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

Percentage Accurate: 93.1% → 97.3%

Time: 7.6s

Alternatives: 8

Speedup: 1.0×

• 24.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.1% 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: 97.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.7%

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

   1. sub-neg 93.7%

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

   2. +-commutative 93.7%

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

   3. associate-*l/ 97.7%

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

   4. distribute-rgt-neg-in 97.7%

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

   5. fma-def 97.7%

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

   6. sub-neg 97.7%

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

   7. +-commutative 97.7%

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

   8. distribute-neg-in 97.7%

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

   9. unsub-neg 97.7%

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

   10. remove-double-neg 97.7%

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

3. Simplified 97.7%

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

4. Final simplification 97.7%

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

Alternative 2: 68.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -100000000 \lor \neg \left(y \leq -7 \cdot 10^{-33}\right) \land \left(y \leq -3.15 \cdot 10^{-58} \lor \neg \left(y \leq -1.6 \cdot 10^{-108}\right) \land \left(y \leq -9.3 \cdot 10^{-181} \lor \neg \left(y \leq 2.4 \cdot 10^{-60}\right)\right)\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -100000000.0)
         (and (not (<= y -7e-33))
              (or (<= y -3.15e-58)
                  (and (not (<= y -1.6e-108))
                       (or (<= y -9.3e-181) (not (<= y 2.4e-60)))))))
   (* y (/ (- t z) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -100000000.0) || (!(y <= -7e-33) && ((y <= -3.15e-58) || (!(y <= -1.6e-108) && ((y <= -9.3e-181) || !(y <= 2.4e-60)))))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-100000000.0d0)) .or. (.not. (y <= (-7d-33))) .and. (y <= (-3.15d-58)) .or. (.not. (y <= (-1.6d-108))) .and. (y <= (-9.3d-181)) .or. (.not. (y <= 2.4d-60))) then
        tmp = y * ((t - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -100000000.0) || (!(y <= -7e-33) && ((y <= -3.15e-58) || (!(y <= -1.6e-108) && ((y <= -9.3e-181) || !(y <= 2.4e-60)))))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -100000000.0) or (not (y <= -7e-33) and ((y <= -3.15e-58) or (not (y <= -1.6e-108) and ((y <= -9.3e-181) or not (y <= 2.4e-60))))):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -100000000.0) || (!(y <= -7e-33) && ((y <= -3.15e-58) || (!(y <= -1.6e-108) && ((y <= -9.3e-181) || !(y <= 2.4e-60))))))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -100000000.0) || (~((y <= -7e-33)) && ((y <= -3.15e-58) || (~((y <= -1.6e-108)) && ((y <= -9.3e-181) || ~((y <= 2.4e-60)))))))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -100000000.0], And[N[Not[LessEqual[y, -7e-33]], $MachinePrecision], Or[LessEqual[y, -3.15e-58], And[N[Not[LessEqual[y, -1.6e-108]], $MachinePrecision], Or[LessEqual[y, -9.3e-181], N[Not[LessEqual[y, 2.4e-60]], $MachinePrecision]]]]]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1e8 or -6.9999999999999997e-33 < y < -3.14999999999999999e-58 or -1.6e-108 < y < -9.3000000000000001e-181 or 2.40000000000000009e-60 < y

   1. Initial program 90.0%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around 0 71.6%

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

      1. mul-1-neg 71.6%

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

      2. associate-*r/ 77.7%

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

      3. distribute-rgt-neg-in 77.7%

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

      4. distribute-neg-frac 77.7%

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

      5. neg-sub0 77.7%

         \[\leadsto y \cdot \frac{\color{blue}{0 - \left(z - t\right)}}{a} \]

      6. associate--r- 77.7%

         \[\leadsto y \cdot \frac{\color{blue}{\left(0 - z\right) + t}}{a} \]

      7. neg-sub0 77.7%

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

      8. +-commutative 77.7%

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

      9. sub-neg 77.7%

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

   6. Simplified 77.7%

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

   if -1e8 < y < -6.9999999999999997e-33 or -3.14999999999999999e-58 < y < -1.6e-108 or -9.3000000000000001e-181 < y < 2.40000000000000009e-60

   1. Initial program 99.0%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around inf 66.2%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -100000000 \lor \neg \left(y \leq -7 \cdot 10^{-33}\right) \land \left(y \leq -3.15 \cdot 10^{-58} \lor \neg \left(y \leq -1.6 \cdot 10^{-108}\right) \land \left(y \leq -9.3 \cdot 10^{-181} \lor \neg \left(y \leq 2.4 \cdot 10^{-60}\right)\right)\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 50.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))))
   (if (<= z -9.6e+87)
     t_1
     (if (<= z 4.4e-274) x (if (<= z 1.45e+68) (* (/ y a) t) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (z <= -9.6e+87) {
		tmp = t_1;
	} else if (z <= 4.4e-274) {
		tmp = x;
	} else if (z <= 1.45e+68) {
		tmp = (y / a) * t;
	} 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 = z * (y / -a)
    if (z <= (-9.6d+87)) then
        tmp = t_1
    else if (z <= 4.4d-274) then
        tmp = x
    else if (z <= 1.45d+68) then
        tmp = (y / a) * t
    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 = z * (y / -a);
	double tmp;
	if (z <= -9.6e+87) {
		tmp = t_1;
	} else if (z <= 4.4e-274) {
		tmp = x;
	} else if (z <= 1.45e+68) {
		tmp = (y / a) * t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	tmp = 0
	if z <= -9.6e+87:
		tmp = t_1
	elif z <= 4.4e-274:
		tmp = x
	elif z <= 1.45e+68:
		tmp = (y / a) * t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	tmp = 0.0
	if (z <= -9.6e+87)
		tmp = t_1;
	elseif (z <= 4.4e-274)
		tmp = x;
	elseif (z <= 1.45e+68)
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	tmp = 0.0;
	if (z <= -9.6e+87)
		tmp = t_1;
	elseif (z <= 4.4e-274)
		tmp = x;
	elseif (z <= 1.45e+68)
		tmp = (y / a) * t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e+87], t$95$1, If[LessEqual[z, 4.4e-274], x, If[LessEqual[z, 1.45e+68], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.59999999999999926e87 or 1.45000000000000006e68 < z

   1. Initial program 89.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. associate-*l/ 64.2%

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

      3. *-commutative 64.2%

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

      4. distribute-rgt-neg-in 64.2%

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

      5. distribute-frac-neg 64.2%

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

      6. *-lft-identity 64.2%

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

      7. metadata-eval 64.2%

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

      8. times-frac 64.2%

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

      9. neg-mul-1 64.2%

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

      10. remove-double-neg 64.2%

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

      11. neg-mul-1 64.2%

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

   6. Simplified 64.2%

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

   if -9.59999999999999926e87 < z < 4.3999999999999999e-274

   1. Initial program 96.9%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 60.3%

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

   if 4.3999999999999999e-274 < z < 1.45000000000000006e68

   1. Initial program 95.0%

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

      1. associate-*l/ 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around inf 57.0%

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

      1. *-commutative 57.0%

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

      2. associate-*r/ 63.1%

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

   6. Simplified 63.1%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{+87}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-274}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]

Alternative 4: 82.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-22} \lor \neg \left(z \leq 7 \cdot 10^{+67}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e-22) (not (<= z 7e+67)))
   (- x (/ y (/ a z)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e-22) || !(z <= 7e+67)) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.65d-22)) .or. (.not. (z <= 7d+67))) then
        tmp = x - (y / (a / z))
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e-22) || !(z <= 7e+67)) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e-22) or not (z <= 7e+67):
		tmp = x - (y / (a / z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e-22) || !(z <= 7e+67))
		tmp = Float64(x - Float64(y / Float64(a / z)));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e-22) || ~((z <= 7e+67)))
		tmp = x - (y / (a / z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e-22], N[Not[LessEqual[z, 7e+67]], $MachinePrecision]], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e-22 or 7e67 < z

   1. Initial program 90.7%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in z around inf 82.8%

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

   if -1.65e-22 < z < 7e67

   1. Initial program 96.0%

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

      1. sub-neg 96.0%

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

      2. +-commutative 96.0%

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

      3. associate-*l/ 97.9%

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

      4. distribute-rgt-neg-in 97.9%

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

      5. fma-def 97.9%

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

      6. sub-neg 97.9%

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

      7. +-commutative 97.9%

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

      8. distribute-neg-in 97.9%

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

      9. unsub-neg 97.9%

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

      10. remove-double-neg 97.9%

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

   3. Simplified 97.9%

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

   4. Taylor expanded in z around 0 91.4%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-22} \lor \neg \left(z \leq 7 \cdot 10^{+67}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 5: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+88}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1e+88)
   (* z (/ y (- a)))
   (if (<= z 3.7e+37) (+ x (/ (* y t) a)) (* y (/ (- t z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+88) {
		tmp = z * (y / -a);
	} else if (z <= 3.7e+37) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1d+88)) then
        tmp = z * (y / -a)
    else if (z <= 3.7d+37) then
        tmp = x + ((y * t) / a)
    else
        tmp = y * ((t - z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1e+88) {
		tmp = z * (y / -a);
	} else if (z <= 3.7e+37) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = y * ((t - z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1e+88:
		tmp = z * (y / -a)
	elif z <= 3.7e+37:
		tmp = x + ((y * t) / a)
	else:
		tmp = y * ((t - z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1e+88)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (z <= 3.7e+37)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = Float64(y * Float64(Float64(t - z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1e+88)
		tmp = z * (y / -a);
	elseif (z <= 3.7e+37)
		tmp = x + ((y * t) / a);
	else
		tmp = y * ((t - z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1e+88], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+37], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.99999999999999959e87

   1. Initial program 87.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around inf 64.7%

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

      1. mul-1-neg 64.7%

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

      2. associate-*l/ 70.4%

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

      3. *-commutative 70.4%

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

      4. distribute-rgt-neg-in 70.4%

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

      5. distribute-frac-neg 70.4%

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

      6. *-lft-identity 70.4%

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

      7. metadata-eval 70.4%

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

      8. times-frac 70.4%

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

      9. neg-mul-1 70.4%

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

      10. remove-double-neg 70.4%

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

      11. neg-mul-1 70.4%

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

   6. Simplified 70.4%

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

   if -9.99999999999999959e87 < z < 3.6999999999999999e37

   1. Initial program 97.0%

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

      1. sub-neg 97.0%

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

      2. +-commutative 97.0%

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

      3. associate-*l/ 97.6%

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

      4. distribute-rgt-neg-in 97.6%

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

      5. fma-def 97.6%

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

      6. sub-neg 97.6%

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

      7. +-commutative 97.6%

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

      8. distribute-neg-in 97.6%

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

      9. unsub-neg 97.6%

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

      10. remove-double-neg 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in z around 0 89.9%

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

   if 3.6999999999999999e37 < z

   1. Initial program 88.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 63.3%

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

      1. mul-1-neg 63.3%

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

      2. associate-*r/ 66.9%

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

      3. distribute-rgt-neg-in 66.9%

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

      4. distribute-neg-frac 66.9%

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

      5. neg-sub0 66.9%

         \[\leadsto y \cdot \frac{\color{blue}{0 - \left(z - t\right)}}{a} \]

      6. associate--r- 66.9%

         \[\leadsto y \cdot \frac{\color{blue}{\left(0 - z\right) + t}}{a} \]

      7. neg-sub0 66.9%

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

      8. +-commutative 66.9%

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

      9. sub-neg 66.9%

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

   6. Simplified 66.9%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+88}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+37}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \end{array} \]

Alternative 6: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-129}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.7e+25) x (if (<= a 5e-129) (* (/ y a) t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.7e+25) {
		tmp = x;
	} else if (a <= 5e-129) {
		tmp = (y / a) * t;
	} 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 <= (-1.7d+25)) then
        tmp = x
    else if (a <= 5d-129) then
        tmp = (y / a) * t
    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 <= -1.7e+25) {
		tmp = x;
	} else if (a <= 5e-129) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.7e+25:
		tmp = x
	elif a <= 5e-129:
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.7e+25)
		tmp = x;
	elseif (a <= 5e-129)
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.7e+25)
		tmp = x;
	elseif (a <= 5e-129)
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.7e+25], x, If[LessEqual[a, 5e-129], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.69999999999999992e25 or 5.00000000000000027e-129 < a

   1. Initial program 89.0%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in x around inf 59.0%

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

   if -1.69999999999999992e25 < a < 5.00000000000000027e-129

   1. Initial program 99.1%

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

      1. associate-*l/ 98.3%

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

   3. Simplified 98.3%

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

   4. Taylor expanded in t around inf 52.6%

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

      1. *-commutative 52.6%

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

      2. associate-*r/ 55.8%

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

   6. Simplified 55.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-129}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.7%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. Final simplification 97.7%

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

Alternative 8: 39.3% 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 93.7%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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 40.7%

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

5. Final simplification 40.7%

   \[\leadsto x \]

Developer target: 99.1% 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 2023199 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :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)))