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

Percentage Accurate: 93.1% → 98.7%

Time: 9.8s

Alternatives: 13

Speedup: 1.0×

• 25.2% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+98} \lor \neg \left(a \leq 3.5 \cdot 10^{-78}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -7.5e+98) (not (<= a 3.5e-78)))
   (+ x (* y (/ (- t z) a)))
   (+ x (/ (* y (- t z)) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -7.5e+98) || !(a <= 3.5e-78)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * (t - z)) / 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 ((a <= (-7.5d+98)) .or. (.not. (a <= 3.5d-78))) then
        tmp = x + (y * ((t - z) / a))
    else
        tmp = x + ((y * (t - z)) / 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 ((a <= -7.5e+98) || !(a <= 3.5e-78)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((y * (t - z)) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -7.5e+98) or not (a <= 3.5e-78):
		tmp = x + (y * ((t - z) / a))
	else:
		tmp = x + ((y * (t - z)) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -7.5e+98) || !(a <= 3.5e-78))
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	else
		tmp = Float64(x + Float64(Float64(y * Float64(t - z)) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -7.5e+98) || ~((a <= 3.5e-78)))
		tmp = x + (y * ((t - z) / a));
	else
		tmp = x + ((y * (t - z)) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -7.5e+98], N[Not[LessEqual[a, 3.5e-78]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -7.50000000000000036e98 or 3.4999999999999999e-78 < a

   1. Initial program 88.7%

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

   if -7.50000000000000036e98 < a < 3.4999999999999999e-78

   1. Initial program 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+98} \lor \neg \left(a \leq 3.5 \cdot 10^{-78}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(t - z\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 48.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -7.2e-43)
   x
   (if (<= x 3.4e-234) (* y (/ (- z) a)) (if (<= x 4.5e+23) (/ t (/ a y)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.2e-43) {
		tmp = x;
	} else if (x <= 3.4e-234) {
		tmp = y * (-z / a);
	} else if (x <= 4.5e+23) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-7.2d-43)) then
        tmp = x
    else if (x <= 3.4d-234) then
        tmp = y * (-z / a)
    else if (x <= 4.5d+23) then
        tmp = t / (a / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -7.2e-43) {
		tmp = x;
	} else if (x <= 3.4e-234) {
		tmp = y * (-z / a);
	} else if (x <= 4.5e+23) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -7.2e-43:
		tmp = x
	elif x <= 3.4e-234:
		tmp = y * (-z / a)
	elif x <= 4.5e+23:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -7.2e-43)
		tmp = x;
	elseif (x <= 3.4e-234)
		tmp = Float64(y * Float64(Float64(-z) / a));
	elseif (x <= 4.5e+23)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -7.2e-43)
		tmp = x;
	elseif (x <= 3.4e-234)
		tmp = y * (-z / a);
	elseif (x <= 4.5e+23)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -7.2e-43], x, If[LessEqual[x, 3.4e-234], N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.5e+23], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.1999999999999998e-43 or 4.49999999999999979e23 < x

   1. Initial program 91.5%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in x around inf 64.2%

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

   if -7.1999999999999998e-43 < x < 3.39999999999999986e-234

   1. Initial program 96.0%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. associate-/l* 53.6%

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

      3. distribute-rgt-neg-in 53.6%

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

      4. distribute-neg-frac 53.6%

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

   7. Simplified 53.6%

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

   if 3.39999999999999986e-234 < x < 4.49999999999999979e23

   1. Initial program 96.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 78.2%

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

      1. mul-1-neg 78.2%

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

      2. distribute-frac-neg2 78.2%

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

      3. *-commutative 78.2%

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

      4. associate-/l* 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in z around 0 52.5%

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

      1. associate-*r/ 54.0%

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

   10. Simplified 54.0%

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

       1. clear-num 54.0%

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

       2. un-div-inv 54.0%

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

   12. Applied egg-rr 54.0%

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

4. Final simplification 58.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-234}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.36e-42)
   x
   (if (<= x 2.8e-235) (* (/ y a) (- z)) (if (<= x 3.1e+31) (/ t (/ a y)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.36e-42) {
		tmp = x;
	} else if (x <= 2.8e-235) {
		tmp = (y / a) * -z;
	} else if (x <= 3.1e+31) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.36d-42)) then
        tmp = x
    else if (x <= 2.8d-235) then
        tmp = (y / a) * -z
    else if (x <= 3.1d+31) then
        tmp = t / (a / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.36e-42) {
		tmp = x;
	} else if (x <= 2.8e-235) {
		tmp = (y / a) * -z;
	} else if (x <= 3.1e+31) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.36e-42:
		tmp = x
	elif x <= 2.8e-235:
		tmp = (y / a) * -z
	elif x <= 3.1e+31:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.36e-42)
		tmp = x;
	elseif (x <= 2.8e-235)
		tmp = Float64(Float64(y / a) * Float64(-z));
	elseif (x <= 3.1e+31)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.36e-42)
		tmp = x;
	elseif (x <= 2.8e-235)
		tmp = (y / a) * -z;
	elseif (x <= 3.1e+31)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.36e-42], x, If[LessEqual[x, 2.8e-235], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[x, 3.1e+31], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.36e-42 or 3.1000000000000002e31 < x

   1. Initial program 91.5%

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

      1. associate-/l* 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in x around inf 64.2%

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

   if -1.36e-42 < x < 2.79999999999999995e-235

   1. Initial program 96.0%

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

      1. associate-/l* 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in z around inf 52.3%

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

      1. mul-1-neg 52.3%

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

      2. associate-/l* 53.6%

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

      3. distribute-rgt-neg-in 53.6%

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

      4. distribute-neg-frac 53.6%

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

   7. Simplified 53.6%

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

   8. Taylor expanded in y around 0 52.3%

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

      1. mul-1-neg 52.3%

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

      2. associate-*l/ 56.0%

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

      3. *-commutative 56.0%

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

      4. distribute-lft-neg-in 56.0%

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

   10. Simplified 56.0%

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

   if 2.79999999999999995e-235 < x < 3.1000000000000002e31

   1. Initial program 96.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 78.2%

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

      1. mul-1-neg 78.2%

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

      2. distribute-frac-neg2 78.2%

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

      3. *-commutative 78.2%

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

      4. associate-/l* 76.4%

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

   7. Simplified 76.4%

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

   8. Taylor expanded in z around 0 52.5%

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

      1. associate-*r/ 54.0%

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

   10. Simplified 54.0%

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

       1. clear-num 54.0%

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

       2. un-div-inv 54.0%

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

   12. Applied egg-rr 54.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-42}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-235}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+31}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-26} \lor \neg \left(a \leq 2 \cdot 10^{+22}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.4e-26) (not (<= a 2e+22)))
   (+ x (* y (/ t a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.4e-26) || !(a <= 2e+22)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.4d-26)) .or. (.not. (a <= 2d+22))) then
        tmp = x + (y * (t / a))
    else
        tmp = (y / a) * (t - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.4e-26) || !(a <= 2e+22)) {
		tmp = x + (y * (t / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.4e-26) or not (a <= 2e+22):
		tmp = x + (y * (t / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.4e-26) || !(a <= 2e+22))
		tmp = Float64(x + Float64(y * Float64(t / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.4e-26) || ~((a <= 2e+22)))
		tmp = x + (y * (t / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.4e-26], N[Not[LessEqual[a, 2e+22]], $MachinePrecision]], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.4000000000000001e-26 or 2e22 < a

   1. Initial program 88.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around 0 75.7%

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

      1. associate-*r/ 75.7%

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

      2. mul-1-neg 75.7%

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

      3. distribute-lft-neg-out 75.7%

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

      4. *-commutative 75.7%

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

   7. Simplified 75.7%

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

      1. sub-neg 75.7%

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

      2. +-commutative 75.7%

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

      3. associate-/l* 81.7%

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

      4. distribute-rgt-neg-in 81.7%

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

      5. add-sqr-sqrt 45.6%

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

      6. sqrt-unprod 61.0%

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

      7. sqr-neg 61.0%

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

      8. sqrt-unprod 27.6%

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

      9. add-sqr-sqrt 62.8%

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

      10. distribute-frac-neg 62.8%

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

      11. add-sqr-sqrt 35.2%

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

      12. sqrt-unprod 60.9%

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

      13. sqr-neg 60.9%

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

      14. sqrt-unprod 36.1%

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

      15. add-sqr-sqrt 81.7%

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

   9. Applied egg-rr 81.7%

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

   if -1.4000000000000001e-26 < a < 2e22

   1. Initial program 99.9%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

      1. clear-num 88.0%

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

      2. un-div-inv 90.1%

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

   6. Applied egg-rr 90.1%

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

   7. Taylor expanded in x around 0 83.7%

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

      1. mul-1-neg 83.7%

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

      2. associate-*r/ 74.3%

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

      3. distribute-rgt-neg-out 74.3%

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

      4. neg-sub0 74.3%

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

      5. div-sub 71.1%

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

      6. associate--r- 71.1%

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

      7. neg-sub0 71.1%

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

      8. +-commutative 71.1%

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

      9. sub-neg 71.1%

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

      10. distribute-lft-out-- 64.8%

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

      11. associate-*r/ 70.0%

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

      12. associate-*l/ 66.1%

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

      13. associate-*r/ 71.2%

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

      14. associate-*l/ 69.6%

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

      15. distribute-lft-out-- 80.8%

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

   9. Simplified 80.8%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-26} \lor \neg \left(a \leq 2 \cdot 10^{+22}\right):\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+32} \lor \neg \left(t \leq 7 \cdot 10^{-7}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.95e+32) (not (<= t 7e-7)))
   (+ x (* t (/ y a)))
   (- x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.95e+32) || !(t <= 7e-7)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y * (z / 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 ((t <= (-1.95d+32)) .or. (.not. (t <= 7d-7))) then
        tmp = x + (t * (y / a))
    else
        tmp = x - (y * (z / 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 ((t <= -1.95e+32) || !(t <= 7e-7)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.95e+32) or not (t <= 7e-7):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.95e+32) || !(t <= 7e-7))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.95e+32) || ~((t <= 7e-7)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.95e+32], N[Not[LessEqual[t, 7e-7]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.95e32 or 6.99999999999999968e-7 < t

   1. Initial program 91.5%

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

      1. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in z around 0 82.2%

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

      1. mul-1-neg 82.2%

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

      2. associate-/l* 86.5%

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

      3. distribute-rgt-neg-in 86.5%

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

      4. distribute-neg-frac2 86.5%

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

   7. Simplified 86.5%

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

   if -1.95e32 < t < 6.99999999999999968e-7

   1. Initial program 96.0%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around inf 88.8%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+32} \lor \neg \left(t \leq 7 \cdot 10^{-7}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+55}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.9e+115) x (if (<= a 1.15e+55) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.9e+115) {
		tmp = x;
	} else if (a <= 1.15e+55) {
		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 (a <= (-1.9d+115)) then
        tmp = x
    else if (a <= 1.15d+55) 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 (a <= -1.9e+115) {
		tmp = x;
	} else if (a <= 1.15e+55) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.9e+115:
		tmp = x
	elif a <= 1.15e+55:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.9e+115)
		tmp = x;
	elseif (a <= 1.15e+55)
		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 (a <= -1.9e+115)
		tmp = x;
	elseif (a <= 1.15e+55)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.9e+115], x, If[LessEqual[a, 1.15e+55], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.9e115 or 1.14999999999999994e55 < a

   1. Initial program 86.6%

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

   5. Taylor expanded in x around inf 69.3%

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

   if -1.9e115 < a < 1.14999999999999994e55

   1. Initial program 99.2%

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

      1. associate-/l* 89.8%

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

   3. Simplified 89.8%

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

      1. clear-num 89.8%

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

      2. un-div-inv 91.5%

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

   6. Applied egg-rr 91.5%

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

   7. Taylor expanded in x around 0 80.6%

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

      1. mul-1-neg 80.6%

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

      2. associate-*r/ 73.2%

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

      3. distribute-rgt-neg-out 73.2%

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

      4. neg-sub0 73.2%

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

      5. div-sub 70.4%

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

      6. associate--r- 70.4%

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

      7. neg-sub0 70.4%

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

      8. +-commutative 70.4%

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

      9. sub-neg 70.4%

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

      10. distribute-lft-out-- 64.4%

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

      11. associate-*r/ 68.2%

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

      12. associate-*l/ 65.5%

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

      13. associate-*r/ 69.9%

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

      14. associate-*l/ 68.4%

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

      15. distribute-lft-out-- 78.7%

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

   9. Simplified 78.7%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.9 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.15 \cdot 10^{+55}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.2e+115)
   x
   (if (<= a 9.5e+23) (* (/ y a) (- t z)) (+ x (/ (* y t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.2e+115) {
		tmp = x;
	} else if (a <= 9.5e+23) {
		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 (a <= (-1.2d+115)) then
        tmp = x
    else if (a <= 9.5d+23) 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 (a <= -1.2e+115) {
		tmp = x;
	} else if (a <= 9.5e+23) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.2e+115:
		tmp = x
	elif a <= 9.5e+23:
		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 (a <= -1.2e+115)
		tmp = x;
	elseif (a <= 9.5e+23)
		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 (a <= -1.2e+115)
		tmp = x;
	elseif (a <= 9.5e+23)
		tmp = (y / a) * (t - z);
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.2e+115], x, If[LessEqual[a, 9.5e+23], 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 3 regimes

2. if a < -1.2e115

   1. Initial program 79.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 71.2%

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

   if -1.2e115 < a < 9.50000000000000038e23

   1. Initial program 99.2%

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

      1. associate-/l* 89.5%

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

   3. Simplified 89.5%

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

      1. clear-num 89.5%

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

      2. un-div-inv 91.3%

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

   6. Applied egg-rr 91.3%

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

   7. Taylor expanded in x around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. associate-*r/ 73.1%

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

      3. distribute-rgt-neg-out 73.1%

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

      4. neg-sub0 73.1%

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

      5. div-sub 70.2%

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

      6. associate--r- 70.2%

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

      7. neg-sub0 70.2%

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

      8. +-commutative 70.2%

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

      9. sub-neg 70.2%

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

      10. distribute-lft-out-- 64.1%

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

      11. associate-*r/ 68.0%

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

      12. associate-*l/ 65.2%

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

      13. associate-*r/ 69.7%

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

      14. associate-*l/ 68.2%

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

      15. distribute-lft-out-- 78.7%

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

   9. Simplified 78.7%

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

   if 9.50000000000000038e23 < a

   1. Initial program 92.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around 0 86.7%

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

      1. associate-*r/ 86.7%

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

      2. mul-1-neg 86.7%

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

      3. distribute-lft-neg-out 86.7%

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

      4. *-commutative 86.7%

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

   7. Simplified 86.7%

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

   8. Taylor expanded in y around 0 86.7%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.2 \cdot 10^{+115}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+32}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e+32)
   (+ x (* y (/ t a)))
   (if (<= t 7.5e-7) (- x (* y (/ z a))) (+ x (/ (* y t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+32) {
		tmp = x + (y * (t / a));
	} else if (t <= 7.5e-7) {
		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 (t <= (-6.5d+32)) then
        tmp = x + (y * (t / a))
    else if (t <= 7.5d-7) 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 (t <= -6.5e+32) {
		tmp = x + (y * (t / a));
	} else if (t <= 7.5e-7) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e+32:
		tmp = x + (y * (t / a))
	elif t <= 7.5e-7:
		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 (t <= -6.5e+32)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (t <= 7.5e-7)
		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 (t <= -6.5e+32)
		tmp = x + (y * (t / a));
	elseif (t <= 7.5e-7)
		tmp = x - (y * (z / a));
	else
		tmp = x + ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+32], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-7], 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 3 regimes

2. if t < -6.4999999999999994e32

   1. Initial program 90.0%

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

      1. associate-/l* 95.0%

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

   3. Simplified 95.0%

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

   5. Taylor expanded in z around 0 79.6%

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

      1. associate-*r/ 79.6%

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

      2. mul-1-neg 79.6%

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

      3. distribute-lft-neg-out 79.6%

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

      4. *-commutative 79.6%

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

   7. Simplified 79.6%

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

      1. sub-neg 79.6%

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

      2. +-commutative 79.6%

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

      3. associate-/l* 81.5%

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

      4. distribute-rgt-neg-in 81.5%

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

      5. add-sqr-sqrt 81.4%

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

      6. sqrt-unprod 57.6%

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

      7. sqr-neg 57.6%

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

      8. sqrt-unprod 0.0%

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

      9. add-sqr-sqrt 26.8%

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

      10. distribute-frac-neg 26.8%

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

      11. add-sqr-sqrt 26.8%

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

      12. sqrt-unprod 15.1%

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

      13. sqr-neg 15.1%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 81.5%

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

   9. Applied egg-rr 81.5%

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

   if -6.4999999999999994e32 < t < 7.5000000000000002e-7

   1. Initial program 96.0%

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

      1. associate-/l* 96.5%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in z around inf 88.8%

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

      1. associate-/l* 89.3%

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

   7. Simplified 89.3%

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

   if 7.5000000000000002e-7 < t

   1. Initial program 93.0%

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

      1. associate-/l* 86.4%

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

   3. Simplified 86.4%

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

   5. Taylor expanded in z around 0 84.9%

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

      1. associate-*r/ 84.9%

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

      2. mul-1-neg 84.9%

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

      3. distribute-lft-neg-out 84.9%

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

      4. *-commutative 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in y around 0 84.9%

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

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+32}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-7}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 51.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.7e-82) x (if (<= a 1.45e+47) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.7e-82) {
		tmp = x;
	} else if (a <= 1.45e+47) {
		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 <= (-2.7d-82)) then
        tmp = x
    else if (a <= 1.45d+47) 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 <= -2.7e-82) {
		tmp = x;
	} else if (a <= 1.45e+47) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.7e-82:
		tmp = x
	elif a <= 1.45e+47:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.7e-82)
		tmp = x;
	elseif (a <= 1.45e+47)
		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 <= -2.7e-82)
		tmp = x;
	elseif (a <= 1.45e+47)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.7e-82], x, If[LessEqual[a, 1.45e+47], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -2.7000000000000001e-82 or 1.4499999999999999e47 < a

   1. Initial program 89.1%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around inf 60.9%

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

   if -2.7000000000000001e-82 < a < 1.4499999999999999e47

   1. Initial program 99.9%

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

      1. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. distribute-frac-neg2 85.6%

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

      3. *-commutative 85.6%

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

      4. associate-/l* 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in z around 0 48.8%

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

      1. associate-*r/ 49.6%

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

   10. Simplified 49.6%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.7 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+47}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+42}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.8e-82) x (if (<= a 1.08e+42) (/ t (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e-82) {
		tmp = x;
	} else if (a <= 1.08e+42) {
		tmp = t / (a / y);
	} 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 <= (-3.8d-82)) then
        tmp = x
    else if (a <= 1.08d+42) then
        tmp = t / (a / y)
    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 <= -3.8e-82) {
		tmp = x;
	} else if (a <= 1.08e+42) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.8e-82:
		tmp = x
	elif a <= 1.08e+42:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.8e-82)
		tmp = x;
	elseif (a <= 1.08e+42)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.8e-82)
		tmp = x;
	elseif (a <= 1.08e+42)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.8e-82], x, If[LessEqual[a, 1.08e+42], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.8000000000000002e-82 or 1.08e42 < a

   1. Initial program 89.1%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in x around inf 60.9%

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

   if -3.8000000000000002e-82 < a < 1.08e42

   1. Initial program 99.9%

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

      1. associate-/l* 88.7%

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

   3. Simplified 88.7%

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

   5. Taylor expanded in x around 0 85.6%

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

      1. mul-1-neg 85.6%

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

      2. distribute-frac-neg2 85.6%

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

      3. *-commutative 85.6%

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

      4. associate-/l* 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in z around 0 48.8%

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

      1. associate-*r/ 49.6%

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

   10. Simplified 49.6%

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

       1. clear-num 49.6%

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

       2. un-div-inv 49.6%

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

   12. Applied egg-rr 49.6%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{-82}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.08 \cdot 10^{+42}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.3% 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 94.0%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. Final simplification 94.0%

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

Alternative 12: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.0%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. 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 94.9%

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

6. Applied egg-rr 94.9%

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

7. Final simplification 94.9%

   \[\leadsto x + \frac{y}{\frac{a}{t - z}} \]
8. Add Preprocessing

Alternative 13: 40.0% 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 94.0%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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 x around inf 40.1%

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

6. Final simplification 40.1%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 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 2024089 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (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)))