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

Percentage Accurate: 93.0% → 97.2%

Time: 9.9s

Alternatives: 12

Speedup: 1.0×

• 25.1% 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: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.4%

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

   1. associate-*l/ 97.9%

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

3. Simplified 97.9%

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

4. Final simplification 97.9%

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

Alternative 2: 46.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-308}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-39}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.04e+123)
   x
   (if (<= x -8.5e-308)
     (* z (/ y (- a)))
     (if (<= x 1.25e-39)
       (/ y (/ a t))
       (if (<= x 8e+32) x (if (<= x 1.15e+109) (* (/ y a) t) x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.04e+123) {
		tmp = x;
	} else if (x <= -8.5e-308) {
		tmp = z * (y / -a);
	} else if (x <= 1.25e-39) {
		tmp = y / (a / t);
	} else if (x <= 8e+32) {
		tmp = x;
	} else if (x <= 1.15e+109) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.04d+123)) then
        tmp = x
    else if (x <= (-8.5d-308)) then
        tmp = z * (y / -a)
    else if (x <= 1.25d-39) then
        tmp = y / (a / t)
    else if (x <= 8d+32) then
        tmp = x
    else if (x <= 1.15d+109) then
        tmp = (y / a) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.04e+123) {
		tmp = x;
	} else if (x <= -8.5e-308) {
		tmp = z * (y / -a);
	} else if (x <= 1.25e-39) {
		tmp = y / (a / t);
	} else if (x <= 8e+32) {
		tmp = x;
	} else if (x <= 1.15e+109) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.04e+123:
		tmp = x
	elif x <= -8.5e-308:
		tmp = z * (y / -a)
	elif x <= 1.25e-39:
		tmp = y / (a / t)
	elif x <= 8e+32:
		tmp = x
	elif x <= 1.15e+109:
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.04e+123)
		tmp = x;
	elseif (x <= -8.5e-308)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (x <= 1.25e-39)
		tmp = Float64(y / Float64(a / t));
	elseif (x <= 8e+32)
		tmp = x;
	elseif (x <= 1.15e+109)
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.04e+123)
		tmp = x;
	elseif (x <= -8.5e-308)
		tmp = z * (y / -a);
	elseif (x <= 1.25e-39)
		tmp = y / (a / t);
	elseif (x <= 8e+32)
		tmp = x;
	elseif (x <= 1.15e+109)
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.04e+123], x, If[LessEqual[x, -8.5e-308], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-39], N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8e+32], x, If[LessEqual[x, 1.15e+109], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.04000000000000003e123 or 1.25e-39 < x < 8.00000000000000043e32 or 1.15000000000000005e109 < x

   1. Initial program 94.8%

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

      1. associate-*r/ 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around inf 69.2%

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

   if -1.04000000000000003e123 < x < -8.49999999999999972e-308

   1. Initial program 90.4%

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

      1. associate-*r/ 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in z around inf 48.7%

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

      1. mul-1-neg 48.7%

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

      2. associate-*l/ 56.7%

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

      3. *-commutative 56.7%

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

      4. distribute-rgt-neg-in 56.7%

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

      5. distribute-frac-neg 56.7%

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

      6. *-lft-identity 56.7%

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

      7. metadata-eval 56.7%

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

      8. times-frac 56.7%

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

      9. neg-mul-1 56.7%

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

      10. neg-mul-1 56.7%

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

      11. remove-double-neg 56.7%

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

   6. Simplified 56.7%

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

   if -8.49999999999999972e-308 < x < 1.25e-39

   1. Initial program 89.4%

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

      1. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in t around inf 53.0%

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

      1. associate-/l* 56.5%

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

   6. Simplified 56.5%

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

   if 8.00000000000000043e32 < x < 1.15000000000000005e109

   1. Initial program 79.6%

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

      1. associate-*r/ 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in t around inf 58.9%

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

      1. associate-*l/ 72.3%

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

      2. *-commutative 72.3%

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

   6. Simplified 72.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{+123}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-308}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-39}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{+109}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 67.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-34} \lor \neg \left(x \leq 1650000000\right) \land x \leq 1.9 \cdot 10^{+112}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.2e+125)
   x
   (if (or (<= x 9.5e-34) (and (not (<= x 1650000000.0)) (<= x 1.9e+112)))
     (* (/ y a) (- t z))
     x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.2e+125) {
		tmp = x;
	} else if ((x <= 9.5e-34) || (!(x <= 1650000000.0) && (x <= 1.9e+112))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.2d+125)) then
        tmp = x
    else if ((x <= 9.5d-34) .or. (.not. (x <= 1650000000.0d0)) .and. (x <= 1.9d+112)) then
        tmp = (y / a) * (t - z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.2e+125) {
		tmp = x;
	} else if ((x <= 9.5e-34) || (!(x <= 1650000000.0) && (x <= 1.9e+112))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.2e+125:
		tmp = x
	elif (x <= 9.5e-34) or (not (x <= 1650000000.0) and (x <= 1.9e+112)):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.2e+125)
		tmp = x;
	elseif ((x <= 9.5e-34) || (!(x <= 1650000000.0) && (x <= 1.9e+112)))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.2e+125)
		tmp = x;
	elseif ((x <= 9.5e-34) || (~((x <= 1650000000.0)) && (x <= 1.9e+112)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.2e+125], x, If[Or[LessEqual[x, 9.5e-34], And[N[Not[LessEqual[x, 1650000000.0]], $MachinePrecision], LessEqual[x, 1.9e+112]]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.19999999999999991e125 or 9.49999999999999985e-34 < x < 1.65e9 or 1.90000000000000004e112 < x

   1. Initial program 94.6%

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

      1. associate-*r/ 94.6%

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

   3. Simplified 94.6%

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

   4. Taylor expanded in x around inf 70.9%

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

   if -2.19999999999999991e125 < x < 9.49999999999999985e-34 or 1.65e9 < x < 1.90000000000000004e112

   1. Initial program 89.3%

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

      1. associate-*r/ 91.7%

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

   3. Simplified 91.7%

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

      1. associate-*r/ 89.3%

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

      2. associate-/l* 92.0%

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

      3. div-inv 91.9%

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

      4. associate-/r* 96.4%

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

   5. Applied egg-rr 96.4%

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

   6. Taylor expanded in x around 0 74.7%

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

      1. mul-1-neg 74.7%

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

      2. *-commutative 74.7%

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

      3. neg-sub0 74.7%

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

      4. *-commutative 74.7%

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

      5. associate-/l* 76.7%

         \[\leadsto 0 - \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

      6. associate-/r/ 81.9%

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

      7. sub-neg 81.9%

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

      8. distribute-lft-out 73.3%

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

      9. distribute-rgt-neg-in 73.3%

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

      10. unsub-neg 73.3%

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

      11. associate-+l- 73.3%

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

      12. neg-sub0 73.3%

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

      13. distribute-rgt-neg-in 73.3%

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

      14. distribute-lft-in 81.9%

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

      15. +-commutative 81.9%

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

      16. unsub-neg 81.9%

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

   8. Simplified 81.9%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-34} \lor \neg \left(x \leq 1650000000\right) \land x \leq 1.9 \cdot 10^{+112}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 76.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+123} \lor \neg \left(x \leq 4 \cdot 10^{-38}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.02e+123) (not (<= x 4e-38)))
   (+ x (* (/ y a) t))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.02e+123) || !(x <= 4e-38)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = (y / a) * (t - 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 ((x <= (-1.02d+123)) .or. (.not. (x <= 4d-38))) then
        tmp = x + ((y / a) * t)
    else
        tmp = (y / a) * (t - 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 ((x <= -1.02e+123) || !(x <= 4e-38)) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.02e+123) or not (x <= 4e-38):
		tmp = x + ((y / a) * t)
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.02e+123) || !(x <= 4e-38))
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.02e+123) || ~((x <= 4e-38)))
		tmp = x + ((y / a) * t);
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.02e+123], N[Not[LessEqual[x, 4e-38]], $MachinePrecision]], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e123 or 3.9999999999999998e-38 < x

   1. Initial program 93.0%

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

      1. associate-*r/ 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 83.7%

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

      1. cancel-sign-sub-inv 83.7%

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

      2. metadata-eval 83.7%

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

      3. *-lft-identity 83.7%

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

      4. +-commutative 83.7%

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

      5. associate-*l/ 89.1%

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

      6. *-commutative 89.1%

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

   6. Simplified 89.1%

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

   if -1.02e123 < x < 3.9999999999999998e-38

   1. Initial program 90.0%

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

      1. associate-*r/ 92.8%

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

   3. Simplified 92.8%

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

      1. associate-*r/ 90.0%

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

      2. associate-/l* 92.9%

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

      3. div-inv 92.8%

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

      4. associate-/r* 96.0%

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

   5. Applied egg-rr 96.0%

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

   6. Taylor expanded in x around 0 74.3%

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

      1. mul-1-neg 74.3%

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

      2. *-commutative 74.3%

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

      3. neg-sub0 74.3%

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

      4. *-commutative 74.3%

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

      5. associate-/l* 77.0%

         \[\leadsto 0 - \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

      6. associate-/r/ 80.9%

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

      7. sub-neg 80.9%

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

      8. distribute-lft-out 73.5%

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

      9. distribute-rgt-neg-in 73.5%

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

      10. unsub-neg 73.5%

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

      11. associate-+l- 73.5%

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

      12. neg-sub0 73.5%

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

      13. distribute-rgt-neg-in 73.5%

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

      14. distribute-lft-in 80.9%

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

      15. +-commutative 80.9%

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

      16. unsub-neg 80.9%

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

   8. Simplified 80.9%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+123} \lor \neg \left(x \leq 4 \cdot 10^{-38}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

Alternative 5: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+88} \lor \neg \left(z \leq 1.9 \cdot 10^{-40}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.4e+88) (not (<= z 1.9e-40)))
   (- x (* y (/ z a)))
   (+ x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.4e+88) || !(z <= 1.9e-40)) {
		tmp = x - (y * (z / a));
	} 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 <= (-1.4d+88)) .or. (.not. (z <= 1.9d-40))) then
        tmp = x - (y * (z / a))
    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 <= -1.4e+88) || !(z <= 1.9e-40)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.4e+88) or not (z <= 1.9e-40):
		tmp = x - (y * (z / a))
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.4e+88) || !(z <= 1.9e-40))
		tmp = Float64(x - Float64(y * Float64(z / a)));
	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 <= -1.4e+88) || ~((z <= 1.9e-40)))
		tmp = x - (y * (z / a));
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.4e+88], N[Not[LessEqual[z, 1.9e-40]], $MachinePrecision]], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.39999999999999994e88 or 1.8999999999999999e-40 < z

   1. Initial program 87.4%

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

      1. associate-*r/ 89.6%

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

   3. Simplified 89.6%

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

      1. associate-*r/ 87.4%

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

      2. associate-/l* 89.9%

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

      3. div-inv 89.9%

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

      4. associate-/r* 97.4%

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

   5. Applied egg-rr 97.4%

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

   6. Taylor expanded in z around inf 78.4%

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

      1. associate-*r/ 80.6%

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

   8. Simplified 80.6%

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

   if -1.39999999999999994e88 < z < 1.8999999999999999e-40

   1. Initial program 95.5%

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

      1. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around 0 89.4%

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

      1. cancel-sign-sub-inv 89.4%

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

      2. metadata-eval 89.4%

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

      3. *-lft-identity 89.4%

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

      4. +-commutative 89.4%

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

      5. associate-*l/ 92.3%

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

      6. *-commutative 92.3%

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

   6. Simplified 92.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+88} \lor \neg \left(z \leq 1.9 \cdot 10^{-40}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 6: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+88} \lor \neg \left(z \leq 1.66 \cdot 10^{-40}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.3e+88) (not (<= z 1.66e-40)))
   (- 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 <= -1.3e+88) || !(z <= 1.66e-40)) {
		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 <= (-1.3d+88)) .or. (.not. (z <= 1.66d-40))) 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 <= -1.3e+88) || !(z <= 1.66e-40)) {
		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 <= -1.3e+88) or not (z <= 1.66e-40):
		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 <= -1.3e+88) || !(z <= 1.66e-40))
		tmp = Float64(x - Float64(y / Float64(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 <= -1.3e+88) || ~((z <= 1.66e-40)))
		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, -1.3e+88], N[Not[LessEqual[z, 1.66e-40]], $MachinePrecision]], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e88 or 1.6600000000000001e-40 < z

   1. Initial program 87.4%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in z around inf 80.7%

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

   if -1.3e88 < z < 1.6600000000000001e-40

   1. Initial program 95.5%

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

      1. associate-*r/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in z around 0 89.4%

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

      1. cancel-sign-sub-inv 89.4%

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

      2. metadata-eval 89.4%

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

      3. *-lft-identity 89.4%

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

      4. +-commutative 89.4%

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

      5. associate-*l/ 92.3%

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

      6. *-commutative 92.3%

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

   6. Simplified 92.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+88} \lor \neg \left(z \leq 1.66 \cdot 10^{-40}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 7: 82.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.8e+26)
   (- x (/ (* y z) a))
   (if (<= z 1.9e-40) (+ x (* (/ y a) t)) (- x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+26) {
		tmp = x - ((y * z) / a);
	} else if (z <= 1.9e-40) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.8d+26)) then
        tmp = x - ((y * z) / a)
    else if (z <= 1.9d-40) then
        tmp = x + ((y / a) * t)
    else
        tmp = x - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.8e+26) {
		tmp = x - ((y * z) / a);
	} else if (z <= 1.9e-40) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.8e+26:
		tmp = x - ((y * z) / a)
	elif z <= 1.9e-40:
		tmp = x + ((y / a) * t)
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.8e+26)
		tmp = Float64(x - Float64(Float64(y * z) / a));
	elseif (z <= 1.9e-40)
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.8e+26)
		tmp = x - ((y * z) / a);
	elseif (z <= 1.9e-40)
		tmp = x + ((y / a) * t);
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.8e+26], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e-40], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.80000000000000012e26

   1. Initial program 90.8%

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

      1. associate-*r/ 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 83.0%

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

   if -1.80000000000000012e26 < z < 1.8999999999999999e-40

   1. Initial program 95.1%

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

      1. associate-*r/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 90.1%

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

      1. cancel-sign-sub-inv 90.1%

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

      2. metadata-eval 90.1%

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

      3. *-lft-identity 90.1%

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

      4. +-commutative 90.1%

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

      5. associate-*l/ 93.3%

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

      6. *-commutative 93.3%

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

   6. Simplified 93.3%

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

   if 1.8999999999999999e-40 < z

   1. Initial program 86.4%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in z around inf 80.4%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+26}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-40}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]

Alternative 8: 51.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2200000 \lor \neg \left(t \leq 1.1 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2200000.0) (not (<= t 1.1e+20))) (* (/ y a) t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2200000.0) || !(t <= 1.1e+20)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2200000.0d0)) .or. (.not. (t <= 1.1d+20))) then
        tmp = (y / a) * t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2200000.0) || !(t <= 1.1e+20)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2200000.0) or not (t <= 1.1e+20):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2200000.0) || !(t <= 1.1e+20))
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2200000.0) || ~((t <= 1.1e+20)))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2200000.0], N[Not[LessEqual[t, 1.1e+20]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -2.2e6 or 1.1e20 < t

   1. Initial program 90.0%

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

      1. associate-*r/ 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 57.0%

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

      1. associate-*l/ 60.6%

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

      2. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   if -2.2e6 < t < 1.1e20

   1. Initial program 92.7%

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

      1. associate-*r/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in x around inf 51.6%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2200000 \lor \neg \left(t \leq 1.1 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2800000:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2800000.0) (* y (/ t a)) (if (<= t 1.05e+20) x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2800000.0) {
		tmp = y * (t / a);
	} else if (t <= 1.05e+20) {
		tmp = x;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2800000.0d0)) then
        tmp = y * (t / a)
    else if (t <= 1.05d+20) then
        tmp = x
    else
        tmp = (y / a) * t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2800000.0) {
		tmp = y * (t / a);
	} else if (t <= 1.05e+20) {
		tmp = x;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2800000.0:
		tmp = y * (t / a)
	elif t <= 1.05e+20:
		tmp = x
	else:
		tmp = (y / a) * t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2800000.0)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= 1.05e+20)
		tmp = x;
	else
		tmp = Float64(Float64(y / a) * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2800000.0)
		tmp = y * (t / a);
	elseif (t <= 1.05e+20)
		tmp = x;
	else
		tmp = (y / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2800000.0], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+20], x, N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.8e6

   1. Initial program 93.7%

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

      1. associate-*r/ 90.5%

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

   3. Simplified 90.5%

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

      1. associate-*r/ 93.7%

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

      2. associate-/l* 90.6%

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

      3. div-inv 90.6%

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

      4. 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. Taylor expanded in t around inf 57.1%

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

      1. associate-*r/ 58.5%

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

   8. Simplified 58.5%

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

   if -2.8e6 < t < 1.05e20

   1. Initial program 92.7%

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

      1. associate-*r/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in x around inf 51.6%

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

   if 1.05e20 < t

   1. Initial program 86.4%

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

      1. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around inf 56.8%

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

      1. associate-*l/ 62.8%

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

      2. *-commutative 62.8%

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

   6. Simplified 62.8%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2800000:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \]

Alternative 10: 50.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3000000:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3000000.0) (* y (/ t a)) (if (<= t 1.05e+20) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3000000.0) {
		tmp = y * (t / a);
	} else if (t <= 1.05e+20) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	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 <= (-3000000.0d0)) then
        tmp = y * (t / a)
    else if (t <= 1.05d+20) then
        tmp = x
    else
        tmp = t / (a / y)
    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 <= -3000000.0) {
		tmp = y * (t / a);
	} else if (t <= 1.05e+20) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3000000.0:
		tmp = y * (t / a)
	elif t <= 1.05e+20:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3000000.0)
		tmp = Float64(y * Float64(t / a));
	elseif (t <= 1.05e+20)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3000000.0)
		tmp = y * (t / a);
	elseif (t <= 1.05e+20)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3000000.0], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+20], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3e6

   1. Initial program 93.7%

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

      1. associate-*r/ 90.5%

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

   3. Simplified 90.5%

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

      1. associate-*r/ 93.7%

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

      2. associate-/l* 90.6%

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

      3. div-inv 90.6%

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

      4. 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. Taylor expanded in t around inf 57.1%

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

      1. associate-*r/ 58.5%

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

   8. Simplified 58.5%

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

   if -3e6 < t < 1.05e20

   1. Initial program 92.7%

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

      1. associate-*r/ 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in x around inf 51.6%

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

   if 1.05e20 < t

   1. Initial program 86.4%

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

      1. associate-*r/ 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around inf 56.8%

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

      1. associate-*l/ 62.8%

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

      2. *-commutative 62.8%

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

   6. Simplified 62.8%

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

      1. clear-num 62.7%

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

      2. un-div-inv 62.8%

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

   8. Applied egg-rr 62.8%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3000000:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 11: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.4%

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

   1. associate-*r/ 92.9%

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

3. Simplified 92.9%

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

4. Final simplification 92.9%

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

Alternative 12: 39.1% 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 91.4%

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

   1. associate-*r/ 92.9%

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

3. Simplified 92.9%

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

4. Taylor expanded in x around inf 38.8%

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

5. Final simplification 38.8%

   \[\leadsto x \]

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 2023262 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

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