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

Percentage Accurate: 93.1% → 97.3%

Time: 8.5s

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, 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 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%

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

Alternative 2: 79.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+45} \lor \neg \left(t \leq 8.4 \cdot 10^{+24} \lor \neg \left(t \leq 1.4 \cdot 10^{+95}\right) \land t \leq 9.2 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -4.4e+45)
         (not (or (<= t 8.4e+24) (and (not (<= t 1.4e+95)) (<= t 9.2e+174)))))
   (* (/ y a) (- z t))
   (+ x (* (/ y a) z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -4.4e+45) || !((t <= 8.4e+24) || (!(t <= 1.4e+95) && (t <= 9.2e+174)))) {
		tmp = (y / a) * (z - 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 <= (-4.4d+45)) .or. (.not. (t <= 8.4d+24) .or. (.not. (t <= 1.4d+95)) .and. (t <= 9.2d+174))) then
        tmp = (y / a) * (z - 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 <= -4.4e+45) || !((t <= 8.4e+24) || (!(t <= 1.4e+95) && (t <= 9.2e+174)))) {
		tmp = (y / a) * (z - t);
	} else {
		tmp = x + ((y / a) * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -4.4e+45) or not ((t <= 8.4e+24) or (not (t <= 1.4e+95) and (t <= 9.2e+174))):
		tmp = (y / a) * (z - t)
	else:
		tmp = x + ((y / a) * z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -4.4e+45) || !((t <= 8.4e+24) || (!(t <= 1.4e+95) && (t <= 9.2e+174))))
		tmp = Float64(Float64(y / a) * Float64(z - 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 <= -4.4e+45) || ~(((t <= 8.4e+24) || (~((t <= 1.4e+95)) && (t <= 9.2e+174)))))
		tmp = (y / a) * (z - t);
	else
		tmp = x + ((y / a) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -4.4e+45], N[Not[Or[LessEqual[t, 8.4e+24], And[N[Not[LessEqual[t, 1.4e+95]], $MachinePrecision], LessEqual[t, 9.2e+174]]]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.4000000000000001e45 or 8.4000000000000005e24 < t < 1.3999999999999999e95 or 9.1999999999999991e174 < t

   1. Initial program 90.8%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

      1. associate-/r/ 89.9%

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

      2. div-inv 89.9%

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

      3. associate-/r* 98.8%

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

   5. Applied egg-rr 98.8%

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

      1. flip-+ 29.2%

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

      2. pow2 29.2%

         \[\leadsto \frac{x \cdot x - \color{blue}{{\left(\frac{\frac{y}{a}}{\frac{1}{z - t}}\right)}^{2}}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      3. div-inv 29.2%

         \[\leadsto \frac{x \cdot x - {\color{blue}{\left(\frac{y}{a} \cdot \frac{1}{\frac{1}{z - t}}\right)}}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      4. inv-pow 29.2%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \frac{1}{\color{blue}{{\left(z - t\right)}^{-1}}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      5. pow-flip 29.2%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \color{blue}{{\left(z - t\right)}^{\left(--1\right)}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      6. metadata-eval 29.2%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot {\left(z - t\right)}^{\color{blue}{1}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      7. pow1 29.2%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \color{blue}{\left(z - t\right)}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      8. div-inv 29.3%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \color{blue}{\frac{y}{a} \cdot \frac{1}{\frac{1}{z - t}}}} \]

      9. inv-pow 29.3%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \frac{1}{\color{blue}{{\left(z - t\right)}^{-1}}}} \]

      10. pow-flip 29.2%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \color{blue}{{\left(z - t\right)}^{\left(--1\right)}}} \]

      11. metadata-eval 29.2%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot {\left(z - t\right)}^{\color{blue}{1}}} \]

      12. pow1 29.2%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \color{blue}{\left(z - t\right)}} \]

   7. Applied egg-rr 29.2%

      \[\leadsto \color{blue}{\frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \left(z - t\right)}} \]

   8. Taylor expanded in x around 0 70.3%

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

      1. *-commutative 70.3%

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

      2. associate-*l/ 77.6%

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

      3. *-commutative 77.6%

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

   10. Simplified 77.6%

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

   if -4.4000000000000001e45 < t < 8.4000000000000005e24 or 1.3999999999999999e95 < t < 9.1999999999999991e174

   1. Initial program 95.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around 0 86.4%

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

      1. associate-/l* 85.8%

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

   6. Simplified 85.8%

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

      1. associate-/r/ 87.0%

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

   8. Applied egg-rr 87.0%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+45} \lor \neg \left(t \leq 8.4 \cdot 10^{+24} \lor \neg \left(t \leq 1.4 \cdot 10^{+95}\right) \land t \leq 9.2 \cdot 10^{+174}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \end{array} \]

Alternative 3: 79.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+95} \lor \neg \left(t \leq 1.02 \cdot 10^{+175}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) (- z t))))
   (if (<= t -2.4e+48)
     t_1
     (if (<= t 8.4e+24)
       (+ x (* (/ y a) z))
       (if (or (<= t 1.95e+95) (not (<= t 1.02e+175)))
         t_1
         (+ x (/ y (/ a z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * (z - t);
	double tmp;
	if (t <= -2.4e+48) {
		tmp = t_1;
	} else if (t <= 8.4e+24) {
		tmp = x + ((y / a) * z);
	} else if ((t <= 1.95e+95) || !(t <= 1.02e+175)) {
		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 = (y / a) * (z - t)
    if (t <= (-2.4d+48)) then
        tmp = t_1
    else if (t <= 8.4d+24) then
        tmp = x + ((y / a) * z)
    else if ((t <= 1.95d+95) .or. (.not. (t <= 1.02d+175))) 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 = (y / a) * (z - t);
	double tmp;
	if (t <= -2.4e+48) {
		tmp = t_1;
	} else if (t <= 8.4e+24) {
		tmp = x + ((y / a) * z);
	} else if ((t <= 1.95e+95) || !(t <= 1.02e+175)) {
		tmp = t_1;
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * (z - t)
	tmp = 0
	if t <= -2.4e+48:
		tmp = t_1
	elif t <= 8.4e+24:
		tmp = x + ((y / a) * z)
	elif (t <= 1.95e+95) or not (t <= 1.02e+175):
		tmp = t_1
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * Float64(z - t))
	tmp = 0.0
	if (t <= -2.4e+48)
		tmp = t_1;
	elseif (t <= 8.4e+24)
		tmp = Float64(x + Float64(Float64(y / a) * z));
	elseif ((t <= 1.95e+95) || !(t <= 1.02e+175))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * (z - t);
	tmp = 0.0;
	if (t <= -2.4e+48)
		tmp = t_1;
	elseif (t <= 8.4e+24)
		tmp = x + ((y / a) * z);
	elseif ((t <= 1.95e+95) || ~((t <= 1.02e+175)))
		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[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.4e+48], t$95$1, If[LessEqual[t, 8.4e+24], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 1.95e+95], N[Not[LessEqual[t, 1.02e+175]], $MachinePrecision]], t$95$1, N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4000000000000001e48 or 8.4000000000000005e24 < t < 1.9499999999999999e95 or 1.0199999999999999e175 < t

   1. Initial program 90.8%

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

      1. associate-*l/ 99.0%

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

   3. Simplified 99.0%

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

      1. associate-/r/ 89.9%

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

      2. div-inv 89.9%

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

      3. associate-/r* 98.8%

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

   5. Applied egg-rr 98.8%

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

      1. flip-+ 29.2%

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

      2. pow2 29.2%

         \[\leadsto \frac{x \cdot x - \color{blue}{{\left(\frac{\frac{y}{a}}{\frac{1}{z - t}}\right)}^{2}}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      3. div-inv 29.2%

         \[\leadsto \frac{x \cdot x - {\color{blue}{\left(\frac{y}{a} \cdot \frac{1}{\frac{1}{z - t}}\right)}}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      4. inv-pow 29.2%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \frac{1}{\color{blue}{{\left(z - t\right)}^{-1}}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      5. pow-flip 29.2%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \color{blue}{{\left(z - t\right)}^{\left(--1\right)}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      6. metadata-eval 29.2%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot {\left(z - t\right)}^{\color{blue}{1}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      7. pow1 29.2%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \color{blue}{\left(z - t\right)}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      8. div-inv 29.3%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \color{blue}{\frac{y}{a} \cdot \frac{1}{\frac{1}{z - t}}}} \]

      9. inv-pow 29.3%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \frac{1}{\color{blue}{{\left(z - t\right)}^{-1}}}} \]

      10. pow-flip 29.2%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \color{blue}{{\left(z - t\right)}^{\left(--1\right)}}} \]

      11. metadata-eval 29.2%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot {\left(z - t\right)}^{\color{blue}{1}}} \]

      12. pow1 29.2%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \color{blue}{\left(z - t\right)}} \]

   7. Applied egg-rr 29.2%

      \[\leadsto \color{blue}{\frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \left(z - t\right)}} \]

   8. Taylor expanded in x around 0 70.3%

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

      1. *-commutative 70.3%

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

      2. associate-*l/ 77.6%

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

      3. *-commutative 77.6%

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

   10. Simplified 77.6%

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

   if -2.4000000000000001e48 < t < 8.4000000000000005e24

   1. Initial program 96.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around 0 87.4%

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

      1. associate-/l* 85.4%

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

   6. Simplified 85.4%

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

      1. associate-/r/ 87.4%

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

   8. Applied egg-rr 87.4%

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

   if 1.9499999999999999e95 < t < 1.0199999999999999e175

   1. Initial program 89.8%

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

      1. associate-*l/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in t around 0 79.0%

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

      1. associate-/l* 89.2%

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

   6. Simplified 89.2%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+48}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{elif}\;t \leq 8.4 \cdot 10^{+24}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+95} \lor \neg \left(t \leq 1.02 \cdot 10^{+175}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 4: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot z\\ \mathbf{if}\;z \leq -3.5 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y a) z)))
   (if (<= z -3.5e+83)
     t_1
     (if (<= z 4.5e-278) x (if (<= z 1.7e+68) (* t (/ (- y) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * z;
	double tmp;
	if (z <= -3.5e+83) {
		tmp = t_1;
	} else if (z <= 4.5e-278) {
		tmp = x;
	} else if (z <= 1.7e+68) {
		tmp = t * (-y / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / a) * z
    if (z <= (-3.5d+83)) then
        tmp = t_1
    else if (z <= 4.5d-278) then
        tmp = x
    else if (z <= 1.7d+68) then
        tmp = t * (-y / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / a) * z;
	double tmp;
	if (z <= -3.5e+83) {
		tmp = t_1;
	} else if (z <= 4.5e-278) {
		tmp = x;
	} else if (z <= 1.7e+68) {
		tmp = t * (-y / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / a) * z
	tmp = 0
	if z <= -3.5e+83:
		tmp = t_1
	elif z <= 4.5e-278:
		tmp = x
	elif z <= 1.7e+68:
		tmp = t * (-y / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / a) * z)
	tmp = 0.0
	if (z <= -3.5e+83)
		tmp = t_1;
	elseif (z <= 4.5e-278)
		tmp = x;
	elseif (z <= 1.7e+68)
		tmp = Float64(t * Float64(Float64(-y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / a) * z;
	tmp = 0.0;
	if (z <= -3.5e+83)
		tmp = t_1;
	elseif (z <= 4.5e-278)
		tmp = x;
	elseif (z <= 1.7e+68)
		tmp = t * (-y / a);
	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] * z), $MachinePrecision]}, If[LessEqual[z, -3.5e+83], t$95$1, If[LessEqual[z, 4.5e-278], x, If[LessEqual[z, 1.7e+68], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.49999999999999977e83 or 1.70000000000000008e68 < z

   1. Initial program 89.7%

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

      1. associate-/r/ 90.7%

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

      2. div-inv 90.7%

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

      3. associate-/r* 96.8%

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

   5. Applied egg-rr 96.8%

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

      1. flip-+ 28.6%

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

      2. pow2 28.6%

         \[\leadsto \frac{x \cdot x - \color{blue}{{\left(\frac{\frac{y}{a}}{\frac{1}{z - t}}\right)}^{2}}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      3. div-inv 28.5%

         \[\leadsto \frac{x \cdot x - {\color{blue}{\left(\frac{y}{a} \cdot \frac{1}{\frac{1}{z - t}}\right)}}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      4. inv-pow 28.5%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \frac{1}{\color{blue}{{\left(z - t\right)}^{-1}}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      5. pow-flip 28.5%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \color{blue}{{\left(z - t\right)}^{\left(--1\right)}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      6. metadata-eval 28.5%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot {\left(z - t\right)}^{\color{blue}{1}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      7. pow1 28.5%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \color{blue}{\left(z - t\right)}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      8. div-inv 28.5%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \color{blue}{\frac{y}{a} \cdot \frac{1}{\frac{1}{z - t}}}} \]

      9. inv-pow 28.5%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \frac{1}{\color{blue}{{\left(z - t\right)}^{-1}}}} \]

      10. pow-flip 28.5%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \color{blue}{{\left(z - t\right)}^{\left(--1\right)}}} \]

      11. metadata-eval 28.5%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot {\left(z - t\right)}^{\color{blue}{1}}} \]

      12. pow1 28.5%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \color{blue}{\left(z - t\right)}} \]

   7. Applied egg-rr 28.5%

      \[\leadsto \color{blue}{\frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \left(z - t\right)}} \]

   8. Taylor expanded in x around 0 67.5%

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

      1. *-commutative 67.5%

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

      2. associate-*l/ 71.5%

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

      3. *-commutative 71.5%

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

   10. Simplified 71.5%

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

   11. Taylor expanded in z around inf 61.1%

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

       1. associate-*l/ 63.5%

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

       2. *-commutative 63.5%

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

   13. Simplified 63.5%

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

   if -3.49999999999999977e83 < z < 4.4999999999999998e-278

   1. Initial program 96.6%

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

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

   if 4.4999999999999998e-278 < z < 1.70000000000000008e68

   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. Step-by-step derivation

      1. associate-/r/ 92.6%

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

      2. div-inv 92.5%

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

      3. associate-/r* 98.6%

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

   5. Applied egg-rr 98.6%

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

   6. Taylor expanded in z around 0 90.0%

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

      1. fma-def 90.0%

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

      2. associate-*r/ 87.5%

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

      3. fma-def 87.5%

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

      4. neg-mul-1 87.5%

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

      5. +-commutative 87.5%

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

      6. sub-neg 87.5%

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

      7. *-commutative 87.5%

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

      8. associate-*l/ 90.0%

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

      9. associate-*r/ 96.1%

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

   8. Simplified 96.1%

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

   9. Taylor expanded in x around 0 57.2%

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

       1. mul-1-neg 57.2%

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

       2. associate-*l/ 63.3%

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

       3. *-commutative 63.3%

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

       4. distribute-rgt-neg-in 63.3%

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

       5. distribute-neg-frac 63.3%

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

   11. Simplified 63.3%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5 \cdot 10^{+83}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-278}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \]

Alternative 5: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-19} \lor \neg \left(z \leq 1.25 \cdot 10^{+68}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.65e-19) (not (<= z 1.25e+68)))
   (+ x (* (/ y a) z))
   (- x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.65e-19) || !(z <= 1.25e+68)) {
		tmp = x + ((y / a) * z);
	} else {
		tmp = x - ((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) :: tmp
    if ((z <= (-1.65d-19)) .or. (.not. (z <= 1.25d+68))) then
        tmp = x + ((y / a) * z)
    else
        tmp = x - ((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 tmp;
	if ((z <= -1.65e-19) || !(z <= 1.25e+68)) {
		tmp = x + ((y / a) * z);
	} else {
		tmp = x - ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.65e-19) or not (z <= 1.25e+68):
		tmp = x + ((y / a) * z)
	else:
		tmp = x - ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.65e-19) || !(z <= 1.25e+68))
		tmp = Float64(x + Float64(Float64(y / a) * z));
	else
		tmp = Float64(x - Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.65e-19) || ~((z <= 1.25e+68)))
		tmp = x + ((y / a) * z);
	else
		tmp = x - ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.65e-19], N[Not[LessEqual[z, 1.25e+68]], $MachinePrecision]], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6499999999999999e-19 or 1.2500000000000001e68 < z

   1. Initial program 91.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 t around 0 82.4%

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

      1. associate-/l* 82.6%

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

   6. Simplified 82.6%

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

      1. associate-/r/ 86.7%

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

   8. Applied egg-rr 86.7%

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

   if -1.6499999999999999e-19 < z < 1.2500000000000001e68

   1. Initial program 95.4%

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

      1. associate-*l/ 98.0%

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

   3. Simplified 98.0%

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

      1. associate-/r/ 94.2%

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

      2. div-inv 94.1%

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

      3. associate-/r* 97.9%

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

   5. Applied egg-rr 97.9%

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

   6. Taylor expanded in z around 0 90.8%

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

      1. fma-def 90.8%

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

      2. associate-*r/ 89.5%

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

      3. fma-def 89.5%

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

      4. neg-mul-1 89.5%

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

      5. +-commutative 89.5%

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

      6. sub-neg 89.5%

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

      7. *-commutative 89.5%

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

      8. associate-*l/ 90.8%

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

      9. associate-*r/ 95.3%

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

   8. Simplified 95.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-19} \lor \neg \left(z \leq 1.25 \cdot 10^{+68}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 6: 68.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.8e+25) x (if (<= a 2.9e+100) (* (/ y a) (- z t)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.8e+25) {
		tmp = x;
	} else if (a <= 2.9e+100) {
		tmp = (y / a) * (z - 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 <= (-4.8d+25)) then
        tmp = x
    else if (a <= 2.9d+100) then
        tmp = (y / a) * (z - 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 <= -4.8e+25) {
		tmp = x;
	} else if (a <= 2.9e+100) {
		tmp = (y / a) * (z - t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.8e+25:
		tmp = x
	elif a <= 2.9e+100:
		tmp = (y / a) * (z - t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.8e+25)
		tmp = x;
	elseif (a <= 2.9e+100)
		tmp = Float64(Float64(y / a) * Float64(z - t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.8e+25)
		tmp = x;
	elseif (a <= 2.9e+100)
		tmp = (y / a) * (z - t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.8e+25], x, If[LessEqual[a, 2.9e+100], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -4.79999999999999992e25 or 2.9e100 < a

   1. Initial program 88.4%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in x around inf 65.4%

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

   if -4.79999999999999992e25 < a < 2.9e100

   1. Initial program 96.9%

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

      1. associate-/r/ 89.4%

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

      2. div-inv 89.3%

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

      3. associate-/r* 98.6%

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

   5. Applied egg-rr 98.6%

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

      1. flip-+ 27.1%

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

      2. pow2 27.1%

         \[\leadsto \frac{x \cdot x - \color{blue}{{\left(\frac{\frac{y}{a}}{\frac{1}{z - t}}\right)}^{2}}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      3. div-inv 27.1%

         \[\leadsto \frac{x \cdot x - {\color{blue}{\left(\frac{y}{a} \cdot \frac{1}{\frac{1}{z - t}}\right)}}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      4. inv-pow 27.1%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \frac{1}{\color{blue}{{\left(z - t\right)}^{-1}}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      5. pow-flip 27.1%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \color{blue}{{\left(z - t\right)}^{\left(--1\right)}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      6. metadata-eval 27.1%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot {\left(z - t\right)}^{\color{blue}{1}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      7. pow1 27.1%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \color{blue}{\left(z - t\right)}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      8. div-inv 27.1%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \color{blue}{\frac{y}{a} \cdot \frac{1}{\frac{1}{z - t}}}} \]

      9. inv-pow 27.1%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \frac{1}{\color{blue}{{\left(z - t\right)}^{-1}}}} \]

      10. pow-flip 27.2%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \color{blue}{{\left(z - t\right)}^{\left(--1\right)}}} \]

      11. metadata-eval 27.2%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot {\left(z - t\right)}^{\color{blue}{1}}} \]

      12. pow1 27.2%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \color{blue}{\left(z - t\right)}} \]

   7. Applied egg-rr 27.2%

      \[\leadsto \color{blue}{\frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \left(z - t\right)}} \]

   8. Taylor expanded in x around 0 72.8%

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

      1. *-commutative 72.8%

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

      2. associate-*l/ 74.5%

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

      3. *-commutative 74.5%

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

   10. Simplified 74.5%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{+100}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+83} \lor \neg \left(z \leq 2.9 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.1e+83) (not (<= z 2.9e+98))) (* (/ y a) z) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.1e+83) || !(z <= 2.9e+98)) {
		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 ((z <= (-1.1d+83)) .or. (.not. (z <= 2.9d+98))) 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 ((z <= -1.1e+83) || !(z <= 2.9e+98)) {
		tmp = (y / a) * z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.1e+83) or not (z <= 2.9e+98):
		tmp = (y / a) * z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.1e+83) || !(z <= 2.9e+98))
		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 ((z <= -1.1e+83) || ~((z <= 2.9e+98)))
		tmp = (y / a) * z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.1e+83], N[Not[LessEqual[z, 2.9e+98]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.09999999999999999e83 or 2.9000000000000001e98 < z

   1. Initial program 88.9%

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

      1. associate-/r/ 89.9%

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

      2. div-inv 90.0%

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

      3. associate-/r* 96.5%

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

   5. Applied egg-rr 96.5%

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

      1. flip-+ 26.1%

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

      2. pow2 26.1%

         \[\leadsto \frac{x \cdot x - \color{blue}{{\left(\frac{\frac{y}{a}}{\frac{1}{z - t}}\right)}^{2}}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      3. div-inv 26.0%

         \[\leadsto \frac{x \cdot x - {\color{blue}{\left(\frac{y}{a} \cdot \frac{1}{\frac{1}{z - t}}\right)}}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      4. inv-pow 26.0%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \frac{1}{\color{blue}{{\left(z - t\right)}^{-1}}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      5. pow-flip 26.0%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \color{blue}{{\left(z - t\right)}^{\left(--1\right)}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      6. metadata-eval 26.0%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot {\left(z - t\right)}^{\color{blue}{1}}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      7. pow1 26.0%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \color{blue}{\left(z - t\right)}\right)}^{2}}{x - \frac{\frac{y}{a}}{\frac{1}{z - t}}} \]

      8. div-inv 26.0%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \color{blue}{\frac{y}{a} \cdot \frac{1}{\frac{1}{z - t}}}} \]

      9. inv-pow 26.0%

         \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \frac{1}{\color{blue}{{\left(z - t\right)}^{-1}}}} \]

      10. pow-flip 26.0%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \color{blue}{{\left(z - t\right)}^{\left(--1\right)}}} \]

      11. metadata-eval 26.0%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot {\left(z - t\right)}^{\color{blue}{1}}} \]

      12. pow1 26.0%

          \[\leadsto \frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \color{blue}{\left(z - t\right)}} \]

   7. Applied egg-rr 26.0%

      \[\leadsto \color{blue}{\frac{x \cdot x - {\left(\frac{y}{a} \cdot \left(z - t\right)\right)}^{2}}{x - \frac{y}{a} \cdot \left(z - t\right)}} \]

   8. Taylor expanded in x around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*l/ 73.8%

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

      3. *-commutative 73.8%

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

   10. Simplified 73.8%

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

   11. Taylor expanded in z around inf 63.6%

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

       1. associate-*l/ 66.3%

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

       2. *-commutative 66.3%

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

   13. Simplified 66.3%

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

   if -1.09999999999999999e83 < z < 2.9000000000000001e98

   1. Initial program 96.1%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 48.9%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+83} \lor \neg \left(z \leq 2.9 \cdot 10^{+98}\right):\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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 40.4%

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

5. Final simplification 40.4%

   \[\leadsto x \]

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, 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)))