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

Percentage Accurate: 93.1% → 97.5%

Time: 15.1s

Alternatives: 15

Speedup: 1.0×

• 24.8% 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: 97.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.9 \cdot 10^{-108}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -5.9e-108) (fma y (/ (- z t) a) x) (+ x (/ (- z t) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -5.9e-108) {
		tmp = fma(y, ((z - t) / a), x);
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -5.9e-108)
		tmp = fma(y, Float64(Float64(z - t) / a), x);
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -5.9e-108], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.89999999999999965e-108

   1. Initial program 94.6%

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

      1. +-commutative 94.6%

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

      2. associate-/l* 99.9%

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

      3. fma-define 99.9%

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

   3. Simplified 99.9%

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

   if -5.89999999999999965e-108 < a

   1. Initial program 92.6%

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

      1. clear-num 92.6%

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

      2. inv-pow 92.6%

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

      3. associate-/r* 99.2%

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

   4. Applied egg-rr 99.2%

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

      1. unpow-1 99.2%

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

      2. clear-num 99.3%

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

   6. Applied egg-rr 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.9 \cdot 10^{-108}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z - t}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+80} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+132}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -1e+80) (not (<= t_1 5e+132)))
     (* (- z t) (/ y a))
     (- x (/ (* y t) a)))))

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 <= -1e+80) || !(t_1 <= 5e+132)) {
		tmp = (z - t) * (y / 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) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if ((t_1 <= (-1d+80)) .or. (.not. (t_1 <= 5d+132))) then
        tmp = (z - t) * (y / 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 t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -1e+80) || !(t_1 <= 5e+132)) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x - ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if (t_1 <= -1e+80) or not (t_1 <= 5e+132):
		tmp = (z - t) * (y / a)
	else:
		tmp = x - ((y * t) / a)
	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 <= -1e+80) || !(t_1 <= 5e+132))
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x - Float64(Float64(y * t) / a));
	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 <= -1e+80) || ~((t_1 <= 5e+132)))
		tmp = (z - t) * (y / a);
	else
		tmp = x - ((y * t) / a);
	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[Or[LessEqual[t$95$1, -1e+80], N[Not[LessEqual[t$95$1, 5e+132]], $MachinePrecision]], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -1e80 or 5.0000000000000001e132 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0 83.9%

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

      1. *-commutative 83.9%

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

      2. associate-*r/ 92.7%

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

      3. *-commutative 92.7%

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

   5. Applied egg-rr 92.7%

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

   if -1e80 < (/.f64 (*.f64 y (-.f64 z t)) a) < 5.0000000000000001e132

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 89.8%

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

      1. mul-1-neg 89.8%

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

      2. unsub-neg 89.8%

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

      3. associate-/l* 89.1%

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

   5. Simplified 89.1%

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

      1. *-commutative 89.1%

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

      2. associate-*l/ 89.8%

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

   7. Applied egg-rr 89.8%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -1 \cdot 10^{+80} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 5 \cdot 10^{+132}\right):\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;x \leq 370:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.1e-54)
   x
   (if (<= x 3.8e-114) (* t (/ (- y) a)) (if (<= x 370.0) (/ z (/ a y)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.1e-54) {
		tmp = x;
	} else if (x <= 3.8e-114) {
		tmp = t * (-y / a);
	} else if (x <= 370.0) {
		tmp = z / (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 <= (-2.1d-54)) then
        tmp = x
    else if (x <= 3.8d-114) then
        tmp = t * (-y / a)
    else if (x <= 370.0d0) then
        tmp = z / (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 <= -2.1e-54) {
		tmp = x;
	} else if (x <= 3.8e-114) {
		tmp = t * (-y / a);
	} else if (x <= 370.0) {
		tmp = z / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.1e-54:
		tmp = x
	elif x <= 3.8e-114:
		tmp = t * (-y / a)
	elif x <= 370.0:
		tmp = z / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.1e-54)
		tmp = x;
	elseif (x <= 3.8e-114)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (x <= 370.0)
		tmp = Float64(z / 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 <= -2.1e-54)
		tmp = x;
	elseif (x <= 3.8e-114)
		tmp = t * (-y / a);
	elseif (x <= 370.0)
		tmp = z / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.1e-54], x, If[LessEqual[x, 3.8e-114], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 370.0], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1e-54 or 370 < x

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf 63.5%

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

   if -2.1e-54 < x < 3.7999999999999998e-114

   1. Initial program 92.8%

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

   3. Taylor expanded in x around 0 80.9%

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

   4. Taylor expanded in z around 0 50.8%

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

      1. mul-1-neg 50.8%

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

      2. associate-/l* 55.5%

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

      3. distribute-rgt-neg-in 55.5%

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

   6. Simplified 55.5%

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

   if 3.7999999999999998e-114 < x < 370

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0 58.6%

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

   4. Taylor expanded in z around inf 40.3%

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

      1. associate-/l* 36.6%

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

   6. Simplified 36.6%

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

      1. associate-*r/ 40.3%

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

      2. clear-num 40.3%

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

   8. Applied egg-rr 40.3%

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

      1. associate-/r/ 40.3%

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

   10. Simplified 40.3%

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

       1. associate-*l/ 40.3%

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

       2. *-un-lft-identity 40.3%

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

       3. associate-*l/ 53.0%

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

       4. clear-num 52.9%

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

       5. associate-*l/ 53.0%

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

       6. *-un-lft-identity 53.0%

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

   12. Applied egg-rr 53.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{-54}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;x \leq 370:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 48.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-114}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{elif}\;x \leq 55000000000:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.1e-52)
   x
   (if (<= x 2.6e-114)
     (/ t (/ a (- y)))
     (if (<= x 55000000000.0) (/ z (/ a y)) x))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.1e-52) {
		tmp = x;
	} else if (x <= 2.6e-114) {
		tmp = t / (a / -y);
	} else if (x <= 55000000000.0) {
		tmp = z / (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 <= (-1.1d-52)) then
        tmp = x
    else if (x <= 2.6d-114) then
        tmp = t / (a / -y)
    else if (x <= 55000000000.0d0) then
        tmp = z / (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 <= -1.1e-52) {
		tmp = x;
	} else if (x <= 2.6e-114) {
		tmp = t / (a / -y);
	} else if (x <= 55000000000.0) {
		tmp = z / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.1e-52:
		tmp = x
	elif x <= 2.6e-114:
		tmp = t / (a / -y)
	elif x <= 55000000000.0:
		tmp = z / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.1e-52)
		tmp = x;
	elseif (x <= 2.6e-114)
		tmp = Float64(t / Float64(a / Float64(-y)));
	elseif (x <= 55000000000.0)
		tmp = Float64(z / 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 <= -1.1e-52)
		tmp = x;
	elseif (x <= 2.6e-114)
		tmp = t / (a / -y);
	elseif (x <= 55000000000.0)
		tmp = z / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.1e-52], x, If[LessEqual[x, 2.6e-114], N[(t / N[(a / (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 55000000000.0], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.10000000000000005e-52 or 5.5e10 < x

   1. Initial program 95.0%

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

   3. Taylor expanded in x around inf 63.5%

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

   if -1.10000000000000005e-52 < x < 2.60000000000000013e-114

   1. Initial program 92.8%

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

   3. Taylor expanded in x around 0 80.9%

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

   4. Taylor expanded in z around 0 50.8%

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

      1. associate-*r/ 50.8%

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

      2. mul-1-neg 50.8%

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

      3. distribute-lft-neg-out 50.8%

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

      4. *-commutative 50.8%

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

      5. associate-/l* 51.6%

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

   6. Simplified 51.6%

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

      1. *-commutative 51.6%

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

      2. div-inv 51.6%

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

      3. associate-*l* 55.4%

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

      4. add-sqr-sqrt 24.4%

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

      5. sqrt-unprod 21.0%

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

      6. sqr-neg 21.0%

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

      7. sqrt-unprod 3.4%

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

      8. add-sqr-sqrt 7.6%

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

      9. associate-/r/ 7.5%

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

      10. div-inv 7.5%

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

      11. frac-2neg 7.5%

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

      12. add-sqr-sqrt 4.1%

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

      13. sqrt-unprod 20.7%

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

      14. sqr-neg 20.7%

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

      15. sqrt-unprod 30.9%

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

      16. add-sqr-sqrt 55.7%

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

      17. distribute-neg-frac2 55.7%

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

   8. Applied egg-rr 55.7%

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

   if 2.60000000000000013e-114 < x < 5.5e10

   1. Initial program 87.1%

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

   3. Taylor expanded in x around 0 58.6%

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

   4. Taylor expanded in z around inf 40.3%

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

      1. associate-/l* 36.6%

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

   6. Simplified 36.6%

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

      1. associate-*r/ 40.3%

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

      2. clear-num 40.3%

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

   8. Applied egg-rr 40.3%

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

      1. associate-/r/ 40.3%

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

   10. Simplified 40.3%

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

       1. associate-*l/ 40.3%

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

       2. *-un-lft-identity 40.3%

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

       3. associate-*l/ 53.0%

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

       4. clear-num 52.9%

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

       5. associate-*l/ 53.0%

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

       6. *-un-lft-identity 53.0%

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

   12. Applied egg-rr 53.0%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-114}:\\ \;\;\;\;\frac{t}{\frac{a}{-y}}\\ \mathbf{elif}\;x \leq 55000000000:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq 4 \cdot 10^{+298}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (* y (- z t)) 4e+298) (- x (/ (* y (- t z)) a)) (* (- z t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y * (z - t)) <= 4e+298) {
		tmp = x - ((y * (t - z)) / a);
	} else {
		tmp = (z - 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 ((y * (z - t)) <= 4d+298) then
        tmp = x - ((y * (t - z)) / a)
    else
        tmp = (z - 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 ((y * (z - t)) <= 4e+298) {
		tmp = x - ((y * (t - z)) / a);
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y * (z - t)) <= 4e+298:
		tmp = x - ((y * (t - z)) / a)
	else:
		tmp = (z - t) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(y * Float64(z - t)) <= 4e+298)
		tmp = Float64(x - Float64(Float64(y * Float64(t - z)) / a));
	else
		tmp = Float64(Float64(z - t) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y * (z - t)) <= 4e+298)
		tmp = x - ((y * (t - z)) / a);
	else
		tmp = (z - t) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision], 4e+298], N[(x - N[(N[(y * N[(t - z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < 3.9999999999999998e298

   1. Initial program 96.6%

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

   if 3.9999999999999998e298 < (*.f64 y (-.f64 z t))

   1. Initial program 68.9%

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

   3. Taylor expanded in x around 0 68.9%

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

      1. *-commutative 68.9%

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

      2. associate-*r/ 99.9%

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

      3. *-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 97.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq 4 \cdot 10^{+298}:\\ \;\;\;\;x - \frac{y \cdot \left(t - z\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-53} \lor \neg \left(x \leq 205\right):\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.05e-53) (not (<= x 205.0)))
   (+ x (/ (* y z) a))
   (* (- z t) (/ y a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.05e-53) || !(x <= 205.0)) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = (z - 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 ((x <= (-1.05d-53)) .or. (.not. (x <= 205.0d0))) then
        tmp = x + ((y * z) / a)
    else
        tmp = (z - 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 ((x <= -1.05e-53) || !(x <= 205.0)) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = (z - t) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.05e-53) or not (x <= 205.0):
		tmp = x + ((y * z) / a)
	else:
		tmp = (z - t) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.05e-53) || !(x <= 205.0))
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(Float64(z - t) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.05e-53) || ~((x <= 205.0)))
		tmp = x + ((y * z) / a);
	else
		tmp = (z - t) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.05e-53], N[Not[LessEqual[x, 205.0]], $MachinePrecision]], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.04999999999999989e-53 or 205 < x

   1. Initial program 95.0%

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

   3. Taylor expanded in z around inf 81.8%

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

   if -1.04999999999999989e-53 < x < 205

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-*r/ 79.7%

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

      3. *-commutative 79.7%

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

   5. Applied egg-rr 79.7%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{-53} \lor \neg \left(x \leq 205\right):\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -155000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+106}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -155000000000.0) x (if (<= a 2.6e+106) (* (- z t) (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -155000000000.0) {
		tmp = x;
	} else if (a <= 2.6e+106) {
		tmp = (z - 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 <= (-155000000000.0d0)) then
        tmp = x
    else if (a <= 2.6d+106) then
        tmp = (z - 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 <= -155000000000.0) {
		tmp = x;
	} else if (a <= 2.6e+106) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -155000000000.0:
		tmp = x
	elif a <= 2.6e+106:
		tmp = (z - t) * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -155000000000.0)
		tmp = x;
	elseif (a <= 2.6e+106)
		tmp = Float64(Float64(z - 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 <= -155000000000.0)
		tmp = x;
	elseif (a <= 2.6e+106)
		tmp = (z - t) * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -155000000000.0], x, If[LessEqual[a, 2.6e+106], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.55e11 or 2.6000000000000002e106 < a

   1. Initial program 87.8%

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

   3. Taylor expanded in x around inf 67.7%

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

   if -1.55e11 < a < 2.6000000000000002e106

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0 74.0%

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

      1. *-commutative 74.0%

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

      2. associate-*r/ 75.6%

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

      3. *-commutative 75.6%

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

   5. Applied egg-rr 75.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -155000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+106}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-52}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 6700000:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -4.2e-52)
   (+ x (* y (/ z a)))
   (if (<= x 6700000.0) (* (- z t) (/ y a)) (+ x (/ (* y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -4.2e-52) {
		tmp = x + (y * (z / a));
	} else if (x <= 6700000.0) {
		tmp = (z - 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 (x <= (-4.2d-52)) then
        tmp = x + (y * (z / a))
    else if (x <= 6700000.0d0) then
        tmp = (z - 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 (x <= -4.2e-52) {
		tmp = x + (y * (z / a));
	} else if (x <= 6700000.0) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -4.2e-52:
		tmp = x + (y * (z / a))
	elif x <= 6700000.0:
		tmp = (z - t) * (y / a)
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -4.2e-52)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (x <= 6700000.0)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -4.2e-52)
		tmp = x + (y * (z / a));
	elseif (x <= 6700000.0)
		tmp = (z - t) * (y / a);
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -4.2e-52], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6700000.0], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.1999999999999997e-52

   1. Initial program 91.9%

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

   3. Taylor expanded in t around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   if -4.1999999999999997e-52 < x < 6.7e6

   1. Initial program 91.4%

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

   3. Taylor expanded in x around 0 75.5%

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

      1. *-commutative 75.5%

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

      2. associate-*r/ 79.7%

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

      3. *-commutative 79.7%

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

   5. Applied egg-rr 79.7%

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

   if 6.7e6 < x

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 83.4%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-52}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 6700000:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 0.000145:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -2.7e-53)
   (+ x (* y (/ z a)))
   (if (<= x 0.000145) (* (- z t) (/ y a)) (+ x (/ y (/ a z))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.7e-53) {
		tmp = x + (y * (z / a));
	} else if (x <= 0.000145) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-2.7d-53)) then
        tmp = x + (y * (z / a))
    else if (x <= 0.000145d0) then
        tmp = (z - t) * (y / a)
    else
        tmp = x + (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -2.7e-53) {
		tmp = x + (y * (z / a));
	} else if (x <= 0.000145) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = x + (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -2.7e-53:
		tmp = x + (y * (z / a))
	elif x <= 0.000145:
		tmp = (z - t) * (y / a)
	else:
		tmp = x + (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -2.7e-53)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (x <= 0.000145)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -2.7e-53)
		tmp = x + (y * (z / a));
	elseif (x <= 0.000145)
		tmp = (z - t) * (y / a);
	else
		tmp = x + (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -2.7e-53], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.000145], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.6999999999999999e-53

   1. Initial program 91.9%

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

   3. Taylor expanded in t around 0 80.4%

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

      1. +-commutative 80.4%

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

      2. associate-/l* 81.8%

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

   5. Simplified 81.8%

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

   if -2.6999999999999999e-53 < x < 1.45e-4

   1. Initial program 92.1%

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

   3. Taylor expanded in x around 0 76.1%

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

      1. *-commutative 76.1%

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

      2. associate-*r/ 79.5%

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

      3. *-commutative 79.5%

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

   5. Applied egg-rr 79.5%

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

   if 1.45e-4 < x

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 82.2%

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

      1. +-commutative 82.2%

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

      2. associate-/l* 83.6%

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

   5. Simplified 83.6%

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

      1. clear-num 21.6%

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

      2. un-div-inv 21.6%

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

   7. Applied egg-rr 83.6%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-53}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 0.000145:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.02e+52)
   (+ x (/ y (/ a z)))
   (if (<= z 3.2e+67) (- x (* t (/ y a))) (+ x (/ (* y z) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.02e+52) {
		tmp = x + (y / (a / z));
	} else if (z <= 3.2e+67) {
		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 (z <= (-1.02d+52)) then
        tmp = x + (y / (a / z))
    else if (z <= 3.2d+67) 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 (z <= -1.02e+52) {
		tmp = x + (y / (a / z));
	} else if (z <= 3.2e+67) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.02e+52:
		tmp = x + (y / (a / z))
	elif z <= 3.2e+67:
		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 (z <= -1.02e+52)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (z <= 3.2e+67)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.02e+52)
		tmp = x + (y / (a / z));
	elseif (z <= 3.2e+67)
		tmp = x - (t * (y / a));
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.02e+52], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+67], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.02000000000000002e52

   1. Initial program 80.4%

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

   3. Taylor expanded in t around 0 81.5%

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

      1. +-commutative 81.5%

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

      2. associate-/l* 87.0%

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

   5. Simplified 87.0%

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

      1. clear-num 56.5%

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

      2. un-div-inv 56.5%

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

   7. Applied egg-rr 87.0%

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

   if -1.02000000000000002e52 < z < 3.19999999999999983e67

   1. Initial program 96.4%

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

   3. Taylor expanded in z around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

      3. associate-/l* 91.3%

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

   5. Simplified 91.3%

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

   if 3.19999999999999983e67 < z

   1. Initial program 96.0%

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

   3. Taylor expanded in z around inf 90.0%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.02 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+67}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-63}:\\ \;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -6.4e-63)
   (+ x (* y (* (- z t) (/ 1.0 a))))
   (+ x (/ (- z t) (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.4e-63) {
		tmp = x + (y * ((z - t) * (1.0 / a)));
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-6.4d-63)) then
        tmp = x + (y * ((z - t) * (1.0d0 / a)))
    else
        tmp = x + ((z - t) / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -6.4e-63) {
		tmp = x + (y * ((z - t) * (1.0 / a)));
	} else {
		tmp = x + ((z - t) / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -6.4e-63:
		tmp = x + (y * ((z - t) * (1.0 / a)))
	else:
		tmp = x + ((z - t) / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -6.4e-63)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) * Float64(1.0 / a))));
	else
		tmp = Float64(x + Float64(Float64(z - t) / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -6.4e-63)
		tmp = x + (y * ((z - t) * (1.0 / a)));
	else
		tmp = x + ((z - t) / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -6.4e-63], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.39999999999999978e-63

   1. Initial program 94.1%

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

      1. clear-num 94.1%

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

      2. inv-pow 94.1%

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

      3. associate-/r* 93.6%

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

   4. Applied egg-rr 93.6%

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

      1. unpow-1 93.6%

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

      2. associate-/r/ 93.3%

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

      3. clear-num 93.6%

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

      4. div-inv 93.5%

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

      5. associate-*l* 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -6.39999999999999978e-63 < a

   1. Initial program 92.9%

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

      1. clear-num 92.9%

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

      2. inv-pow 92.9%

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

      3. associate-/r* 99.2%

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

   4. Applied egg-rr 99.2%

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

      1. unpow-1 99.2%

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

      2. clear-num 99.3%

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

   6. Applied egg-rr 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.4 \cdot 10^{-63}:\\ \;\;\;\;x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+47} \lor \neg \left(z \leq 1.3 \cdot 10^{+61}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9e+47) (not (<= z 1.3e+61))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+47) || !(z <= 1.3e+61)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9d+47)) .or. (.not. (z <= 1.3d+61))) then
        tmp = y * (z / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9e+47) || !(z <= 1.3e+61)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9e+47) or not (z <= 1.3e+61):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9e+47) || !(z <= 1.3e+61))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9e+47) || ~((z <= 1.3e+61)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9e+47], N[Not[LessEqual[z, 1.3e+61]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.99999999999999958e47 or 1.29999999999999986e61 < z

   1. Initial program 88.7%

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

   3. Taylor expanded in x around 0 66.3%

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

   4. Taylor expanded in z around inf 58.9%

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

      1. associate-/l* 60.5%

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

   6. Simplified 60.5%

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

   if -8.99999999999999958e47 < z < 1.29999999999999986e61

   1. Initial program 96.3%

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

   3. Taylor expanded in x around inf 50.3%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+47} \lor \neg \left(z \leq 1.3 \cdot 10^{+61}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 49.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7200000:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.75e-67) x (if (<= x 7200000.0) (* z (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.75e-67) {
		tmp = x;
	} else if (x <= 7200000.0) {
		tmp = z * (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 (x <= (-1.75d-67)) then
        tmp = x
    else if (x <= 7200000.0d0) then
        tmp = z * (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 (x <= -1.75e-67) {
		tmp = x;
	} else if (x <= 7200000.0) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.75e-67:
		tmp = x
	elif x <= 7200000.0:
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.75e-67)
		tmp = x;
	elseif (x <= 7200000.0)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.75e-67)
		tmp = x;
	elseif (x <= 7200000.0)
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.75e-67], x, If[LessEqual[x, 7200000.0], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75e-67 or 7.2e6 < x

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf 62.5%

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

   if -1.75e-67 < x < 7.2e6

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0 76.3%

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

   4. Taylor expanded in z around inf 39.9%

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

      1. associate-/l* 40.6%

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

   6. Simplified 40.6%

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

      1. clear-num 40.6%

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

      2. un-div-inv 40.6%

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

   8. Applied egg-rr 40.6%

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

      1. associate-/r/ 43.6%

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

   10. Applied egg-rr 43.6%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-67}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7200000:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 + ((z - t) / (a / y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.3%

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

   1. clear-num 93.3%

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

   2. inv-pow 93.3%

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

   3. associate-/r* 97.4%

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

4. Applied egg-rr 97.4%

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

   1. unpow-1 97.4%

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

   2. clear-num 97.4%

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

6. Applied egg-rr 97.4%

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

7. Final simplification 97.4%

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

Alternative 15: 39.2% 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 93.3%

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

3. Taylor expanded in x around inf 41.3%

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

4. Final simplification 41.3%

   \[\leadsto x \]
5. 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 2024046 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))