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

Percentage Accurate: 93.1% → 98.7%

Time: 10.2s

Alternatives: 12

Speedup: 0.5×

• 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: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+253}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 (- INFINITY))
     (- x (* y (/ (- z t) a)))
     (if (<= t_1 1e+253) (+ x (/ (* y (- t z)) a)) (/ (- t z) (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x - (y * ((z - t) / a));
	} else if (t_1 <= 1e+253) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = (t - z) / (a / y);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x - (y * ((z - t) / a));
	} else if (t_1 <= 1e+253) {
		tmp = x + ((y * (t - z)) / a);
	} else {
		tmp = (t - z) / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x - (y * ((z - t) / a))
	elif t_1 <= 1e+253:
		tmp = x + ((y * (t - z)) / a)
	else:
		tmp = (t - z) / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / a)));
	elseif (t_1 <= 1e+253)
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = Float64(Float64(t - z) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x - (y * ((z - t) / a));
	elseif (t_1 <= 1e+253)
		tmp = x + ((y * (t - z)) / a);
	else
		tmp = (t - z) / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+253], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -inf.0

   1. Initial program 75.6%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a) < 9.9999999999999994e252

   1. Initial program 99.1%

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

   if 9.9999999999999994e252 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 90.0%

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

      1. associate-/l* 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in x around 0 90.0%

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

      1. associate-*r/ 90.0%

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

      2. neg-mul-1 90.0%

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

      3. *-commutative 90.0%

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

      4. distribute-lft-neg-in 90.0%

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

      5. associate-*r/ 100.0%

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

      6. *-commutative 100.0%

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

      7. neg-sub0 100.0%

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

      8. sub-neg 100.0%

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

      9. +-commutative 100.0%

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

      10. associate--r+ 100.0%

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

      11. neg-sub0 100.0%

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

      12. remove-double-neg 100.0%

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

   7. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. clear-num 100.0%

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

      3. un-div-inv 100.0%

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

   9. Applied egg-rr 100.0%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -\infty:\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 10^{+253}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-246} \lor \neg \left(a \leq 4.8 \cdot 10^{-195}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.9e-246) (not (<= a 4.8e-195)))
   (+ x (/ y (/ a (- t z))))
   (/ (- t z) (/ a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.9e-246) || !(a <= 4.8e-195)) {
		tmp = x + (y / (a / (t - z)));
	} else {
		tmp = (t - z) / (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 ((a <= (-3.9d-246)) .or. (.not. (a <= 4.8d-195))) then
        tmp = x + (y / (a / (t - z)))
    else
        tmp = (t - z) / (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 ((a <= -3.9e-246) || !(a <= 4.8e-195)) {
		tmp = x + (y / (a / (t - z)));
	} else {
		tmp = (t - z) / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.9e-246) or not (a <= 4.8e-195):
		tmp = x + (y / (a / (t - z)))
	else:
		tmp = (t - z) / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.9e-246) || !(a <= 4.8e-195))
		tmp = Float64(x + Float64(y / Float64(a / Float64(t - z))));
	else
		tmp = Float64(Float64(t - z) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.9e-246) || ~((a <= 4.8e-195)))
		tmp = x + (y / (a / (t - z)));
	else
		tmp = (t - z) / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.9e-246], N[Not[LessEqual[a, 4.8e-195]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.89999999999999979e-246 or 4.8e-195 < a

   1. Initial program 91.7%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

      1. clear-num 97.4%

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

      2. un-div-inv 98.2%

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

   6. Applied egg-rr 98.2%

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

   if -3.89999999999999979e-246 < a < 4.8e-195

   1. Initial program 97.9%

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

      1. associate-/l* 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in x around 0 88.9%

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

      1. associate-*r/ 88.9%

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

      2. neg-mul-1 88.9%

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

      3. *-commutative 88.9%

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

      4. distribute-lft-neg-in 88.9%

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

      5. associate-*r/ 90.3%

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

      6. *-commutative 90.3%

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

      7. neg-sub0 90.3%

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

      8. sub-neg 90.3%

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

      9. +-commutative 90.3%

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

      10. associate--r+ 90.3%

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

      11. neg-sub0 90.3%

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

      12. remove-double-neg 90.3%

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

   7. Simplified 90.3%

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

      1. *-commutative 90.3%

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

      2. clear-num 90.3%

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

      3. un-div-inv 90.4%

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

   9. Applied egg-rr 90.4%

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

4. Final simplification 96.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-246} \lor \neg \left(a \leq 4.8 \cdot 10^{-195}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{t - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-244} \lor \neg \left(a \leq 6.6 \cdot 10^{-195}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.9e-244) (not (<= a 6.6e-195)))
   (+ x (* y (/ (- t z) a)))
   (/ (- t z) (/ a y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.9e-244) || !(a <= 6.6e-195)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = (t - z) / (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 ((a <= (-1.9d-244)) .or. (.not. (a <= 6.6d-195))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = (t - z) / (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 ((a <= -1.9e-244) || !(a <= 6.6e-195)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = (t - z) / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.9e-244) or not (a <= 6.6e-195):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = (t - z) / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.9e-244) || !(a <= 6.6e-195))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(Float64(t - z) / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.9e-244) || ~((a <= 6.6e-195)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = (t - z) / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.9e-244], N[Not[LessEqual[a, 6.6e-195]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t - z), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e-244 or 6.6e-195 < a

   1. Initial program 91.7%

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

      1. associate-/l* 97.4%

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

   3. Simplified 97.4%

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

   if -1.9e-244 < a < 6.6e-195

   1. Initial program 97.9%

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

      1. associate-/l* 74.6%

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

   3. Simplified 74.6%

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

   5. Taylor expanded in x around 0 88.9%

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

      1. associate-*r/ 88.9%

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

      2. neg-mul-1 88.9%

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

      3. *-commutative 88.9%

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

      4. distribute-lft-neg-in 88.9%

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

      5. associate-*r/ 90.3%

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

      6. *-commutative 90.3%

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

      7. neg-sub0 90.3%

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

      8. sub-neg 90.3%

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

      9. +-commutative 90.3%

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

      10. associate--r+ 90.3%

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

      11. neg-sub0 90.3%

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

      12. remove-double-neg 90.3%

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

   7. Simplified 90.3%

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

      1. *-commutative 90.3%

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

      2. clear-num 90.3%

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

      3. un-div-inv 90.4%

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

   9. Applied egg-rr 90.4%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-244} \lor \neg \left(a \leq 6.6 \cdot 10^{-195}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - z}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+32} \lor \neg \left(z \leq 3.3 \cdot 10^{+92}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.85e+32) (not (<= z 3.3e+92)))
   (- x (/ y (/ a z)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.85e+32) || !(z <= 3.3e+92)) {
		tmp = x - (y / (a / 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 <= (-2.85d+32)) .or. (.not. (z <= 3.3d+92))) then
        tmp = x - (y / (a / 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 <= -2.85e+32) || !(z <= 3.3e+92)) {
		tmp = x - (y / (a / z));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.85e+32) or not (z <= 3.3e+92):
		tmp = x - (y / (a / z))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.85e+32) || !(z <= 3.3e+92))
		tmp = Float64(x - Float64(y / Float64(a / 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 ((z <= -2.85e+32) || ~((z <= 3.3e+92)))
		tmp = x - (y / (a / z));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.85e+32], N[Not[LessEqual[z, 3.3e+92]], $MachinePrecision]], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.85e32 or 3.29999999999999974e92 < z

   1. Initial program 89.7%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

      1. clear-num 93.9%

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

      2. un-div-inv 95.3%

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

   6. Applied egg-rr 95.3%

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

   7. Taylor expanded in z around inf 85.5%

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

   if -2.85e32 < z < 3.29999999999999974e92

   1. Initial program 95.9%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in z around 0 83.0%

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

      1. neg-mul-1 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in y around 0 87.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.85 \cdot 10^{+32} \lor \neg \left(z \leq 3.3 \cdot 10^{+92}\right):\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+33} \lor \neg \left(z \leq 1.85 \cdot 10^{+92}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e+33) (not (<= z 1.85e+92)))
   (- x (* y (/ z a)))
   (+ x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e+33) || !(z <= 1.85e+92)) {
		tmp = x - (y * (z / a));
	} 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 <= (-6.8d+33)) .or. (.not. (z <= 1.85d+92))) then
        tmp = x - (y * (z / a))
    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 <= -6.8e+33) || !(z <= 1.85e+92)) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e+33) or not (z <= 1.85e+92):
		tmp = x - (y * (z / a))
	else:
		tmp = x + ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e+33) || !(z <= 1.85e+92))
		tmp = Float64(x - Float64(y * Float64(z / a)));
	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 ((z <= -6.8e+33) || ~((z <= 1.85e+92)))
		tmp = x - (y * (z / a));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.8e+33], N[Not[LessEqual[z, 1.85e+92]], $MachinePrecision]], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7999999999999999e33 or 1.84999999999999999e92 < z

   1. Initial program 89.7%

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

      1. associate-/l* 93.9%

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

   3. Simplified 93.9%

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

   5. Taylor expanded in z around inf 80.6%

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

      1. associate-/l* 85.4%

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

   7. Simplified 85.4%

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

   if -6.7999999999999999e33 < z < 1.84999999999999999e92

   1. Initial program 95.9%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in z around 0 83.0%

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

      1. neg-mul-1 83.0%

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

   7. Simplified 83.0%

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

   8. Taylor expanded in y around 0 87.1%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+33} \lor \neg \left(z \leq 1.85 \cdot 10^{+92}\right):\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-46} \lor \neg \left(y \leq 5 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.15e-46) (not (<= y 5e-70)))
   (* (/ 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 <= -3.15e-46) || !(y <= 5e-70)) {
		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 <= (-3.15d-46)) .or. (.not. (y <= 5d-70))) 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 <= -3.15e-46) || !(y <= 5e-70)) {
		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 <= -3.15e-46) or not (y <= 5e-70):
		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 <= -3.15e-46) || !(y <= 5e-70))
		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 <= -3.15e-46) || ~((y <= 5e-70)))
		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, -3.15e-46], N[Not[LessEqual[y, 5e-70]], $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 < -3.15e-46 or 4.9999999999999998e-70 < y

   1. Initial program 88.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around 0 74.5%

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

      1. associate-*r/ 74.5%

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

      2. neg-mul-1 74.5%

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

      3. *-commutative 74.5%

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

      4. distribute-lft-neg-in 74.5%

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

      5. associate-*r/ 85.2%

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

      6. *-commutative 85.2%

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

      7. neg-sub0 85.2%

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

      8. sub-neg 85.2%

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

      9. +-commutative 85.2%

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

      10. associate--r+ 85.2%

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

      11. neg-sub0 85.2%

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

      12. remove-double-neg 85.2%

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

   7. Simplified 85.2%

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

   if -3.15e-46 < y < 4.9999999999999998e-70

   1. Initial program 98.8%

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

      1. associate-/l* 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in z around 0 69.6%

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

      1. neg-mul-1 69.6%

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

   7. Simplified 69.6%

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

   8. Taylor expanded in y around 0 81.2%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-46} \lor \neg \left(y \leq 5 \cdot 10^{-70}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-187} \lor \neg \left(y \leq 6.6 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.5e-187) (not (<= y 6.6e-105))) (* (/ y a) (- t z)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.5e-187) || !(y <= 6.6e-105)) {
		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 <= (-5.5d-187)) .or. (.not. (y <= 6.6d-105))) 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 <= -5.5e-187) || !(y <= 6.6e-105)) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.5e-187) or not (y <= 6.6e-105):
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.5e-187) || !(y <= 6.6e-105))
		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 <= -5.5e-187) || ~((y <= 6.6e-105)))
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.5e-187], N[Not[LessEqual[y, 6.6e-105]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.50000000000000033e-187 or 6.5999999999999997e-105 < y

   1. Initial program 91.5%

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

      1. associate-/l* 95.9%

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

   3. Simplified 95.9%

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

   5. Taylor expanded in x around 0 73.1%

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

      1. associate-*r/ 73.1%

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

      2. neg-mul-1 73.1%

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

      3. *-commutative 73.1%

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

      4. distribute-lft-neg-in 73.1%

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

      5. associate-*r/ 80.2%

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

      6. *-commutative 80.2%

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

      7. neg-sub0 80.2%

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

      8. sub-neg 80.2%

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

      9. +-commutative 80.2%

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

      10. associate--r+ 80.2%

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

      11. neg-sub0 80.2%

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

      12. remove-double-neg 80.2%

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

   7. Simplified 80.2%

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

   if -5.50000000000000033e-187 < y < 6.5999999999999997e-105

   1. Initial program 98.1%

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

      1. associate-/l* 80.8%

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

   3. Simplified 80.8%

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

   5. Taylor expanded in x around inf 68.2%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-187} \lor \neg \left(y \leq 6.6 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+25} \lor \neg \left(z \leq 1.7 \cdot 10^{+26}\right):\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.6e+25) (not (<= z 1.7e+26)))
   (* z (/ (- y) a))
   (* t (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.6e+25) || !(z <= 1.7e+26)) {
		tmp = z * (-y / a);
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.6d+25)) .or. (.not. (z <= 1.7d+26))) then
        tmp = z * (-y / a)
    else
        tmp = t * (y / 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 <= -1.6e+25) || !(z <= 1.7e+26)) {
		tmp = z * (-y / a);
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.6e+25) or not (z <= 1.7e+26):
		tmp = z * (-y / a)
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.6e+25) || !(z <= 1.7e+26))
		tmp = Float64(z * Float64(Float64(-y) / a));
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.6e+25) || ~((z <= 1.7e+26)))
		tmp = z * (-y / a);
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.6e+25], N[Not[LessEqual[z, 1.7e+26]], $MachinePrecision]], N[(z * N[((-y) / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6e25 or 1.7000000000000001e26 < z

   1. Initial program 90.3%

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

      1. associate-/l* 91.0%

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

   3. Simplified 91.0%

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

   5. Taylor expanded in x around 0 64.3%

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

      1. associate-*r/ 64.3%

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

      2. neg-mul-1 64.3%

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

      3. *-commutative 64.3%

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

      4. distribute-lft-neg-in 64.3%

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

      5. associate-*r/ 72.7%

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

      6. *-commutative 72.7%

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

      7. neg-sub0 72.7%

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

      8. sub-neg 72.7%

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

      9. +-commutative 72.7%

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

      10. associate--r+ 72.7%

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

      11. neg-sub0 72.7%

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

      12. remove-double-neg 72.7%

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

   7. Simplified 72.7%

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

   8. Taylor expanded in t around 0 59.6%

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

      1. neg-mul-1 59.6%

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

   10. Simplified 59.6%

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

   if -1.6e25 < z < 1.7000000000000001e26

   1. Initial program 96.1%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around 0 60.0%

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

      1. associate-*r/ 60.0%

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

      2. neg-mul-1 60.0%

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

      3. *-commutative 60.0%

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

      4. distribute-lft-neg-in 60.0%

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

      5. associate-*r/ 62.1%

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

      6. *-commutative 62.1%

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

      7. neg-sub0 62.1%

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

      8. sub-neg 62.1%

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

      9. +-commutative 62.1%

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

      10. associate--r+ 62.1%

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

      11. neg-sub0 62.1%

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

      12. remove-double-neg 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in t around inf 56.3%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+25} \lor \neg \left(z \leq 1.7 \cdot 10^{+26}\right):\\ \;\;\;\;z \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+25} \lor \neg \left(z \leq 1.45 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.75e+25) (not (<= z 1.45e+93)))
   (* y (/ (- z) a))
   (* t (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e+25) || !(z <= 1.45e+93)) {
		tmp = y * (-z / a);
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-2.75d+25)) .or. (.not. (z <= 1.45d+93))) then
        tmp = y * (-z / a)
    else
        tmp = t * (y / 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 <= -2.75e+25) || !(z <= 1.45e+93)) {
		tmp = y * (-z / a);
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.75e+25) or not (z <= 1.45e+93):
		tmp = y * (-z / a)
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.75e+25) || !(z <= 1.45e+93))
		tmp = Float64(y * Float64(Float64(-z) / a));
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -2.75e+25) || ~((z <= 1.45e+93)))
		tmp = y * (-z / a);
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.75e+25], N[Not[LessEqual[z, 1.45e+93]], $MachinePrecision]], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.75000000000000009e25 or 1.4499999999999999e93 < z

   1. Initial program 89.8%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in z around inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. associate-/l* 60.6%

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

      3. distribute-rgt-neg-in 60.6%

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

      4. distribute-frac-neg2 60.6%

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

   7. Simplified 60.6%

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

   if -2.75000000000000009e25 < z < 1.4499999999999999e93

   1. Initial program 95.8%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around 0 59.8%

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

      1. associate-*r/ 59.8%

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

      2. neg-mul-1 59.8%

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

      3. *-commutative 59.8%

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

      4. distribute-lft-neg-in 59.8%

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

      5. associate-*r/ 62.3%

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

      6. *-commutative 62.3%

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

      7. neg-sub0 62.3%

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

      8. sub-neg 62.3%

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

      9. +-commutative 62.3%

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

      10. associate--r+ 62.3%

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

      11. neg-sub0 62.3%

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

      12. remove-double-neg 62.3%

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

   7. Simplified 62.3%

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

   8. Taylor expanded in t around inf 53.2%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+25} \lor \neg \left(z \leq 1.45 \cdot 10^{+93}\right):\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-68} \lor \neg \left(t \leq 7.2 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.2e-68) (not (<= t 7.2e-26))) (* y (/ t a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.2e-68) || !(t <= 7.2e-26)) {
		tmp = y * (t / 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 ((t <= (-5.2d-68)) .or. (.not. (t <= 7.2d-26))) then
        tmp = y * (t / 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 ((t <= -5.2e-68) || !(t <= 7.2e-26)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.2e-68) or not (t <= 7.2e-26):
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.2e-68) || !(t <= 7.2e-26))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.2e-68) || ~((t <= 7.2e-26)))
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.2e-68], N[Not[LessEqual[t, 7.2e-26]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -5.1999999999999996e-68 or 7.2000000000000003e-26 < t

   1. Initial program 92.1%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in t around inf 56.6%

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

      1. *-commutative 56.6%

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

      2. associate-/l* 53.5%

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

   7. Simplified 53.5%

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

   if -5.1999999999999996e-68 < t < 7.2000000000000003e-26

   1. Initial program 94.5%

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

      1. associate-/l* 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 48.6%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{-68} \lor \neg \left(t \leq 7.2 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e-13) x (if (<= a 1.7e+61) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e-13) {
		tmp = x;
	} else if (a <= 1.7e+61) {
		tmp = t * (y / 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 (a <= (-1.9d-13)) then
        tmp = x
    else if (a <= 1.7d+61) then
        tmp = t * (y / 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 (a <= -1.9e-13) {
		tmp = x;
	} else if (a <= 1.7e+61) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e-13:
		tmp = x
	elif a <= 1.7e+61:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e-13)
		tmp = x;
	elseif (a <= 1.7e+61)
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.9e-13)
		tmp = x;
	elseif (a <= 1.7e+61)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e-13], x, If[LessEqual[a, 1.7e+61], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e-13 or 1.70000000000000013e61 < a

   1. Initial program 85.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 57.9%

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

   if -1.9e-13 < a < 1.70000000000000013e61

   1. Initial program 98.0%

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

      1. associate-/l* 87.1%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in x around 0 83.5%

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

      1. associate-*r/ 83.5%

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

      2. neg-mul-1 83.5%

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

      3. *-commutative 83.5%

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

      4. distribute-lft-neg-in 83.5%

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

      5. associate-*r/ 85.2%

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

      6. *-commutative 85.2%

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

      7. neg-sub0 85.2%

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

      8. sub-neg 85.2%

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

      9. +-commutative 85.2%

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

      10. associate--r+ 85.2%

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

      11. neg-sub0 85.2%

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

      12. remove-double-neg 85.2%

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

   7. Simplified 85.2%

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

   8. Taylor expanded in t around inf 54.6%

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

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+61}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.2% 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 93.2%

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

   1. associate-/l* 92.1%

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

3. Simplified 92.1%

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

5. Taylor expanded in x around inf 32.1%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.2% 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 2024146 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

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

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