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

Percentage Accurate: 93.3% → 98.9%

Time: 7.0s

Alternatives: 9

Speedup: 0.5×

• 24.5% 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: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+173}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+273}:\\ \;\;\;\;x - \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (<= t_1 -5e+173)
     (- x (/ y (/ a (- z t))))
     (if (<= t_1 4e+273) (- x (/ t_1 a)) (* (- t z) (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if (t_1 <= -5e+173) {
		tmp = x - (y / (a / (z - t)));
	} else if (t_1 <= 4e+273) {
		tmp = x - (t_1 / a);
	} else {
		tmp = (t - 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) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * y
    if (t_1 <= (-5d+173)) then
        tmp = x - (y / (a / (z - t)))
    else if (t_1 <= 4d+273) then
        tmp = x - (t_1 / a)
    else
        tmp = (t - 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 t_1 = (z - t) * y;
	double tmp;
	if (t_1 <= -5e+173) {
		tmp = x - (y / (a / (z - t)));
	} else if (t_1 <= 4e+273) {
		tmp = x - (t_1 / a);
	} else {
		tmp = (t - z) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	tmp = 0
	if t_1 <= -5e+173:
		tmp = x - (y / (a / (z - t)))
	elif t_1 <= 4e+273:
		tmp = x - (t_1 / a)
	else:
		tmp = (t - z) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * y)
	tmp = 0.0
	if (t_1 <= -5e+173)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	elseif (t_1 <= 4e+273)
		tmp = Float64(x - Float64(t_1 / a));
	else
		tmp = Float64(Float64(t - z) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * y;
	tmp = 0.0;
	if (t_1 <= -5e+173)
		tmp = x - (y / (a / (z - t)));
	elseif (t_1 <= 4e+273)
		tmp = x - (t_1 / a);
	else
		tmp = (t - z) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+173], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4e+273], N[(x - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -5.00000000000000034e173

   1. Initial program 74.6%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. clear-num N/A

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

      5. un-div-inv N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 100.0

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

   4. Applied rewrites 100.0%

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

   if -5.00000000000000034e173 < (*.f64 y (-.f64 z t)) < 3.99999999999999978e273

   1. Initial program 99.3%

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

   if 3.99999999999999978e273 < (*.f64 y (-.f64 z t))

   1. Initial program 79.7%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

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

      7. associate-+l- N/A

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

      8. neg-sub0 N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 100.0

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

   5. Applied rewrites 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -5 \cdot 10^{+173}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;\left(z - t\right) \cdot y \leq 4 \cdot 10^{+273}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a}\\ t_2 := \left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) a)) (t_2 (* (- t z) (/ y a))))
   (if (<= t_1 -2e+124) t_2 (if (<= t_1 2e+112) (fma (/ y a) t x) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double t_2 = (t - z) * (y / a);
	double tmp;
	if (t_1 <= -2e+124) {
		tmp = t_2;
	} else if (t_1 <= 2e+112) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / a)
	t_2 = Float64(Float64(t - z) * Float64(y / a))
	tmp = 0.0
	if (t_1 <= -2e+124)
		tmp = t_2;
	elseif (t_1 <= 2e+112)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+124], t$95$2, If[LessEqual[t$95$1, 2e+112], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -1.9999999999999999e124 or 1.9999999999999999e112 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 86.4%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

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

      7. associate-+l- N/A

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

      8. neg-sub0 N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 90.3

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

   5. Applied rewrites 90.3%

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

   if -1.9999999999999999e124 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.9999999999999999e112

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*l/ N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 83.7

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

   5. Applied rewrites 83.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a} \leq -2 \cdot 10^{+124}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a} \leq 2 \cdot 10^{+112}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ t_2 := \left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4 \cdot 10^{+273}:\\ \;\;\;\;x - \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)) (t_2 (* (- t z) (/ y a))))
   (if (<= t_1 (- INFINITY)) t_2 (if (<= t_1 4e+273) (- x (/ t_1 a)) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double t_2 = (t - z) * (y / a);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2;
	} else if (t_1 <= 4e+273) {
		tmp = x - (t_1 / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double t_2 = (t - z) * (y / a);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else if (t_1 <= 4e+273) {
		tmp = x - (t_1 / a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	t_2 = (t - z) * (y / a)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = t_2
	elif t_1 <= 4e+273:
		tmp = x - (t_1 / a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * y)
	t_2 = Float64(Float64(t - z) * Float64(y / a))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = t_2;
	elseif (t_1 <= 4e+273)
		tmp = Float64(x - Float64(t_1 / a));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * y;
	t_2 = (t - z) * (y / a);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = t_2;
	elseif (t_1 <= 4e+273)
		tmp = x - (t_1 / a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], t$95$2, If[LessEqual[t$95$1, 4e+273], N[(x - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -inf.0 or 3.99999999999999978e273 < (*.f64 y (-.f64 z t))

   1. Initial program 69.7%

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

   3. Taylor expanded in a around 0

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

      1. *-commutative N/A

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

      2. associate-/l* N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. neg-sub0 N/A

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

      7. associate-+l- N/A

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

      8. neg-sub0 N/A

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

      9. mul-1-neg N/A

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

      10. +-commutative N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 94.6

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

   5. Applied rewrites 94.6%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 3.99999999999999978e273

   1. Initial program 99.3%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -\infty:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;\left(z - t\right) \cdot y \leq 4 \cdot 10^{+273}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a} \leq 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (/ (* (- z t) y) a) 1e+172) (fma y (/ t a) x) (* (/ y a) t)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((((z - t) * y) / a) <= 1e+172) {
		tmp = fma(y, (t / a), x);
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(Float64(z - t) * y) / a) <= 1e+172)
		tmp = fma(y, Float64(t / a), x);
	else
		tmp = Float64(Float64(y / a) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision], 1e+172], N[(y * N[(t / a), $MachinePrecision] + x), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < 1.0000000000000001e172

   1. Initial program 93.9%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*l/ N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 79.0

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

   5. Applied rewrites 79.0%

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

   7. Applied rewrites 74.8%

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

   if 1.0000000000000001e172 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 90.0%

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

   3. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 53.7

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

   5. Applied rewrites 53.7%

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

   7. Applied rewrites 61.7%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a} \leq 10^{+172}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+25}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) t x)))
   (if (<= t -9e-18) t_1 (if (<= t 3.6e+25) (- x (/ (* z y) a)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), t, x);
	double tmp;
	if (t <= -9e-18) {
		tmp = t_1;
	} else if (t <= 3.6e+25) {
		tmp = x - ((z * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), t, x)
	tmp = 0.0
	if (t <= -9e-18)
		tmp = t_1;
	elseif (t <= 3.6e+25)
		tmp = Float64(x - Float64(Float64(z * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision]}, If[LessEqual[t, -9e-18], t$95$1, If[LessEqual[t, 3.6e+25], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -8.99999999999999987e-18 or 3.60000000000000015e25 < t

   1. Initial program 89.5%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*l/ N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 88.4

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

   5. Applied rewrites 88.4%

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

   if -8.99999999999999987e-18 < t < 3.60000000000000015e25

   1. Initial program 97.3%

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

   3. Taylor expanded in t around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 91.8

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

   5. Applied rewrites 91.8%

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

Alternative 6: 76.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+202}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+225}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z) (/ y a))))
   (if (<= z -1.95e+202) t_1 (if (<= z 3.2e+225) (fma (/ y a) t x) 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 <= -1.95e+202) {
		tmp = t_1;
	} else if (z <= 3.2e+225) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-z) * Float64(y / a))
	tmp = 0.0
	if (z <= -1.95e+202)
		tmp = t_1;
	elseif (z <= 3.2e+225)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-z) * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+202], t$95$1, If[LessEqual[z, 3.2e+225], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.94999999999999992e202 or 3.1999999999999999e225 < z

   1. Initial program 86.7%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. associate-*r/ N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lower-/.f64 78.8

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

   5. Applied rewrites 78.8%

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

   if -1.94999999999999992e202 < z < 3.1999999999999999e225

   1. Initial program 94.2%

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

   3. Taylor expanded in z around 0

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

      1. sub-neg N/A

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

      2. mul-1-neg N/A

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

      3. remove-double-neg N/A

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

      4. +-commutative N/A

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

      5. *-commutative N/A

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

      6. associate-*l/ N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 82.8

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

   5. Applied rewrites 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t, x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 7: 71.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.2%

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

3. Taylor expanded in z around 0

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

   1. sub-neg N/A

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

   2. mul-1-neg N/A

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

   3. remove-double-neg N/A

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

   4. +-commutative N/A

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

   5. *-commutative N/A

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

   6. associate-*l/ N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 75.9

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

5. Applied rewrites 75.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, t, x\right)} \]
6. Add Preprocessing

Alternative 8: 34.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{y}{a} \cdot t \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.2%

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

3. Taylor expanded in t around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 31.0

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

5. Applied rewrites 31.0%

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

7. Applied rewrites 35.5%

   \[\leadsto \color{blue}{\frac{y}{a} \cdot t} \]
8. Add Preprocessing

Alternative 9: 31.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{t}{a} \cdot y \end{array} \]

FPCore

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

C

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

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 = (t / a) * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.2%

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

3. Taylor expanded in t around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 31.0

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

5. Applied rewrites 31.0%

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

7. Applied rewrites 30.7%

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

8. Final simplification 30.7%

   \[\leadsto \frac{t}{a} \cdot y \]
9. Add Preprocessing

Developer Target 1: 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 2024276 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t)))))))

  (- x (/ (* y (- z t)) a)))