1e-80:
		tmp = x
	elif a <= 1.75e-275:
		tmp = (z * y) / a
	elif a <= 1e+15:
		tmp = t * (y / -a)
	elif a <= 3.6e+132:
		tmp = x
	elif a <= 2.1e+214:
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.1e-80)
		tmp = x;
	elseif (a <= 1.75e-275)
		tmp = Float64(Float64(z * y) / a);
	elseif (a <= 1e+15)
		tmp = Float64(t * Float64(y / Float64(-a)));
	elseif (a <= 3.6e+132)
		tmp = x;
	elseif (a <= 2.1e+214)
		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 (a <= -1.1e-80)
		tmp = x;
	elseif (a <= 1.75e-275)
		tmp = (z * y) / a;
	elseif (a <= 1e+15)
		tmp = t * (y / -a);
	elseif (a <= 3.6e+132)
		tmp = x;
	elseif (a <= 2.1e+214)
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.1e-80], x, If[LessEqual[a, 1.75e-275], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[a, 1e+15], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.6e+132], x, If[LessEqual[a, 2.1e+214], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.10000000000000005e-80 or 1e15 < a < 3.60000000000000016e132 or 2.1000000000000001e214 < a

   1. Initial program 93.5%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around inf 64.8%

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

   if -1.10000000000000005e-80 < a < 1.74999999999999984e-275

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-/l* 82.3%

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

      3. fma-define 82.4%

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

   3. Simplified 82.4%

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

      1. fma-undefine 82.3%

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

      2. associate-*r/ 99.0%

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

      3. *-commutative 99.0%

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

      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 71.2%

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

   8. Taylor expanded in y around inf 53.3%

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

   if 1.74999999999999984e-275 < a < 1e15

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      2. associate-/l* 88.5%

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

      3. fma-define 88.5%

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

   3. Simplified 88.5%

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

      1. fma-undefine 88.5%

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

      2. associate-*r/ 98.4%

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

      3. *-commutative 98.4%

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

      4. associate-/l* 98.4%

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

   6. Applied egg-rr 98.4%

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

   7. Taylor expanded in z around 0 73.7%

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

      1. associate-*l/ 66.7%

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

      2. *-commutative 66.7%

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

      3. neg-mul-1 66.7%

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

      4. sub-neg 66.7%

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

      5. associate-*r/ 73.7%

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

      6. associate-*l/ 77.7%

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

      7. *-commutative 77.7%

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

   9. Simplified 77.7%

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

   10. Taylor expanded in x around 0 55.4%

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

       1. mul-1-neg 55.4%

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

       2. distribute-frac-neg 55.4%

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

       3. distribute-rgt-neg-in 55.4%

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

       4. associate-/l* 59.4%

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

   12. Simplified 59.4%

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

   if 3.60000000000000016e132 < a < 2.1000000000000001e214

   1. Initial program 57.1%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. div-sub 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around inf 50.3%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-275}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \mathbf{elif}\;a \leq 10^{+15}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;a \leq 3.6 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t \cdot \left(-y\right)}{a}\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+263}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+207}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* t (- y)) a)))
   (if (<= t -1.5e+273)
     t_1
     (if (<= t -2e+263)
       (+ x (/ (* z y) a))
       (if (<= t -3.3e+113)
         (* t (/ y (- a)))
         (if (<= t 1.15e+207) (+ 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 <= -1.5e+273) {
		tmp = t_1;
	} else if (t <= -2e+263) {
		tmp = x + ((z * y) / a);
	} else if (t <= -3.3e+113) {
		tmp = t * (y / -a);
	} else if (t <= 1.15e+207) {
		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 <= (-1.5d+273)) then
        tmp = t_1
    else if (t <= (-2d+263)) then
        tmp = x + ((z * y) / a)
    else if (t <= (-3.3d+113)) then
        tmp = t * (y / -a)
    else if (t <= 1.15d+207) 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 <= -1.5e+273) {
		tmp = t_1;
	} else if (t <= -2e+263) {
		tmp = x + ((z * y) / a);
	} else if (t <= -3.3e+113) {
		tmp = t * (y / -a);
	} else if (t <= 1.15e+207) {
		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 <= -1.5e+273:
		tmp = t_1
	elif t <= -2e+263:
		tmp = x + ((z * y) / a)
	elif t <= -3.3e+113:
		tmp = t * (y / -a)
	elif t <= 1.15e+207:
		tmp = x + (z * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t * Float64(-y)) / a)
	tmp = 0.0
	if (t <= -1.5e+273)
		tmp = t_1;
	elseif (t <= -2e+263)
		tmp = Float64(x + Float64(Float64(z * y) / a));
	elseif (t <= -3.3e+113)
		tmp = Float64(t * Float64(y / Float64(-a)));
	elseif (t <= 1.15e+207)
		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 <= -1.5e+273)
		tmp = t_1;
	elseif (t <= -2e+263)
		tmp = x + ((z * y) / a);
	elseif (t <= -3.3e+113)
		tmp = t * (y / -a);
	elseif (t <= 1.15e+207)
		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[(N[(t * (-y)), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t, -1.5e+273], t$95$1, If[LessEqual[t, -2e+263], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.3e+113], N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+207], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.5e273 or 1.14999999999999997e207 < t

   1. Initial program 87.2%

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

      1. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in y around inf 79.2%

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

      1. associate--l+ 79.2%

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

      2. div-sub 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in x around 0 73.1%

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

      1. div-sub 73.1%

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

   10. Simplified 73.1%

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

   11. Taylor expanded in z around 0 80.2%

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

       1. associate-*r/ 80.2%

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

       2. mul-1-neg 80.2%

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

       3. distribute-lft-neg-out 80.2%

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

       4. *-commutative 80.2%

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

   13. Simplified 80.2%

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

   if -1.5e273 < t < -2.00000000000000003e263

   1. Initial program 100.0%

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

      1. associate-/l* 81.0%

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

   3. Simplified 81.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   if -2.00000000000000003e263 < t < -3.3000000000000003e113

   1. Initial program 92.7%

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

      1. +-commutative 92.7%

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

      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/ 92.7%

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

      3. *-commutative 92.7%

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

      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 92.7%

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

      1. associate-*l/ 92.5%

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

      2. *-commutative 92.5%

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

      3. neg-mul-1 92.5%

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

      4. sub-neg 92.5%

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

      5. associate-*r/ 92.7%

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

      6. associate-*l/ 99.9%

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

      7. *-commutative 99.9%

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

   9. Simplified 99.9%

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

   10. Taylor expanded in x around 0 77.2%

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

       1. mul-1-neg 77.2%

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

       2. distribute-frac-neg 77.2%

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

       3. distribute-rgt-neg-in 77.2%

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

       4. associate-/l* 84.4%

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

   12. Simplified 84.4%

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

   if -3.3000000000000003e113 < t < 1.14999999999999997e207

   1. Initial program 95.2%

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

      1. associate-/l* 93.4%

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

   3. Simplified 93.4%

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

   5. Taylor expanded in t around 0 78.5%

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

      1. +-commutative 78.5%

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

      2. associate-/l* 78.9%

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

   7. Simplified 78.9%

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

      1. clear-num 78.9%

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

      2. un-div-inv 79.4%

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

   9. Applied egg-rr 79.4%

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

   10. Taylor expanded in y around 0 78.5%

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

       1. associate-*l/ 84.5%

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

   12. Simplified 84.5%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+273}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+263}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+207}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+65} \lor \neg \left(t \leq 2.4 \cdot 10^{+67}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e+65) (not (<= t 2.4e+67)))
   (- x (* t (/ y a)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+65) || !(t <= 2.4e+67)) {
		tmp = x - (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 <= (-4d+65)) .or. (.not. (t <= 2.4d+67))) then
        tmp = x - (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 <= -4e+65) || !(t <= 2.4e+67)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e+65) or not (t <= 2.4e+67):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e+65) || !(t <= 2.4e+67))
		tmp = Float64(x - Float64(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 <= -4e+65) || ~((t <= 2.4e+67)))
		tmp = x - (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, -4e+65], N[Not[LessEqual[t, 2.4e+67]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4e65 or 2.40000000000000002e67 < t

   1. Initial program 92.9%

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

      1. +-commutative 92.9%

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

      2. associate-/l* 89.2%

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

      3. fma-define 89.2%

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

   3. Simplified 89.2%

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

      1. fma-undefine 89.2%

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

      2. associate-*r/ 92.9%

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

      3. *-commutative 92.9%

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

      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 85.4%

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

      1. associate-*l/ 84.4%

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

      2. *-commutative 84.4%

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

      3. neg-mul-1 84.4%

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

      4. sub-neg 84.4%

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

      5. associate-*r/ 85.4%

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

      6. associate-*l/ 88.8%

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

      7. *-commutative 88.8%

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

   9. Simplified 88.8%

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

   if -4e65 < t < 2.40000000000000002e67

   1. Initial program 95.1%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in t around 0 84.0%

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

      1. +-commutative 84.0%

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

      2. associate-/l* 84.4%

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

   7. Simplified 84.4%

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

      1. clear-num 84.4%

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

      2. un-div-inv 85.2%

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

   9. Applied egg-rr 85.2%

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

   10. Taylor expanded in y around 0 84.0%

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

       1. associate-*l/ 88.1%

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

   12. Simplified 88.1%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+65} \lor \neg \left(t \leq 2.4 \cdot 10^{+67}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-9} \lor \neg \left(x \leq 3.2 \cdot 10^{-115}\right):\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -4e-9) (not (<= x 3.2e-115)))
   (+ x (/ (* z y) a))
   (* y (/ (- z t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -4e-9) || !(x <= 3.2e-115)) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = 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 ((x <= (-4d-9)) .or. (.not. (x <= 3.2d-115))) then
        tmp = x + ((z * y) / a)
    else
        tmp = 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 ((x <= -4e-9) || !(x <= 3.2e-115)) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -4e-9) or not (x <= 3.2e-115):
		tmp = x + ((z * y) / a)
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -4e-9) || !(x <= 3.2e-115))
		tmp = Float64(x + Float64(Float64(z * y) / a));
	else
		tmp = 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 ((x <= -4e-9) || ~((x <= 3.2e-115)))
		tmp = x + ((z * y) / a);
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -4e-9], N[Not[LessEqual[x, 3.2e-115]], $MachinePrecision]], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.00000000000000025e-9 or 3.2e-115 < x

   1. Initial program 95.0%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in z around inf 76.1%

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

   if -4.00000000000000025e-9 < x < 3.2e-115

   1. Initial program 93.0%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around inf 91.6%

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

      1. associate--l+ 91.6%

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

      2. div-sub 93.6%

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

   7. Simplified 93.6%

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

   8. Taylor expanded in x around 0 78.5%

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

      1. div-sub 80.5%

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

   10. Simplified 80.5%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-9} \lor \neg \left(x \leq 3.2 \cdot 10^{-115}\right):\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-132} \lor \neg \left(y \leq 1.06 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.7e-132) (not (<= y 1.06e-32))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.7e-132) || !(y <= 1.06e-32)) {
		tmp = y * ((z - t) / 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 <= (-4.7d-132)) .or. (.not. (y <= 1.06d-32))) then
        tmp = y * ((z - t) / 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 <= -4.7e-132) || !(y <= 1.06e-32)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.7e-132) or not (y <= 1.06e-32):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.7e-132) || !(y <= 1.06e-32))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.7e-132) || ~((y <= 1.06e-32)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.7e-132], N[Not[LessEqual[y, 1.06e-32]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.7000000000000002e-132 or 1.05999999999999994e-32 < y

   1. Initial program 91.1%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around inf 95.0%

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

      1. associate--l+ 95.0%

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

      2. div-sub 97.0%

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

   7. Simplified 97.0%

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

   8. Taylor expanded in x around 0 71.7%

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

      1. div-sub 73.7%

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

   10. Simplified 73.7%

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

   if -4.7000000000000002e-132 < y < 1.05999999999999994e-32

   1. Initial program 98.5%

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

      1. associate-/l* 84.8%

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

   3. Simplified 84.8%

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

   5. Taylor expanded in x around inf 63.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-132} \lor \neg \left(y \leq 1.06 \cdot 10^{-32}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -9e-9)
   (+ x (* y (/ z a)))
   (if (<= x 1.55e-115) (* y (/ (- z t) a)) (+ x (/ (* z y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -9e-9) {
		tmp = x + (y * (z / a));
	} else if (x <= 1.55e-115) {
		tmp = y * ((z - t) / 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 (x <= (-9d-9)) then
        tmp = x + (y * (z / a))
    else if (x <= 1.55d-115) then
        tmp = y * ((z - t) / 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 (x <= -9e-9) {
		tmp = x + (y * (z / a));
	} else if (x <= 1.55e-115) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -9e-9:
		tmp = x + (y * (z / a))
	elif x <= 1.55e-115:
		tmp = y * ((z - t) / a)
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -9e-9)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (x <= 1.55e-115)
		tmp = Float64(y * Float64(Float64(z - t) / 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 (x <= -9e-9)
		tmp = x + (y * (z / a));
	elseif (x <= 1.55e-115)
		tmp = y * ((z - t) / a);
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -9e-9], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.55e-115], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.99999999999999953e-9

   1. Initial program 92.5%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in t around 0 82.0%

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

      1. +-commutative 82.0%

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

      2. associate-/l* 83.7%

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

   7. Simplified 83.7%

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

   if -8.99999999999999953e-9 < x < 1.55000000000000003e-115

   1. Initial program 93.0%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around inf 91.6%

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

      1. associate--l+ 91.6%

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

      2. div-sub 93.6%

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

   7. Simplified 93.6%

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

   8. Taylor expanded in x around 0 78.5%

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

      1. div-sub 80.5%

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

   10. Simplified 80.5%

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

   if 1.55000000000000003e-115 < x

   1. Initial program 96.8%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in z around inf 71.8%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{-9}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-115}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-70}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.6e-9) x (if (<= x 5.6e-70) (/ y (/ a z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.6e-9) {
		tmp = x;
	} else if (x <= 5.6e-70) {
		tmp = y / (a / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.6d-9)) then
        tmp = x
    else if (x <= 5.6d-70) then
        tmp = y / (a / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.6e-9) {
		tmp = x;
	} else if (x <= 5.6e-70) {
		tmp = y / (a / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.6e-9:
		tmp = x
	elif x <= 5.6e-70:
		tmp = y / (a / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.6e-9)
		tmp = x;
	elseif (x <= 5.6e-70)
		tmp = Float64(y / Float64(a / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.6e-9)
		tmp = x;
	elseif (x <= 5.6e-70)
		tmp = y / (a / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.6e-9], x, If[LessEqual[x, 5.6e-70], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000006e-9 or 5.5999999999999998e-70 < x

   1. Initial program 94.6%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in x around inf 60.2%

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

   if -1.60000000000000006e-9 < x < 5.5999999999999998e-70

   1. Initial program 93.6%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around inf 91.4%

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

      1. associate--l+ 91.4%

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

      2. div-sub 93.3%

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

   7. Simplified 93.3%

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

   8. Taylor expanded in z around inf 40.7%

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

      1. clear-num 54.2%

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

      2. un-div-inv 54.6%

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

   10. Applied egg-rr 41.1%

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

Alternative 9: 47.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-70}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -6.8e-7) x (if (<= x 2.3e-70) (* y (/ z a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -6.8e-7) {
		tmp = x;
	} else if (x <= 2.3e-70) {
		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 (x <= (-6.8d-7)) then
        tmp = x
    else if (x <= 2.3d-70) 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 (x <= -6.8e-7) {
		tmp = x;
	} else if (x <= 2.3e-70) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -6.8e-7:
		tmp = x
	elif x <= 2.3e-70:
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -6.8e-7)
		tmp = x;
	elseif (x <= 2.3e-70)
		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 (x <= -6.8e-7)
		tmp = x;
	elseif (x <= 2.3e-70)
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -6.8e-7], x, If[LessEqual[x, 2.3e-70], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.79999999999999948e-7 or 2.30000000000000001e-70 < x

   1. Initial program 94.6%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in x around inf 60.2%

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

   if -6.79999999999999948e-7 < x < 2.30000000000000001e-70

   1. Initial program 93.6%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in y around inf 91.4%

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

      1. associate--l+ 91.4%

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

      2. div-sub 93.3%

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

   7. Simplified 93.3%

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

   8. Taylor expanded in z around inf 40.7%

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

Alternative 10: 97.1% 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 94.2%

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

   1. +-commutative 94.2%

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

   2. associate-/l* 92.3%

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

   3. fma-define 92.3%

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

3. Simplified 92.3%

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

   1. fma-undefine 92.3%

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

   2. associate-*r/ 94.2%

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

   3. *-commutative 94.2%

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

   4. associate-/l* 97.3%

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

6. Applied egg-rr 97.3%

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

Alternative 11: 93.5% 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 94.2%

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

   1. associate-/l* 92.3%

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

3. Simplified 92.3%

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

   1. clear-num 92.2%

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

   2. un-div-inv 93.6%

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

6. Applied egg-rr 93.6%

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

Alternative 12: 92.9% 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 94.2%

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

   1. associate-/l* 92.3%

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

3. Simplified 92.3%

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

Alternative 13: 39.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

   1. associate-/l* 92.3%

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

3. Simplified 92.3%

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

5. Taylor expanded in x around inf 40.6%

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

Developer target: 99.3% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024108 
(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)))