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

Percentage Accurate: 93.6% → 97.2%

Time: 8.6s

Alternatives: 10

Speedup: 1.0×

• 24.6% 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: 93.6% 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: 97.2% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 92.4%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Final simplification 97.3%

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

Alternative 2: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(-t\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+132}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+210}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- t))))
   (if (<= y -4.2e+227)
     t_1
     (if (<= y -1.02e+132)
       (/ (* y z) a)
       (if (<= y -5.3e-31)
         t_1
         (if (<= y 1.02e-22) x (if (<= y 4.4e+210) (* (/ y a) z) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -t;
	double tmp;
	if (y <= -4.2e+227) {
		tmp = t_1;
	} else if (y <= -1.02e+132) {
		tmp = (y * z) / a;
	} else if (y <= -5.3e-31) {
		tmp = t_1;
	} else if (y <= 1.02e-22) {
		tmp = x;
	} else if (y <= 4.4e+210) {
		tmp = (y / a) * z;
	} 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 = (y / a) * -t
    if (y <= (-4.2d+227)) then
        tmp = t_1
    else if (y <= (-1.02d+132)) then
        tmp = (y * z) / a
    else if (y <= (-5.3d-31)) then
        tmp = t_1
    else if (y <= 1.02d-22) then
        tmp = x
    else if (y <= 4.4d+210) then
        tmp = (y / a) * z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * -t;
	double tmp;
	if (y <= -4.2e+227) {
		tmp = t_1;
	} else if (y <= -1.02e+132) {
		tmp = (y * z) / a;
	} else if (y <= -5.3e-31) {
		tmp = t_1;
	} else if (y <= 1.02e-22) {
		tmp = x;
	} else if (y <= 4.4e+210) {
		tmp = (y / a) * z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * -t
	tmp = 0
	if y <= -4.2e+227:
		tmp = t_1
	elif y <= -1.02e+132:
		tmp = (y * z) / a
	elif y <= -5.3e-31:
		tmp = t_1
	elif y <= 1.02e-22:
		tmp = x
	elif y <= 4.4e+210:
		tmp = (y / a) * z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(-t))
	tmp = 0.0
	if (y <= -4.2e+227)
		tmp = t_1;
	elseif (y <= -1.02e+132)
		tmp = Float64(Float64(y * z) / a);
	elseif (y <= -5.3e-31)
		tmp = t_1;
	elseif (y <= 1.02e-22)
		tmp = x;
	elseif (y <= 4.4e+210)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * -t;
	tmp = 0.0;
	if (y <= -4.2e+227)
		tmp = t_1;
	elseif (y <= -1.02e+132)
		tmp = (y * z) / a;
	elseif (y <= -5.3e-31)
		tmp = t_1;
	elseif (y <= 1.02e-22)
		tmp = x;
	elseif (y <= 4.4e+210)
		tmp = (y / a) * z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision]}, If[LessEqual[y, -4.2e+227], t$95$1, If[LessEqual[y, -1.02e+132], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -5.3e-31], t$95$1, If[LessEqual[y, 1.02e-22], x, If[LessEqual[y, 4.4e+210], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.20000000000000039e227 or -1.0200000000000001e132 < y < -5.3000000000000001e-31 or 4.39999999999999974e210 < y

   1. Initial program 82.7%

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

      1. associate-*l/ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in z around 0 64.1%

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

      1. mul-1-neg 64.1%

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

      2. associate-*l/ 82.1%

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

      3. distribute-rgt-neg-out 82.1%

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

      4. +-commutative 82.1%

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

      5. *-commutative 82.1%

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

      6. distribute-lft-neg-out 82.1%

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

      7. unsub-neg 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in x around 0 51.8%

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

      1. associate-*l/ 67.4%

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

      2. *-commutative 67.4%

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

      3. neg-mul-1 67.4%

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

      4. distribute-rgt-neg-in 67.4%

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

   9. Simplified 67.4%

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

   if -4.20000000000000039e227 < y < -1.0200000000000001e132

   1. Initial program 91.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 77.8%

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

   5. Taylor expanded in z around inf 56.2%

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

   6. Taylor expanded in z around 0 56.3%

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

   if -5.3000000000000001e-31 < y < 1.02000000000000002e-22

   1. Initial program 99.8%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around inf 64.2%

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

   if 1.02000000000000002e-22 < y < 4.39999999999999974e210

   1. Initial program 87.9%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around inf 82.1%

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

   5. Taylor expanded in z around inf 60.2%

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

   6. Taylor expanded in z around 0 52.4%

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

      1. associate-*l/ 67.7%

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

   8. Simplified 67.7%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+227}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{+132}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+210}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \end{array} \]

Alternative 3: 49.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-t}{a}\\ \mathbf{if}\;y \leq -5 \cdot 10^{+229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+129}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+212}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t) a))))
   (if (<= y -5e+229)
     t_1
     (if (<= y -2.45e+129)
       (/ (* y z) a)
       (if (<= y -2.1e-29)
         t_1
         (if (<= y 1.02e-22)
           x
           (if (<= y 1.52e+212) (* (/ y a) z) (* (/ y a) (- t)))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-t / a);
	double tmp;
	if (y <= -5e+229) {
		tmp = t_1;
	} else if (y <= -2.45e+129) {
		tmp = (y * z) / a;
	} else if (y <= -2.1e-29) {
		tmp = t_1;
	} else if (y <= 1.02e-22) {
		tmp = x;
	} else if (y <= 1.52e+212) {
		tmp = (y / a) * z;
	} else {
		tmp = (y / a) * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (-t / a)
    if (y <= (-5d+229)) then
        tmp = t_1
    else if (y <= (-2.45d+129)) then
        tmp = (y * z) / a
    else if (y <= (-2.1d-29)) then
        tmp = t_1
    else if (y <= 1.02d-22) then
        tmp = x
    else if (y <= 1.52d+212) then
        tmp = (y / a) * z
    else
        tmp = (y / a) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-t / a);
	double tmp;
	if (y <= -5e+229) {
		tmp = t_1;
	} else if (y <= -2.45e+129) {
		tmp = (y * z) / a;
	} else if (y <= -2.1e-29) {
		tmp = t_1;
	} else if (y <= 1.02e-22) {
		tmp = x;
	} else if (y <= 1.52e+212) {
		tmp = (y / a) * z;
	} else {
		tmp = (y / a) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-t / a)
	tmp = 0
	if y <= -5e+229:
		tmp = t_1
	elif y <= -2.45e+129:
		tmp = (y * z) / a
	elif y <= -2.1e-29:
		tmp = t_1
	elif y <= 1.02e-22:
		tmp = x
	elif y <= 1.52e+212:
		tmp = (y / a) * z
	else:
		tmp = (y / a) * -t
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-t) / a))
	tmp = 0.0
	if (y <= -5e+229)
		tmp = t_1;
	elseif (y <= -2.45e+129)
		tmp = Float64(Float64(y * z) / a);
	elseif (y <= -2.1e-29)
		tmp = t_1;
	elseif (y <= 1.02e-22)
		tmp = x;
	elseif (y <= 1.52e+212)
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = Float64(Float64(y / a) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-t / a);
	tmp = 0.0;
	if (y <= -5e+229)
		tmp = t_1;
	elseif (y <= -2.45e+129)
		tmp = (y * z) / a;
	elseif (y <= -2.1e-29)
		tmp = t_1;
	elseif (y <= 1.02e-22)
		tmp = x;
	elseif (y <= 1.52e+212)
		tmp = (y / a) * z;
	else
		tmp = (y / a) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e+229], t$95$1, If[LessEqual[y, -2.45e+129], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, -2.1e-29], t$95$1, If[LessEqual[y, 1.02e-22], x, If[LessEqual[y, 1.52e+212], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.0000000000000005e229 or -2.45e129 < y < -2.09999999999999989e-29

   1. Initial program 89.6%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around inf 82.8%

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

   5. Taylor expanded in z around 0 70.3%

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

      1. associate-*r/ 70.3%

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

      2. neg-mul-1 70.3%

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

   7. Simplified 70.3%

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

   if -5.0000000000000005e229 < y < -2.45e129

   1. Initial program 91.3%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 77.8%

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

   5. Taylor expanded in z around inf 56.2%

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

   6. Taylor expanded in z around 0 56.3%

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

   if -2.09999999999999989e-29 < y < 1.02000000000000002e-22

   1. Initial program 99.8%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around inf 64.2%

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

   if 1.02000000000000002e-22 < y < 1.52000000000000006e212

   1. Initial program 87.9%

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

      1. associate-*l/ 97.8%

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

   3. Simplified 97.8%

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

   4. Taylor expanded in y around inf 82.1%

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

   5. Taylor expanded in z around inf 60.2%

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

   6. Taylor expanded in z around 0 52.4%

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

      1. associate-*l/ 67.7%

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

   8. Simplified 67.7%

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

   if 1.52000000000000006e212 < y

   1. Initial program 66.7%

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

      1. associate-*l/ 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in z around 0 39.7%

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

      1. mul-1-neg 39.7%

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

      2. associate-*l/ 75.6%

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

      3. distribute-rgt-neg-out 75.6%

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

      4. +-commutative 75.6%

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

      5. *-commutative 75.6%

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

      6. distribute-lft-neg-out 75.6%

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

      7. unsub-neg 75.6%

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

   6. Simplified 75.6%

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

   7. Taylor expanded in x around 0 32.7%

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

      1. associate-*l/ 60.8%

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

      2. *-commutative 60.8%

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

      3. neg-mul-1 60.8%

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

      4. distribute-rgt-neg-in 60.8%

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

   9. Simplified 60.8%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;y \leq -2.45 \cdot 10^{+129}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-29}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+212}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \end{array} \]

Alternative 4: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{a} \cdot t\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-25} \lor \neg \left(t \leq 6.4 \cdot 10^{+42}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y a) t))))
   (if (<= t -6.5e-40)
     t_1
     (if (<= t 1.1e-63)
       (+ x (/ (* y z) a))
       (if (or (<= t 1.52e-25) (not (<= t 6.4e+42)))
         t_1
         (+ x (* (/ y a) z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / a) * t);
	double tmp;
	if (t <= -6.5e-40) {
		tmp = t_1;
	} else if (t <= 1.1e-63) {
		tmp = x + ((y * z) / a);
	} else if ((t <= 1.52e-25) || !(t <= 6.4e+42)) {
		tmp = t_1;
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((y / a) * t)
    if (t <= (-6.5d-40)) then
        tmp = t_1
    else if (t <= 1.1d-63) then
        tmp = x + ((y * z) / a)
    else if ((t <= 1.52d-25) .or. (.not. (t <= 6.4d+42))) then
        tmp = t_1
    else
        tmp = x + ((y / a) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / a) * t);
	double tmp;
	if (t <= -6.5e-40) {
		tmp = t_1;
	} else if (t <= 1.1e-63) {
		tmp = x + ((y * z) / a);
	} else if ((t <= 1.52e-25) || !(t <= 6.4e+42)) {
		tmp = t_1;
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / a) * t)
	tmp = 0
	if t <= -6.5e-40:
		tmp = t_1
	elif t <= 1.1e-63:
		tmp = x + ((y * z) / a)
	elif (t <= 1.52e-25) or not (t <= 6.4e+42):
		tmp = t_1
	else:
		tmp = x + ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / a) * t))
	tmp = 0.0
	if (t <= -6.5e-40)
		tmp = t_1;
	elseif (t <= 1.1e-63)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif ((t <= 1.52e-25) || !(t <= 6.4e+42))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(y / a) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / a) * t);
	tmp = 0.0;
	if (t <= -6.5e-40)
		tmp = t_1;
	elseif (t <= 1.1e-63)
		tmp = x + ((y * z) / a);
	elseif ((t <= 1.52e-25) || ~((t <= 6.4e+42)))
		tmp = t_1;
	else
		tmp = x + ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e-40], t$95$1, If[LessEqual[t, 1.1e-63], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.52e-25], N[Not[LessEqual[t, 6.4e+42]], $MachinePrecision]], t$95$1, N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999999e-40 or 1.1e-63 < t < 1.52000000000000006e-25 or 6.40000000000000004e42 < t

   1. Initial program 88.2%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in z around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. associate-*l/ 87.9%

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

      3. distribute-rgt-neg-out 87.9%

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

      4. +-commutative 87.9%

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

      5. *-commutative 87.9%

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

      6. distribute-lft-neg-out 87.9%

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

      7. unsub-neg 87.9%

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

   6. Simplified 87.9%

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

   if -6.4999999999999999e-40 < t < 1.1e-63

   1. Initial program 98.2%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around 0 96.4%

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

   if 1.52000000000000006e-25 < t < 6.40000000000000004e42

   1. Initial program 86.1%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 75.6%

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

      1. associate-*l/ 89.2%

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

      2. *-commutative 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-25} \lor \neg \left(t \leq 6.4 \cdot 10^{+42}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]

Alternative 5: 72.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+253} \lor \neg \left(t \leq 1.25 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.36e+253) (not (<= t 1.25e+73)))
   (* (/ y a) (- t))
   (+ x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.36e+253) || !(t <= 1.25e+73)) {
		tmp = (y / a) * -t;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.36d+253)) .or. (.not. (t <= 1.25d+73))) then
        tmp = (y / a) * -t
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.36e+253) || !(t <= 1.25e+73)) {
		tmp = (y / a) * -t;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.36e+253) or not (t <= 1.25e+73):
		tmp = (y / a) * -t
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.36e+253) || !(t <= 1.25e+73))
		tmp = Float64(Float64(y / a) * Float64(-t));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.36e+253) || ~((t <= 1.25e+73)))
		tmp = (y / a) * -t;
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.36e+253], N[Not[LessEqual[t, 1.25e+73]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.36e253 or 1.24999999999999994e73 < t

   1. Initial program 83.2%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. associate-*l/ 95.9%

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

      3. distribute-rgt-neg-out 95.9%

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

      4. +-commutative 95.9%

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

      5. *-commutative 95.9%

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

      6. distribute-lft-neg-out 95.9%

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

      7. unsub-neg 95.9%

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

   6. Simplified 95.9%

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

   7. Taylor expanded in x around 0 63.2%

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

      1. associate-*l/ 79.9%

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

      2. *-commutative 79.9%

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

      3. neg-mul-1 79.9%

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

      4. distribute-rgt-neg-in 79.9%

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

   9. Simplified 79.9%

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

   if -1.36e253 < t < 1.24999999999999994e73

   1. Initial program 94.7%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around inf 79.1%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.36 \cdot 10^{+253} \lor \neg \left(t \leq 1.25 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 6: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+251} \lor \neg \left(t \leq 5.5 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4e+251) (not (<= t 5.5e+73)))
   (* (/ y a) (- t))
   (+ x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+251) || !(t <= 5.5e+73)) {
		tmp = (y / a) * -t;
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-4d+251)) .or. (.not. (t <= 5.5d+73))) then
        tmp = (y / a) * -t
    else
        tmp = x + ((y / a) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4e+251) || !(t <= 5.5e+73)) {
		tmp = (y / a) * -t;
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4e+251) or not (t <= 5.5e+73):
		tmp = (y / a) * -t
	else:
		tmp = x + ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4e+251) || !(t <= 5.5e+73))
		tmp = Float64(Float64(y / a) * Float64(-t));
	else
		tmp = Float64(x + Float64(Float64(y / a) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -4e+251) || ~((t <= 5.5e+73)))
		tmp = (y / a) * -t;
	else
		tmp = x + ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4e+251], N[Not[LessEqual[t, 5.5e+73]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.0000000000000002e251 or 5.5000000000000003e73 < t

   1. Initial program 83.2%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. associate-*l/ 95.9%

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

      3. distribute-rgt-neg-out 95.9%

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

      4. +-commutative 95.9%

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

      5. *-commutative 95.9%

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

      6. distribute-lft-neg-out 95.9%

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

      7. unsub-neg 95.9%

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

   6. Simplified 95.9%

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

   7. Taylor expanded in x around 0 63.2%

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

      1. associate-*l/ 79.9%

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

      2. *-commutative 79.9%

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

      3. neg-mul-1 79.9%

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

      4. distribute-rgt-neg-in 79.9%

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

   9. Simplified 79.9%

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

   if -4.0000000000000002e251 < t < 5.5000000000000003e73

   1. Initial program 94.7%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around 0 78.6%

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

      1. associate-*l/ 81.4%

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

      2. *-commutative 81.4%

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

   6. Simplified 81.4%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+251} \lor \neg \left(t \leq 5.5 \cdot 10^{+73}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]

Alternative 7: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+21} \lor \neg \left(y \leq 8.2 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3e+21) (not (<= y 8.2e-23))) (* (/ y a) z) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3e+21) || !(y <= 8.2e-23)) {
		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 ((y <= (-3d+21)) .or. (.not. (y <= 8.2d-23))) 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 ((y <= -3e+21) || !(y <= 8.2e-23)) {
		tmp = (y / a) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3e+21) or not (y <= 8.2e-23):
		tmp = (y / a) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3e+21) || !(y <= 8.2e-23))
		tmp = Float64(Float64(y / a) * z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3e+21) || ~((y <= 8.2e-23)))
		tmp = (y / a) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3e+21], N[Not[LessEqual[y, 8.2e-23]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3e21 or 8.20000000000000059e-23 < y

   1. Initial program 85.3%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in y around inf 81.9%

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

   5. Taylor expanded in z around inf 46.8%

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

   6. Taylor expanded in z around 0 44.0%

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

      1. associate-*l/ 49.6%

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

   8. Simplified 49.6%

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

   if -3e21 < y < 8.20000000000000059e-23

   1. Initial program 99.8%

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

      1. associate-*l/ 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in x around inf 62.8%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+21} \lor \neg \left(y \leq 8.2 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 50.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.7e+64) (* y (/ z a)) (if (<= y 6.8e-25) x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.7e+64) {
		tmp = y * (z / a);
	} else if (y <= 6.8e-25) {
		tmp = x;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-3.7d+64)) then
        tmp = y * (z / a)
    else if (y <= 6.8d-25) then
        tmp = x
    else
        tmp = (y / a) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.7e+64) {
		tmp = y * (z / a);
	} else if (y <= 6.8e-25) {
		tmp = x;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.7e+64:
		tmp = y * (z / a)
	elif y <= 6.8e-25:
		tmp = x
	else:
		tmp = (y / a) * z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.7e+64)
		tmp = Float64(y * Float64(z / a));
	elseif (y <= 6.8e-25)
		tmp = x;
	else
		tmp = Float64(Float64(y / a) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.7e+64)
		tmp = y * (z / a);
	elseif (y <= 6.8e-25)
		tmp = x;
	else
		tmp = (y / a) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.7e+64], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-25], x, N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.69999999999999983e64

   1. Initial program 87.2%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in y around inf 84.9%

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

   5. Taylor expanded in z around inf 42.2%

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

   if -3.69999999999999983e64 < y < 6.80000000000000003e-25

   1. Initial program 99.8%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 60.5%

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

   if 6.80000000000000003e-25 < y

   1. Initial program 81.6%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 81.4%

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

   5. Taylor expanded in z around inf 53.2%

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

   6. Taylor expanded in z around 0 47.9%

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

      1. associate-*l/ 58.7%

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

   8. Simplified 58.7%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \]

Alternative 9: 49.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+64}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.9e+64) (/ (* y z) a) (if (<= y 7.8e-25) x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e+64) {
		tmp = (y * z) / a;
	} else if (y <= 7.8e-25) {
		tmp = x;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.9d+64)) then
        tmp = (y * z) / a
    else if (y <= 7.8d-25) then
        tmp = x
    else
        tmp = (y / a) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.9e+64) {
		tmp = (y * z) / a;
	} else if (y <= 7.8e-25) {
		tmp = x;
	} else {
		tmp = (y / a) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.9e+64:
		tmp = (y * z) / a
	elif y <= 7.8e-25:
		tmp = x
	else:
		tmp = (y / a) * z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.9e+64)
		tmp = Float64(Float64(y * z) / a);
	elseif (y <= 7.8e-25)
		tmp = x;
	else
		tmp = Float64(Float64(y / a) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.9e+64)
		tmp = (y * z) / a;
	elseif (y <= 7.8e-25)
		tmp = x;
	else
		tmp = (y / a) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.9e+64], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 7.8e-25], x, N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.89999999999999993e64

   1. Initial program 87.2%

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

      1. associate-*l/ 98.1%

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

   3. Simplified 98.1%

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

   4. Taylor expanded in y around inf 84.9%

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

   5. Taylor expanded in z around inf 42.2%

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

   6. Taylor expanded in z around 0 42.3%

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

   if -2.89999999999999993e64 < y < 7.8e-25

   1. Initial program 99.8%

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

      1. associate-*l/ 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in x around inf 60.5%

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

   if 7.8e-25 < y

   1. Initial program 81.6%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 81.4%

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

   5. Taylor expanded in z around inf 53.2%

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

   6. Taylor expanded in z around 0 47.9%

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

      1. associate-*l/ 58.7%

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

   8. Simplified 58.7%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+64}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \]

Alternative 10: 39.5% 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 92.4%

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

   1. associate-*l/ 97.3%

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

3. Simplified 97.3%

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

4. Taylor expanded in x around inf 40.1%

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

5. Final simplification 40.1%

   \[\leadsto x \]

Developer target: 99.2% accurate, 0.7× 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 2023238 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (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)))