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

Percentage Accurate: 93.2% → 96.8%

Time: 12.3s

Alternatives: 11

Speedup: 1.0×

• 25.3% 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: 93.2% 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: 96.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. associate-*l/ 96.4%

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

3. Simplified 96.4%

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

5. Final simplification 96.4%

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

Alternative 2: 83.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{a} \cdot z\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq -3400000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-195}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* (/ y a) z))))
   (if (<= z -4.8e+107)
     t_1
     (if (<= z -2.5e+36)
       (* (/ y a) (- t z))
       (if (<= z -3400000.0)
         t_1
         (if (<= z -3.8e-195)
           (+ x (* y (/ t a)))
           (if (<= z 1.25e+64) (+ x (/ (* y t) a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((y / a) * z);
	double tmp;
	if (z <= -4.8e+107) {
		tmp = t_1;
	} else if (z <= -2.5e+36) {
		tmp = (y / a) * (t - z);
	} else if (z <= -3400000.0) {
		tmp = t_1;
	} else if (z <= -3.8e-195) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.25e+64) {
		tmp = x + ((y * t) / 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 = x - ((y / a) * z)
    if (z <= (-4.8d+107)) then
        tmp = t_1
    else if (z <= (-2.5d+36)) then
        tmp = (y / a) * (t - z)
    else if (z <= (-3400000.0d0)) then
        tmp = t_1
    else if (z <= (-3.8d-195)) then
        tmp = x + (y * (t / a))
    else if (z <= 1.25d+64) then
        tmp = x + ((y * t) / 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 = x - ((y / a) * z);
	double tmp;
	if (z <= -4.8e+107) {
		tmp = t_1;
	} else if (z <= -2.5e+36) {
		tmp = (y / a) * (t - z);
	} else if (z <= -3400000.0) {
		tmp = t_1;
	} else if (z <= -3.8e-195) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.25e+64) {
		tmp = x + ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((y / a) * z)
	tmp = 0
	if z <= -4.8e+107:
		tmp = t_1
	elif z <= -2.5e+36:
		tmp = (y / a) * (t - z)
	elif z <= -3400000.0:
		tmp = t_1
	elif z <= -3.8e-195:
		tmp = x + (y * (t / a))
	elif z <= 1.25e+64:
		tmp = x + ((y * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(y / a) * z))
	tmp = 0.0
	if (z <= -4.8e+107)
		tmp = t_1;
	elseif (z <= -2.5e+36)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	elseif (z <= -3400000.0)
		tmp = t_1;
	elseif (z <= -3.8e-195)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.25e+64)
		tmp = Float64(x + Float64(Float64(y * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((y / a) * z);
	tmp = 0.0;
	if (z <= -4.8e+107)
		tmp = t_1;
	elseif (z <= -2.5e+36)
		tmp = (y / a) * (t - z);
	elseif (z <= -3400000.0)
		tmp = t_1;
	elseif (z <= -3.8e-195)
		tmp = x + (y * (t / a));
	elseif (z <= 1.25e+64)
		tmp = x + ((y * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+107], t$95$1, If[LessEqual[z, -2.5e+36], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3400000.0], t$95$1, If[LessEqual[z, -3.8e-195], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+64], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.8000000000000001e107 or -2.49999999999999988e36 < z < -3.4e6 or 1.25e64 < z

   1. Initial program 92.3%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

      1. associate-/l* 92.3%

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

      2. clear-num 92.2%

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

      3. associate-/r/ 92.3%

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

   6. Applied egg-rr 92.3%

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

   7. Taylor expanded in z around inf 86.4%

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

      1. associate-*l/ 92.0%

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

      2. *-commutative 92.0%

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

   9. Simplified 92.0%

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

   if -4.8000000000000001e107 < z < -2.49999999999999988e36

   1. Initial program 95.6%

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

      1. associate-/l* 86.5%

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

   3. Simplified 86.5%

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

      1. associate-/l* 95.6%

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

      2. clear-num 95.6%

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

      3. associate-/r/ 95.5%

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

   6. Applied egg-rr 95.5%

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

   7. Taylor expanded in x around 0 76.2%

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

      1. associate-*l/ 77.4%

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

      2. sub-neg 77.4%

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

      3. distribute-lft-out 63.1%

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

      4. *-commutative 63.1%

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

      5. associate-*l/ 58.8%

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

      6. distribute-lft-in 58.8%

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

      7. neg-mul-1 58.8%

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

      8. sub-neg 58.8%

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

      9. cancel-sign-sub 58.8%

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

      10. +-commutative 58.8%

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

      11. mul-1-neg 58.8%

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

      12. sub-neg 58.8%

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

      13. associate-*l/ 63.1%

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

      14. *-commutative 63.1%

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

      15. distribute-rgt-out-- 77.4%

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

   9. Simplified 77.4%

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

   if -3.4e6 < z < -3.80000000000000013e-195

   1. Initial program 84.9%

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

      1. associate-*l/ 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in z around 0 71.6%

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

      1. sub-neg 71.6%

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

      2. mul-1-neg 71.6%

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

      3. remove-double-neg 71.6%

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

      4. +-commutative 71.6%

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

      5. associate-/l* 88.7%

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

      6. associate-/r/ 77.7%

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

   7. Simplified 77.7%

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

   if -3.80000000000000013e-195 < z < 1.25e64

   1. Initial program 97.9%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   5. Taylor expanded in z around 0 92.9%

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

      1. sub-neg 92.9%

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

      2. mul-1-neg 92.9%

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

      3. remove-double-neg 92.9%

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

      4. +-commutative 92.9%

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

      5. associate-/l* 87.8%

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

      6. associate-/r/ 88.9%

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

   7. Simplified 88.9%

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

      1. associate-*l/ 92.9%

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

      2. *-commutative 92.9%

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

   9. Applied egg-rr 92.9%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+107}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;z \leq -3400000:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-195}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+64}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+244}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-98}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.7e+244)
   (/ (- y) (/ a z))
   (if (<= y -8e+61)
     (* y (/ t a))
     (if (<= y -7.4e-17)
       x
       (if (<= y -5.4e-98)
         (/ (* y t) a)
         (if (<= y 3.4e-59) x (/ y (/ a t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.7e+244) {
		tmp = -y / (a / z);
	} else if (y <= -8e+61) {
		tmp = y * (t / a);
	} else if (y <= -7.4e-17) {
		tmp = x;
	} else if (y <= -5.4e-98) {
		tmp = (y * t) / a;
	} else if (y <= 3.4e-59) {
		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 (y <= (-1.7d+244)) then
        tmp = -y / (a / z)
    else if (y <= (-8d+61)) then
        tmp = y * (t / a)
    else if (y <= (-7.4d-17)) then
        tmp = x
    else if (y <= (-5.4d-98)) then
        tmp = (y * t) / a
    else if (y <= 3.4d-59) 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 (y <= -1.7e+244) {
		tmp = -y / (a / z);
	} else if (y <= -8e+61) {
		tmp = y * (t / a);
	} else if (y <= -7.4e-17) {
		tmp = x;
	} else if (y <= -5.4e-98) {
		tmp = (y * t) / a;
	} else if (y <= 3.4e-59) {
		tmp = x;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.7e+244:
		tmp = -y / (a / z)
	elif y <= -8e+61:
		tmp = y * (t / a)
	elif y <= -7.4e-17:
		tmp = x
	elif y <= -5.4e-98:
		tmp = (y * t) / a
	elif y <= 3.4e-59:
		tmp = x
	else:
		tmp = y / (a / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.7e+244)
		tmp = Float64(Float64(-y) / Float64(a / z));
	elseif (y <= -8e+61)
		tmp = Float64(y * Float64(t / a));
	elseif (y <= -7.4e-17)
		tmp = x;
	elseif (y <= -5.4e-98)
		tmp = Float64(Float64(y * t) / a);
	elseif (y <= 3.4e-59)
		tmp = x;
	else
		tmp = Float64(y / Float64(a / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.7e+244)
		tmp = -y / (a / z);
	elseif (y <= -8e+61)
		tmp = y * (t / a);
	elseif (y <= -7.4e-17)
		tmp = x;
	elseif (y <= -5.4e-98)
		tmp = (y * t) / a;
	elseif (y <= 3.4e-59)
		tmp = x;
	else
		tmp = y / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.7e+244], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e+61], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.4e-17], x, If[LessEqual[y, -5.4e-98], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 3.4e-59], x, N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.70000000000000005e244

   1. Initial program 64.9%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 52.9%

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

      1. mul-1-neg 52.9%

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

      2. associate-/l* 88.0%

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

   7. Simplified 88.0%

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

   if -1.70000000000000005e244 < y < -7.9999999999999996e61

   1. Initial program 87.3%

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

      1. associate-*l/ 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in t around inf 54.6%

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

      1. associate-/l* 59.3%

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

      2. associate-/r/ 64.7%

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

   7. Simplified 64.7%

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

   if -7.9999999999999996e61 < y < -7.3999999999999995e-17 or -5.3999999999999997e-98 < y < 3.40000000000000018e-59

   1. Initial program 98.6%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 62.7%

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

   if -7.3999999999999995e-17 < y < -5.3999999999999997e-98

   1. Initial program 99.9%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in t around inf 64.7%

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

   if 3.40000000000000018e-59 < y

   1. Initial program 89.3%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

      1. associate-/l* 89.3%

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

      2. clear-num 89.2%

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

      3. associate-/r/ 89.3%

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

   6. Applied egg-rr 89.3%

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

   7. Taylor expanded in t around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/l* 51.7%

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

   9. Simplified 51.7%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{t}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+244}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+61}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-98}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+172} \lor \neg \left(z \leq -8 \cdot 10^{+108} \lor \neg \left(z \leq -3.4 \cdot 10^{-25}\right) \land z \leq 5.2\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -8.5e+172)
         (not (or (<= z -8e+108) (and (not (<= z -3.4e-25)) (<= z 5.2)))))
   (* (/ y a) (- t z))
   (+ x (* y (/ t a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+172) || !((z <= -8e+108) || (!(z <= -3.4e-25) && (z <= 5.2)))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-8.5d+172)) .or. (.not. (z <= (-8d+108)) .or. (.not. (z <= (-3.4d-25))) .and. (z <= 5.2d0))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + (y * (t / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -8.5e+172) || !((z <= -8e+108) || (!(z <= -3.4e-25) && (z <= 5.2)))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (y * (t / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -8.5e+172) or not ((z <= -8e+108) or (not (z <= -3.4e-25) and (z <= 5.2))):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + (y * (t / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -8.5e+172) || !((z <= -8e+108) || (!(z <= -3.4e-25) && (z <= 5.2))))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(y * Float64(t / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -8.5e+172) || ~(((z <= -8e+108) || (~((z <= -3.4e-25)) && (z <= 5.2)))))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (y * (t / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -8.5e+172], N[Not[Or[LessEqual[z, -8e+108], And[N[Not[LessEqual[z, -3.4e-25]], $MachinePrecision], LessEqual[z, 5.2]]]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.50000000000000053e172 or -8.0000000000000003e108 < z < -3.40000000000000002e-25 or 5.20000000000000018 < z

   1. Initial program 92.7%

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

      1. associate-/l* 85.2%

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

   3. Simplified 85.2%

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

      1. associate-/l* 92.7%

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

      2. clear-num 92.6%

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

      3. associate-/r/ 92.7%

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

   6. Applied egg-rr 92.7%

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

   7. Taylor expanded in x around 0 69.1%

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

      1. associate-*l/ 75.5%

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

      2. sub-neg 75.5%

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

      3. distribute-lft-out 66.9%

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

      4. *-commutative 66.9%

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

      5. associate-*l/ 61.5%

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

      6. distribute-lft-in 61.5%

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

      7. neg-mul-1 61.5%

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

      8. sub-neg 61.5%

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

      9. cancel-sign-sub 61.5%

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

      10. +-commutative 61.5%

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

      11. mul-1-neg 61.5%

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

      12. sub-neg 61.5%

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

      13. associate-*l/ 66.9%

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

      14. *-commutative 66.9%

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

      15. distribute-rgt-out-- 75.5%

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

   9. Simplified 75.5%

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

   if -8.50000000000000053e172 < z < -8.0000000000000003e108 or -3.40000000000000002e-25 < z < 5.20000000000000018

   1. Initial program 93.9%

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

      1. associate-*l/ 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in z around 0 87.6%

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

      1. sub-neg 87.6%

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

      2. mul-1-neg 87.6%

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

      3. remove-double-neg 87.6%

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

      4. +-commutative 87.6%

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

      5. associate-/l* 89.4%

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

      6. associate-/r/ 88.1%

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

   7. Simplified 88.1%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+172} \lor \neg \left(z \leq -8 \cdot 10^{+108} \lor \neg \left(z \leq -3.4 \cdot 10^{-25}\right) \land z \leq 5.2\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+142} \lor \neg \left(y \leq -1.7 \cdot 10^{+16}\right) \land \left(y \leq -9 \cdot 10^{-74} \lor \neg \left(y \leq 5.6 \cdot 10^{-34}\right)\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4.1e+142)
         (and (not (<= y -1.7e+16)) (or (<= y -9e-74) (not (<= y 5.6e-34)))))
   (* (/ y a) (- t z))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.1e+142) || (!(y <= -1.7e+16) && ((y <= -9e-74) || !(y <= 5.6e-34)))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-4.1d+142)) .or. (.not. (y <= (-1.7d+16))) .and. (y <= (-9d-74)) .or. (.not. (y <= 5.6d-34))) then
        tmp = (y / a) * (t - z)
    else
        tmp = x + ((y * t) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4.1e+142) || (!(y <= -1.7e+16) && ((y <= -9e-74) || !(y <= 5.6e-34)))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4.1e+142) or (not (y <= -1.7e+16) and ((y <= -9e-74) or not (y <= 5.6e-34))):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4.1e+142) || (!(y <= -1.7e+16) && ((y <= -9e-74) || !(y <= 5.6e-34))))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = Float64(x + Float64(Float64(y * t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4.1e+142) || (~((y <= -1.7e+16)) && ((y <= -9e-74) || ~((y <= 5.6e-34)))))
		tmp = (y / a) * (t - z);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4.1e+142], And[N[Not[LessEqual[y, -1.7e+16]], $MachinePrecision], Or[LessEqual[y, -9e-74], N[Not[LessEqual[y, 5.6e-34]], $MachinePrecision]]]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.09999999999999982e142 or -1.7e16 < y < -8.9999999999999998e-74 or 5.59999999999999994e-34 < y

   1. Initial program 86.9%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

      1. associate-/l* 86.9%

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

      2. clear-num 86.8%

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

      3. associate-/r/ 86.9%

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

   6. Applied egg-rr 86.9%

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

   7. Taylor expanded in x around 0 76.5%

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

      1. associate-*l/ 85.1%

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

      2. sub-neg 85.1%

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

      3. distribute-lft-out 74.6%

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

      4. *-commutative 74.6%

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

      5. associate-*l/ 70.9%

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

      6. distribute-lft-in 70.9%

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

      7. neg-mul-1 70.9%

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

      8. sub-neg 70.9%

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

      9. cancel-sign-sub 70.9%

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

      10. +-commutative 70.9%

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

      11. mul-1-neg 70.9%

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

      12. sub-neg 70.9%

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

      13. associate-*l/ 74.6%

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

      14. *-commutative 74.6%

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

      15. distribute-rgt-out-- 85.1%

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

   9. Simplified 85.1%

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

   if -4.09999999999999982e142 < y < -1.7e16 or -8.9999999999999998e-74 < y < 5.59999999999999994e-34

   1. Initial program 98.6%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in z around 0 81.3%

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

      1. sub-neg 81.3%

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

      2. mul-1-neg 81.3%

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

      3. remove-double-neg 81.3%

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

      4. +-commutative 81.3%

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

      5. associate-/l* 78.5%

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

      6. associate-/r/ 72.0%

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

   7. Simplified 72.0%

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

      1. associate-*l/ 81.3%

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

      2. *-commutative 81.3%

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

   9. Applied egg-rr 81.3%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{+142} \lor \neg \left(y \leq -1.7 \cdot 10^{+16}\right) \land \left(y \leq -9 \cdot 10^{-74} \lor \neg \left(y \leq 5.6 \cdot 10^{-34}\right)\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+66} \lor \neg \left(y \leq -4.8 \cdot 10^{-15} \lor \neg \left(y \leq -1.9 \cdot 10^{-98}\right) \land y \leq 7 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6e+66)
         (not (or (<= y -4.8e-15) (and (not (<= y -1.9e-98)) (<= y 7e-60)))))
   (* (/ y a) t)
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6e+66) || !((y <= -4.8e-15) || (!(y <= -1.9e-98) && (y <= 7e-60)))) {
		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 ((y <= (-6d+66)) .or. (.not. (y <= (-4.8d-15)) .or. (.not. (y <= (-1.9d-98))) .and. (y <= 7d-60))) 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 ((y <= -6e+66) || !((y <= -4.8e-15) || (!(y <= -1.9e-98) && (y <= 7e-60)))) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6e+66) or not ((y <= -4.8e-15) or (not (y <= -1.9e-98) and (y <= 7e-60))):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6e+66) || !((y <= -4.8e-15) || (!(y <= -1.9e-98) && (y <= 7e-60))))
		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 ((y <= -6e+66) || ~(((y <= -4.8e-15) || (~((y <= -1.9e-98)) && (y <= 7e-60)))))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6e+66], N[Not[Or[LessEqual[y, -4.8e-15], And[N[Not[LessEqual[y, -1.9e-98]], $MachinePrecision], LessEqual[y, 7e-60]]]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000005e66 or -4.7999999999999999e-15 < y < -1.9000000000000002e-98 or 6.99999999999999952e-60 < y

   1. Initial program 88.1%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in t around inf 48.5%

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

      1. associate-*l/ 53.0%

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

      2. div-inv 53.0%

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

      3. associate-*l* 53.0%

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

      4. associate-*l/ 53.0%

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

      5. *-un-lft-identity 53.0%

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

   7. Applied egg-rr 53.0%

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

   if -6.00000000000000005e66 < y < -4.7999999999999999e-15 or -1.9000000000000002e-98 < y < 6.99999999999999952e-60

   1. Initial program 98.6%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 62.7%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+66} \lor \neg \left(y \leq -4.8 \cdot 10^{-15} \lor \neg \left(y \leq -1.9 \cdot 10^{-98}\right) \land y \leq 7 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-20} \lor \neg \left(y \leq -3.6 \cdot 10^{-97}\right) \land y \leq 3.2 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.8e+62)
   (* y (/ t a))
   (if (or (<= y -1.9e-20) (and (not (<= y -3.6e-97)) (<= y 3.2e-59)))
     x
     (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.8e+62) {
		tmp = y * (t / a);
	} else if ((y <= -1.9e-20) || (!(y <= -3.6e-97) && (y <= 3.2e-59))) {
		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 (y <= (-1.8d+62)) then
        tmp = y * (t / a)
    else if ((y <= (-1.9d-20)) .or. (.not. (y <= (-3.6d-97))) .and. (y <= 3.2d-59)) 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 (y <= -1.8e+62) {
		tmp = y * (t / a);
	} else if ((y <= -1.9e-20) || (!(y <= -3.6e-97) && (y <= 3.2e-59))) {
		tmp = x;
	} else {
		tmp = (y / a) * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.8e+62:
		tmp = y * (t / a)
	elif (y <= -1.9e-20) or (not (y <= -3.6e-97) and (y <= 3.2e-59)):
		tmp = x
	else:
		tmp = (y / a) * t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.8e+62)
		tmp = Float64(y * Float64(t / a));
	elseif ((y <= -1.9e-20) || (!(y <= -3.6e-97) && (y <= 3.2e-59)))
		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 (y <= -1.8e+62)
		tmp = y * (t / a);
	elseif ((y <= -1.9e-20) || (~((y <= -3.6e-97)) && (y <= 3.2e-59)))
		tmp = x;
	else
		tmp = (y / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.8e+62], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -1.9e-20], And[N[Not[LessEqual[y, -3.6e-97]], $MachinePrecision], LessEqual[y, 3.2e-59]]], x, N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.8e62

   1. Initial program 83.2%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in t around inf 47.3%

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

      1. associate-/l* 53.3%

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

      2. associate-/r/ 55.6%

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

   7. Simplified 55.6%

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

   if -1.8e62 < y < -1.8999999999999999e-20 or -3.59999999999999997e-97 < y < 3.1999999999999999e-59

   1. Initial program 98.6%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 62.7%

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

   if -1.8999999999999999e-20 < y < -3.59999999999999997e-97 or 3.1999999999999999e-59 < y

   1. Initial program 90.7%

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

      1. associate-*l/ 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in t around inf 49.1%

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

      1. associate-*l/ 51.6%

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

      2. div-inv 51.6%

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

      3. associate-*l* 52.8%

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

      4. associate-*l/ 52.9%

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

      5. *-un-lft-identity 52.9%

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

   7. Applied egg-rr 52.9%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-20} \lor \neg \left(y \leq -3.6 \cdot 10^{-97}\right) \land y \leq 3.2 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -7.4e+62)
   (* y (/ t a))
   (if (<= y -2.5e-14)
     x
     (if (<= y -1.4e-97) (* (/ y a) t) (if (<= y 1.38e-58) x (/ y (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -7.4e+62) {
		tmp = y * (t / a);
	} else if (y <= -2.5e-14) {
		tmp = x;
	} else if (y <= -1.4e-97) {
		tmp = (y / a) * t;
	} else if (y <= 1.38e-58) {
		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 (y <= (-7.4d+62)) then
        tmp = y * (t / a)
    else if (y <= (-2.5d-14)) then
        tmp = x
    else if (y <= (-1.4d-97)) then
        tmp = (y / a) * t
    else if (y <= 1.38d-58) 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 (y <= -7.4e+62) {
		tmp = y * (t / a);
	} else if (y <= -2.5e-14) {
		tmp = x;
	} else if (y <= -1.4e-97) {
		tmp = (y / a) * t;
	} else if (y <= 1.38e-58) {
		tmp = x;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -7.4e+62:
		tmp = y * (t / a)
	elif y <= -2.5e-14:
		tmp = x
	elif y <= -1.4e-97:
		tmp = (y / a) * t
	elif y <= 1.38e-58:
		tmp = x
	else:
		tmp = y / (a / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -7.4e+62)
		tmp = Float64(y * Float64(t / a));
	elseif (y <= -2.5e-14)
		tmp = x;
	elseif (y <= -1.4e-97)
		tmp = Float64(Float64(y / a) * t);
	elseif (y <= 1.38e-58)
		tmp = x;
	else
		tmp = Float64(y / Float64(a / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -7.4e+62)
		tmp = y * (t / a);
	elseif (y <= -2.5e-14)
		tmp = x;
	elseif (y <= -1.4e-97)
		tmp = (y / a) * t;
	elseif (y <= 1.38e-58)
		tmp = x;
	else
		tmp = y / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -7.4e+62], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.5e-14], x, If[LessEqual[y, -1.4e-97], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 1.38e-58], x, N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.40000000000000028e62

   1. Initial program 83.2%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in t around inf 47.3%

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

      1. associate-/l* 53.3%

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

      2. associate-/r/ 55.6%

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

   7. Simplified 55.6%

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

   if -7.40000000000000028e62 < y < -2.5000000000000001e-14 or -1.4000000000000001e-97 < y < 1.37999999999999996e-58

   1. Initial program 98.6%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 62.7%

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

   if -2.5000000000000001e-14 < y < -1.4000000000000001e-97

   1. Initial program 99.9%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in t around inf 64.7%

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

      1. associate-*l/ 56.5%

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

      2. div-inv 56.4%

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

      3. associate-*l* 61.7%

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

      4. associate-*l/ 61.8%

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

      5. *-un-lft-identity 61.8%

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

   7. Applied egg-rr 61.8%

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

   if 1.37999999999999996e-58 < y

   1. Initial program 89.3%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

      1. associate-/l* 89.3%

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

      2. clear-num 89.2%

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

      3. associate-/r/ 89.3%

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

   6. Applied egg-rr 89.3%

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

   7. Taylor expanded in t around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/l* 51.7%

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

   9. Simplified 51.7%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+62}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 49.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-97}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.15e+64)
   (* y (/ t a))
   (if (<= y -2.8e-22)
     x
     (if (<= y -3.6e-97) (/ (* y t) a) (if (<= y 1.25e-58) x (/ y (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.15e+64) {
		tmp = y * (t / a);
	} else if (y <= -2.8e-22) {
		tmp = x;
	} else if (y <= -3.6e-97) {
		tmp = (y * t) / a;
	} else if (y <= 1.25e-58) {
		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 (y <= (-1.15d+64)) then
        tmp = y * (t / a)
    else if (y <= (-2.8d-22)) then
        tmp = x
    else if (y <= (-3.6d-97)) then
        tmp = (y * t) / a
    else if (y <= 1.25d-58) 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 (y <= -1.15e+64) {
		tmp = y * (t / a);
	} else if (y <= -2.8e-22) {
		tmp = x;
	} else if (y <= -3.6e-97) {
		tmp = (y * t) / a;
	} else if (y <= 1.25e-58) {
		tmp = x;
	} else {
		tmp = y / (a / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.15e+64:
		tmp = y * (t / a)
	elif y <= -2.8e-22:
		tmp = x
	elif y <= -3.6e-97:
		tmp = (y * t) / a
	elif y <= 1.25e-58:
		tmp = x
	else:
		tmp = y / (a / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.15e+64)
		tmp = Float64(y * Float64(t / a));
	elseif (y <= -2.8e-22)
		tmp = x;
	elseif (y <= -3.6e-97)
		tmp = Float64(Float64(y * t) / a);
	elseif (y <= 1.25e-58)
		tmp = x;
	else
		tmp = Float64(y / Float64(a / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.15e+64)
		tmp = y * (t / a);
	elseif (y <= -2.8e-22)
		tmp = x;
	elseif (y <= -3.6e-97)
		tmp = (y * t) / a;
	elseif (y <= 1.25e-58)
		tmp = x;
	else
		tmp = y / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.15e+64], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.8e-22], x, If[LessEqual[y, -3.6e-97], N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 1.25e-58], x, N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.15e64

   1. Initial program 83.2%

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

      1. associate-*l/ 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in t around inf 47.3%

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

      1. associate-/l* 53.3%

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

      2. associate-/r/ 55.6%

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

   7. Simplified 55.6%

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

   if -1.15e64 < y < -2.79999999999999995e-22 or -3.59999999999999997e-97 < y < 1.24999999999999994e-58

   1. Initial program 98.6%

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

      1. associate-*l/ 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 62.7%

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

   if -2.79999999999999995e-22 < y < -3.59999999999999997e-97

   1. Initial program 99.9%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in t around inf 64.7%

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

   if 1.24999999999999994e-58 < y

   1. Initial program 89.3%

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

      1. associate-/l* 98.0%

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

   3. Simplified 98.0%

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

      1. associate-/l* 89.3%

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

      2. clear-num 89.2%

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

      3. associate-/r/ 89.3%

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

   6. Applied egg-rr 89.3%

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

   7. Taylor expanded in t around inf 46.7%

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

      1. *-commutative 46.7%

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

      2. associate-/l* 51.7%

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

   9. Simplified 51.7%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+64}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-97}:\\ \;\;\;\;\frac{y \cdot t}{a}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-107} \lor \neg \left(y \leq 4.5 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.8e-107) (not (<= y 4.5e-85))) (* (/ y a) (- t z)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.8e-107) || !(y <= 4.5e-85)) {
		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 ((y <= (-3.8d-107)) .or. (.not. (y <= 4.5d-85))) 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 ((y <= -3.8e-107) || !(y <= 4.5e-85)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.8e-107) or not (y <= 4.5e-85):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.8e-107) || !(y <= 4.5e-85))
		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 ((y <= -3.8e-107) || ~((y <= 4.5e-85)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.8e-107], N[Not[LessEqual[y, 4.5e-85]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000002e-107 or 4.50000000000000004e-85 < y

   1. Initial program 89.7%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

      1. associate-/l* 89.7%

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

      2. clear-num 89.6%

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

      3. associate-/r/ 89.7%

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

   6. Applied egg-rr 89.7%

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

   7. Taylor expanded in x around 0 74.2%

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

      1. associate-*l/ 78.8%

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

      2. sub-neg 78.8%

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

      3. distribute-lft-out 69.8%

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

      4. *-commutative 69.8%

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

      5. associate-*l/ 67.0%

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

      6. distribute-lft-in 67.0%

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

      7. neg-mul-1 67.0%

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

      8. sub-neg 67.0%

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

      9. cancel-sign-sub 67.0%

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

      10. +-commutative 67.0%

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

      11. mul-1-neg 67.0%

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

      12. sub-neg 67.0%

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

      13. associate-*l/ 69.8%

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

      14. *-commutative 69.8%

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

      15. distribute-rgt-out-- 78.8%

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

   9. Simplified 78.8%

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

   if -3.8000000000000002e-107 < y < 4.50000000000000004e-85

   1. Initial program 98.3%

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

   5. Taylor expanded in x around inf 65.7%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-107} \lor \neg \left(y \leq 4.5 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 93.4%

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

   1. associate-*l/ 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in x around inf 38.2%

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

6. Final simplification 38.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (- x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (- x (/ (* y (- z t)) a))
       (- x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x - (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x - ((y * (z - t)) / a)
    else
        tmp = x - (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x - (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x - (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x - (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x - ((y * (z - t)) / a)
	else:
		tmp = x - (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x - Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x - Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x - Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x - (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x - ((y * (z - t)) / a);
	else
		tmp = x - (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x - N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024027 
(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)))