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

Percentage Accurate: 93.2% → 97.1%

Time: 8.9s

Alternatives: 11

Speedup: 1.0×

• 24.3% 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: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.7%

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

   1. associate-*l/ 96.9%

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

3. Simplified 96.9%

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

4. Final simplification 96.9%

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

Alternative 2: 68.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-74} \lor \neg \left(y \leq 3.7 \cdot 10^{-106}\right) \land \left(y \leq 19500000000 \lor \neg \left(y \leq 1.02 \cdot 10^{+58}\right)\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.3e-74)
         (and (not (<= y 3.7e-106))
              (or (<= y 19500000000.0) (not (<= y 1.02e+58)))))
   (* y (/ (- t z) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.3e-74) || (!(y <= 3.7e-106) && ((y <= 19500000000.0) || !(y <= 1.02e+58)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-3.3d-74)) .or. (.not. (y <= 3.7d-106)) .and. (y <= 19500000000.0d0) .or. (.not. (y <= 1.02d+58))) then
        tmp = y * ((t - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.3e-74) || (!(y <= 3.7e-106) && ((y <= 19500000000.0) || !(y <= 1.02e+58)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.3e-74) or (not (y <= 3.7e-106) and ((y <= 19500000000.0) or not (y <= 1.02e+58))):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.3e-74) || (!(y <= 3.7e-106) && ((y <= 19500000000.0) || !(y <= 1.02e+58))))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -3.3e-74) || (~((y <= 3.7e-106)) && ((y <= 19500000000.0) || ~((y <= 1.02e+58)))))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.3e-74], And[N[Not[LessEqual[y, 3.7e-106]], $MachinePrecision], Or[LessEqual[y, 19500000000.0], N[Not[LessEqual[y, 1.02e+58]], $MachinePrecision]]]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999996e-74 or 3.69999999999999979e-106 < y < 1.95e10 or 1.02000000000000005e58 < y

   1. Initial program 85.9%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around 0 73.1%

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

      1. mul-1-neg 73.1%

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

      2. associate-*r/ 83.6%

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

      3. distribute-rgt-neg-in 83.6%

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

      4. neg-sub0 83.6%

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

      5. div-sub 81.7%

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

      6. associate-+l- 81.7%

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

      7. neg-sub0 81.7%

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

      8. +-commutative 81.7%

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

      9. sub-neg 81.7%

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

      10. div-sub 83.6%

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

   6. Simplified 83.6%

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

   if -3.29999999999999996e-74 < y < 3.69999999999999979e-106 or 1.95e10 < y < 1.02000000000000005e58

   1. Initial program 98.9%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in x around inf 73.1%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-74} \lor \neg \left(y \leq 3.7 \cdot 10^{-106}\right) \land \left(y \leq 19500000000 \lor \neg \left(y \leq 1.02 \cdot 10^{+58}\right)\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 51.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -y \cdot \frac{z}{a}\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.09 \cdot 10^{+195}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* y (/ z a)))))
   (if (<= y -2.4e-40)
     t_1
     (if (<= y 3.9e+61) x (if (<= y 1.09e+195) t_1 (/ t (/ a y)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(y * (z / a));
	double tmp;
	if (y <= -2.4e-40) {
		tmp = t_1;
	} else if (y <= 3.9e+61) {
		tmp = x;
	} else if (y <= 1.09e+195) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -(y * (z / a))
    if (y <= (-2.4d-40)) then
        tmp = t_1
    else if (y <= 3.9d+61) then
        tmp = x
    else if (y <= 1.09d+195) then
        tmp = t_1
    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 t_1 = -(y * (z / a));
	double tmp;
	if (y <= -2.4e-40) {
		tmp = t_1;
	} else if (y <= 3.9e+61) {
		tmp = x;
	} else if (y <= 1.09e+195) {
		tmp = t_1;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -(y * (z / a))
	tmp = 0
	if y <= -2.4e-40:
		tmp = t_1
	elif y <= 3.9e+61:
		tmp = x
	elif y <= 1.09e+195:
		tmp = t_1
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(y * Float64(z / a)))
	tmp = 0.0
	if (y <= -2.4e-40)
		tmp = t_1;
	elseif (y <= 3.9e+61)
		tmp = x;
	elseif (y <= 1.09e+195)
		tmp = t_1;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -(y * (z / a));
	tmp = 0.0;
	if (y <= -2.4e-40)
		tmp = t_1;
	elseif (y <= 3.9e+61)
		tmp = x;
	elseif (y <= 1.09e+195)
		tmp = t_1;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = (-N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[y, -2.4e-40], t$95$1, If[LessEqual[y, 3.9e+61], x, If[LessEqual[y, 1.09e+195], t$95$1, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.39999999999999991e-40 or 3.89999999999999987e61 < y < 1.09e195

   1. Initial program 84.4%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in x around 0 74.2%

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

      1. mul-1-neg 74.2%

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

      2. associate-*r/ 86.3%

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

      3. distribute-rgt-neg-in 86.3%

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

      4. neg-sub0 86.3%

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

      5. div-sub 83.7%

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

      6. associate-+l- 83.7%

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

      7. neg-sub0 83.7%

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

      8. +-commutative 83.7%

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

      9. sub-neg 83.7%

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

      10. div-sub 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in t around 0 62.0%

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

      1. neg-mul-1 62.0%

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

      2. distribute-neg-frac 62.0%

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

   9. Simplified 62.0%

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

   if -2.39999999999999991e-40 < y < 3.89999999999999987e61

   1. Initial program 98.3%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 62.9%

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

   if 1.09e195 < y

   1. Initial program 78.9%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 46.3%

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

      1. associate-*l/ 67.3%

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

      2. *-commutative 67.3%

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

   6. Simplified 67.3%

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

      1. clear-num 67.3%

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

      2. div-inv 67.3%

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

   8. Applied egg-rr 67.3%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-40}:\\ \;\;\;\;-y \cdot \frac{z}{a}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.09 \cdot 10^{+195}:\\ \;\;\;\;-y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 4: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-40}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+195}:\\ \;\;\;\;-y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.7e-40)
   (* (/ y a) (- z))
   (if (<= y 6.4e+62) x (if (<= y 3.1e+195) (- (* y (/ z a))) (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.7e-40) {
		tmp = (y / a) * -z;
	} else if (y <= 6.4e+62) {
		tmp = x;
	} else if (y <= 3.1e+195) {
		tmp = -(y * (z / a));
	} 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 (y <= (-2.7d-40)) then
        tmp = (y / a) * -z
    else if (y <= 6.4d+62) then
        tmp = x
    else if (y <= 3.1d+195) then
        tmp = -(y * (z / a))
    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 (y <= -2.7e-40) {
		tmp = (y / a) * -z;
	} else if (y <= 6.4e+62) {
		tmp = x;
	} else if (y <= 3.1e+195) {
		tmp = -(y * (z / a));
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.7e-40:
		tmp = (y / a) * -z
	elif y <= 6.4e+62:
		tmp = x
	elif y <= 3.1e+195:
		tmp = -(y * (z / a))
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.7e-40)
		tmp = Float64(Float64(y / a) * Float64(-z));
	elseif (y <= 6.4e+62)
		tmp = x;
	elseif (y <= 3.1e+195)
		tmp = Float64(-Float64(y * Float64(z / a)));
	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 (y <= -2.7e-40)
		tmp = (y / a) * -z;
	elseif (y <= 6.4e+62)
		tmp = x;
	elseif (y <= 3.1e+195)
		tmp = -(y * (z / a));
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.7e-40], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[y, 6.4e+62], x, If[LessEqual[y, 3.1e+195], (-N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7e-40

   1. Initial program 85.1%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. associate-*l/ 64.1%

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

      3. *-commutative 64.1%

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

      4. distribute-rgt-neg-in 64.1%

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

      5. distribute-frac-neg 64.1%

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

   6. Simplified 64.1%

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

   if -2.7e-40 < y < 6.39999999999999968e62

   1. Initial program 98.3%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 62.9%

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

   if 6.39999999999999968e62 < y < 3.1000000000000002e195

   1. Initial program 83.0%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in x around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. associate-*r/ 84.7%

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

      3. distribute-rgt-neg-in 84.7%

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

      4. neg-sub0 84.7%

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

      5. div-sub 77.0%

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

      6. associate-+l- 77.0%

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

      7. neg-sub0 77.0%

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

      8. +-commutative 77.0%

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

      9. sub-neg 77.0%

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

      10. div-sub 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in t around 0 62.7%

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

      1. neg-mul-1 62.7%

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

      2. distribute-neg-frac 62.7%

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

   9. Simplified 62.7%

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

   if 3.1000000000000002e195 < y

   1. Initial program 78.9%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 46.3%

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

      1. associate-*l/ 67.3%

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

      2. *-commutative 67.3%

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

   6. Simplified 67.3%

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

      1. clear-num 67.3%

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

      2. div-inv 67.3%

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

   8. Applied egg-rr 67.3%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-40}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+62}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+195}:\\ \;\;\;\;-y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 5: 51.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-40}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+194}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.85e-40)
   (* (/ y a) (- z))
   (if (<= y 3.9e+61) x (if (<= y 6.2e+194) (/ (- y) (/ a z)) (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.85e-40) {
		tmp = (y / a) * -z;
	} else if (y <= 3.9e+61) {
		tmp = x;
	} else if (y <= 6.2e+194) {
		tmp = -y / (a / z);
	} 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 (y <= (-1.85d-40)) then
        tmp = (y / a) * -z
    else if (y <= 3.9d+61) then
        tmp = x
    else if (y <= 6.2d+194) then
        tmp = -y / (a / z)
    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 (y <= -1.85e-40) {
		tmp = (y / a) * -z;
	} else if (y <= 3.9e+61) {
		tmp = x;
	} else if (y <= 6.2e+194) {
		tmp = -y / (a / z);
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.85e-40:
		tmp = (y / a) * -z
	elif y <= 3.9e+61:
		tmp = x
	elif y <= 6.2e+194:
		tmp = -y / (a / z)
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.85e-40)
		tmp = Float64(Float64(y / a) * Float64(-z));
	elseif (y <= 3.9e+61)
		tmp = x;
	elseif (y <= 6.2e+194)
		tmp = Float64(Float64(-y) / Float64(a / z));
	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 (y <= -1.85e-40)
		tmp = (y / a) * -z;
	elseif (y <= 3.9e+61)
		tmp = x;
	elseif (y <= 6.2e+194)
		tmp = -y / (a / z);
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.85e-40], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[y, 3.9e+61], x, If[LessEqual[y, 6.2e+194], N[((-y) / N[(a / z), $MachinePrecision]), $MachinePrecision], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.84999999999999999e-40

   1. Initial program 85.1%

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

      1. associate-*l/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around inf 56.7%

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

      1. mul-1-neg 56.7%

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

      2. associate-*l/ 64.1%

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

      3. *-commutative 64.1%

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

      4. distribute-rgt-neg-in 64.1%

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

      5. distribute-frac-neg 64.1%

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

   6. Simplified 64.1%

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

   if -1.84999999999999999e-40 < y < 3.89999999999999987e61

   1. Initial program 98.3%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in x around inf 62.9%

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

   if 3.89999999999999987e61 < y < 6.1999999999999999e194

   1. Initial program 83.0%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in x around 0 70.4%

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

      1. mul-1-neg 70.4%

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

      2. associate-*r/ 84.7%

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

      3. distribute-rgt-neg-in 84.7%

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

      4. neg-sub0 84.7%

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

      5. div-sub 77.0%

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

      6. associate-+l- 77.0%

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

      7. neg-sub0 77.0%

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

      8. +-commutative 77.0%

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

      9. sub-neg 77.0%

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

      10. div-sub 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in t around 0 62.7%

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

      1. neg-mul-1 62.7%

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

      2. distribute-neg-frac 62.7%

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

   9. Simplified 62.7%

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

   10. Taylor expanded in y around 0 48.5%

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

       1. mul-1-neg 48.5%

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

       2. associate-/l* 62.8%

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

       3. distribute-neg-frac 62.8%

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

   12. Simplified 62.8%

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

   if 6.1999999999999999e194 < y

   1. Initial program 78.9%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around inf 46.3%

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

      1. associate-*l/ 67.3%

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

      2. *-commutative 67.3%

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

   6. Simplified 67.3%

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

      1. clear-num 67.3%

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

      2. div-inv 67.3%

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

   8. Applied egg-rr 67.3%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-40}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+61}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+194}:\\ \;\;\;\;\frac{-y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 6: 77.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-40} \lor \neg \left(y \leq 5 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.7e-40) (not (<= y 5e+58)))
   (* y (/ (- t z) a))
   (+ x (* (/ y a) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.7e-40) || !(y <= 5e+58)) {
		tmp = y * ((t - 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 ((y <= (-2.7d-40)) .or. (.not. (y <= 5d+58))) then
        tmp = y * ((t - 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 ((y <= -2.7e-40) || !(y <= 5e+58)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((y / a) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.7e-40) or not (y <= 5e+58):
		tmp = y * ((t - z) / a)
	else:
		tmp = x + ((y / a) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.7e-40) || !(y <= 5e+58))
		tmp = Float64(y * Float64(Float64(t - 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 ((y <= -2.7e-40) || ~((y <= 5e+58)))
		tmp = y * ((t - z) / a);
	else
		tmp = x + ((y / a) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.7e-40], N[Not[LessEqual[y, 5e+58]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7e-40 or 4.99999999999999986e58 < y

   1. Initial program 83.2%

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

      1. associate-*l/ 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in x around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. associate-*r/ 87.6%

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

      3. distribute-rgt-neg-in 87.6%

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

      4. neg-sub0 87.6%

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

      5. div-sub 85.4%

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

      6. associate-+l- 85.4%

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

      7. neg-sub0 85.4%

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

      8. +-commutative 85.4%

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

      9. sub-neg 85.4%

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

      10. div-sub 87.6%

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

   6. Simplified 87.6%

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

   if -2.7e-40 < y < 4.99999999999999986e58

   1. Initial program 99.1%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in z around 0 80.0%

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

      1. cancel-sign-sub-inv 80.0%

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

      2. metadata-eval 80.0%

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

      3. *-lft-identity 80.0%

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

      4. +-commutative 80.0%

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

      5. associate-*l/ 79.8%

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

      6. *-commutative 79.8%

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

   6. Simplified 79.8%

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

4. Final simplification 83.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-40} \lor \neg \left(y \leq 5 \cdot 10^{+58}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 7: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+42} \lor \neg \left(z \leq 4.2 \cdot 10^{+23}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.5e+42) (not (<= z 4.2e+23)))
   (- 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 <= -2.5e+42) || !(z <= 4.2e+23)) {
		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 <= (-2.5d+42)) .or. (.not. (z <= 4.2d+23))) 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 <= -2.5e+42) || !(z <= 4.2e+23)) {
		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 <= -2.5e+42) or not (z <= 4.2e+23):
		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 <= -2.5e+42) || !(z <= 4.2e+23))
		tmp = Float64(x - Float64(Float64(y / a) * z));
	else
		tmp = Float64(x + Float64(Float64(y / a) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.5e+42) || ~((z <= 4.2e+23)))
		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, -2.5e+42], N[Not[LessEqual[z, 4.2e+23]], $MachinePrecision]], N[(x - N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.50000000000000003e42 or 4.2000000000000003e23 < z

   1. Initial program 89.8%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in z around inf 84.0%

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

      1. associate-*l/ 89.5%

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

      2. *-commutative 89.5%

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

   6. Simplified 89.5%

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

   if -2.50000000000000003e42 < z < 4.2000000000000003e23

   1. Initial program 91.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in z around 0 82.3%

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

      1. cancel-sign-sub-inv 82.3%

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

      2. metadata-eval 82.3%

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

      3. *-lft-identity 82.3%

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

      4. +-commutative 82.3%

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

      5. associate-*l/ 90.5%

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

      6. *-commutative 90.5%

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

   6. Simplified 90.5%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+42} \lor \neg \left(z \leq 4.2 \cdot 10^{+23}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \end{array} \]

Alternative 8: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-74} \lor \neg \left(y \leq 1.05 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.6e-74) (not (<= y 1.05e+58))) (* (/ y a) t) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.6e-74) || !(y <= 1.05e+58)) {
		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 <= (-6.6d-74)) .or. (.not. (y <= 1.05d+58))) 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 <= -6.6e-74) || !(y <= 1.05e+58)) {
		tmp = (y / a) * t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.6e-74) or not (y <= 1.05e+58):
		tmp = (y / a) * t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.6e-74) || !(y <= 1.05e+58))
		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 <= -6.6e-74) || ~((y <= 1.05e+58)))
		tmp = (y / a) * t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.6e-74], N[Not[LessEqual[y, 1.05e+58]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.59999999999999992e-74 or 1.05000000000000006e58 < y

   1. Initial program 84.5%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around inf 34.5%

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

      1. associate-*l/ 42.8%

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

      2. *-commutative 42.8%

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

   6. Simplified 42.8%

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

   if -6.59999999999999992e-74 < y < 1.05000000000000006e58

   1. Initial program 99.0%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 66.9%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.6 \cdot 10^{-74} \lor \neg \left(y \leq 1.05 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 50.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -4.8e-74) (* (/ y a) t) (if (<= y 1.04e+58) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -4.8e-74) {
		tmp = (y / a) * t;
	} else if (y <= 1.04e+58) {
		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 (y <= (-4.8d-74)) then
        tmp = (y / a) * t
    else if (y <= 1.04d+58) 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 (y <= -4.8e-74) {
		tmp = (y / a) * t;
	} else if (y <= 1.04e+58) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -4.8e-74:
		tmp = (y / a) * t
	elif y <= 1.04e+58:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -4.8e-74)
		tmp = Float64(Float64(y / a) * t);
	elseif (y <= 1.04e+58)
		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 (y <= -4.8e-74)
		tmp = (y / a) * t;
	elseif (y <= 1.04e+58)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -4.8e-74], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[y, 1.04e+58], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.7999999999999998e-74

   1. Initial program 87.1%

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

      1. associate-*l/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in t around inf 34.9%

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

      1. associate-*l/ 43.3%

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

      2. *-commutative 43.3%

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

   6. Simplified 43.3%

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

   if -4.7999999999999998e-74 < y < 1.04e58

   1. Initial program 99.0%

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

      1. associate-*l/ 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 66.9%

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

   if 1.04e58 < y

   1. Initial program 80.7%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in t around inf 33.9%

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

      1. associate-*l/ 42.0%

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

      2. *-commutative 42.0%

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

   6. Simplified 42.0%

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

      1. clear-num 42.0%

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

      2. div-inv 42.0%

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

   8. Applied egg-rr 42.0%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-74}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]

Alternative 10: 93.4% 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 90.7%

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

   1. associate-*r/ 95.1%

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

3. Simplified 95.1%

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

4. Final simplification 95.1%

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

Alternative 11: 39.9% 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 90.7%

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

   1. associate-*l/ 96.9%

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

3. Simplified 96.9%

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

4. Taylor expanded in x around inf 37.4%

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

5. Final simplification 37.4%

   \[\leadsto x \]

Developer target: 99.1% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023195 
(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)))