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

Percentage Accurate: 93.0% → 99.6%

Time: 12.4s

Alternatives: 12

Speedup: 1.0×

• 24.9% 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: 93.0% 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: 99.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{+275}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 (- INFINITY))
     (+ x (* (- z t) (/ y a)))
     (if (<= t_1 5e+275) (+ x (/ t_1 a)) (+ x (/ y (/ a (- z t))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = x + ((z - t) * (y / a));
	} else if (t_1 <= 5e+275) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = x + ((z - t) * (y / a));
	} else if (t_1 <= 5e+275) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -math.inf:
		tmp = x + ((z - t) * (y / a))
	elif t_1 <= 5e+275:
		tmp = x + (t_1 / a)
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	elseif (t_1 <= 5e+275)
		tmp = Float64(x + Float64(t_1 / a));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = x + ((z - t) * (y / a));
	elseif (t_1 <= 5e+275)
		tmp = x + (t_1 / a);
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+275], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 73.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 5.0000000000000003e275

   1. Initial program 99.9%

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

   if 5.0000000000000003e275 < (*.f64 y (-.f64 z t))

   1. Initial program 73.9%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-/r/ 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -\infty:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \cdot \left(z - t\right) \leq 5 \cdot 10^{+275}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 2: 47.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot t}{-a}\\ \mathbf{if}\;x \leq -3.3 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-87}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-229}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y t) (- a))))
   (if (<= x -3.3e+19)
     x
     (if (<= x -3.9e-87)
       (* (- y) (/ t a))
       (if (<= x -6.6e-209)
         (/ (* y z) a)
         (if (<= x 4.2e-301)
           t_1
           (if (<= x 5.5e-229) (* y (/ z a)) (if (<= x 2.4e-55) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * t) / -a;
	double tmp;
	if (x <= -3.3e+19) {
		tmp = x;
	} else if (x <= -3.9e-87) {
		tmp = -y * (t / a);
	} else if (x <= -6.6e-209) {
		tmp = (y * z) / a;
	} else if (x <= 4.2e-301) {
		tmp = t_1;
	} else if (x <= 5.5e-229) {
		tmp = y * (z / a);
	} else if (x <= 2.4e-55) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (y * t) / -a
    if (x <= (-3.3d+19)) then
        tmp = x
    else if (x <= (-3.9d-87)) then
        tmp = -y * (t / a)
    else if (x <= (-6.6d-209)) then
        tmp = (y * z) / a
    else if (x <= 4.2d-301) then
        tmp = t_1
    else if (x <= 5.5d-229) then
        tmp = y * (z / a)
    else if (x <= 2.4d-55) then
        tmp = t_1
    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 t_1 = (y * t) / -a;
	double tmp;
	if (x <= -3.3e+19) {
		tmp = x;
	} else if (x <= -3.9e-87) {
		tmp = -y * (t / a);
	} else if (x <= -6.6e-209) {
		tmp = (y * z) / a;
	} else if (x <= 4.2e-301) {
		tmp = t_1;
	} else if (x <= 5.5e-229) {
		tmp = y * (z / a);
	} else if (x <= 2.4e-55) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * t) / -a
	tmp = 0
	if x <= -3.3e+19:
		tmp = x
	elif x <= -3.9e-87:
		tmp = -y * (t / a)
	elif x <= -6.6e-209:
		tmp = (y * z) / a
	elif x <= 4.2e-301:
		tmp = t_1
	elif x <= 5.5e-229:
		tmp = y * (z / a)
	elif x <= 2.4e-55:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * t) / Float64(-a))
	tmp = 0.0
	if (x <= -3.3e+19)
		tmp = x;
	elseif (x <= -3.9e-87)
		tmp = Float64(Float64(-y) * Float64(t / a));
	elseif (x <= -6.6e-209)
		tmp = Float64(Float64(y * z) / a);
	elseif (x <= 4.2e-301)
		tmp = t_1;
	elseif (x <= 5.5e-229)
		tmp = Float64(y * Float64(z / a));
	elseif (x <= 2.4e-55)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * t) / -a;
	tmp = 0.0;
	if (x <= -3.3e+19)
		tmp = x;
	elseif (x <= -3.9e-87)
		tmp = -y * (t / a);
	elseif (x <= -6.6e-209)
		tmp = (y * z) / a;
	elseif (x <= 4.2e-301)
		tmp = t_1;
	elseif (x <= 5.5e-229)
		tmp = y * (z / a);
	elseif (x <= 2.4e-55)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * t), $MachinePrecision] / (-a)), $MachinePrecision]}, If[LessEqual[x, -3.3e+19], x, If[LessEqual[x, -3.9e-87], N[((-y) * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.6e-209], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[x, 4.2e-301], t$95$1, If[LessEqual[x, 5.5e-229], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.4e-55], t$95$1, x]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.3e19 or 2.39999999999999991e-55 < x

   1. Initial program 93.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in x around inf 63.3%

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

   if -3.3e19 < x < -3.8999999999999998e-87

   1. Initial program 87.9%

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

      1. associate-*l/ 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around inf 64.6%

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

   5. Taylor expanded in z around 0 64.7%

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

      1. mul-1-neg 64.7%

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

      2. distribute-frac-neg 64.7%

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

   7. Simplified 64.7%

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

   if -3.8999999999999998e-87 < x < -6.59999999999999948e-209

   1. Initial program 99.8%

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

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

   4. Taylor expanded in y around inf 73.3%

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

   5. Taylor expanded in z around inf 44.5%

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

      1. *-commutative 44.5%

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

      2. clear-num 44.5%

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

      3. un-div-inv 48.0%

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

   7. Applied egg-rr 48.0%

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

   8. Taylor expanded in y around 0 55.8%

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

   if -6.59999999999999948e-209 < x < 4.1999999999999997e-301 or 5.5000000000000001e-229 < x < 2.39999999999999991e-55

   1. Initial program 94.8%

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

      1. associate-*l/ 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around inf 85.0%

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

   5. Taylor expanded in z around 0 53.4%

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

      1. mul-1-neg 53.4%

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

      2. distribute-frac-neg 53.4%

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

   7. Simplified 53.4%

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

      1. *-commutative 53.4%

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

      2. frac-2neg 53.4%

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

      3. remove-double-neg 53.4%

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

      4. associate-*r/ 56.5%

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

   9. Applied egg-rr 56.5%

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

   if 4.1999999999999997e-301 < x < 5.5000000000000001e-229

   1. Initial program 94.2%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around inf 82.4%

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

   5. Taylor expanded in z around inf 64.4%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.3 \cdot 10^{+19}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-87}:\\ \;\;\;\;\left(-y\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-209}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-301}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-229}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-55}:\\ \;\;\;\;\frac{y \cdot t}{-a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 50.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -2e+73)
   (/ z (/ a y))
   (if (<= z -3.9e-227)
     x
     (if (<= z -2.8e-278)
       (* (/ y a) (- t))
       (if (<= z 1.2e+20) x (* z (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+73) {
		tmp = z / (a / y);
	} else if (z <= -3.9e-227) {
		tmp = x;
	} else if (z <= -2.8e-278) {
		tmp = (y / a) * -t;
	} else if (z <= 1.2e+20) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-2d+73)) then
        tmp = z / (a / y)
    else if (z <= (-3.9d-227)) then
        tmp = x
    else if (z <= (-2.8d-278)) then
        tmp = (y / a) * -t
    else if (z <= 1.2d+20) then
        tmp = x
    else
        tmp = z * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -2e+73) {
		tmp = z / (a / y);
	} else if (z <= -3.9e-227) {
		tmp = x;
	} else if (z <= -2.8e-278) {
		tmp = (y / a) * -t;
	} else if (z <= 1.2e+20) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -2e+73:
		tmp = z / (a / y)
	elif z <= -3.9e-227:
		tmp = x
	elif z <= -2.8e-278:
		tmp = (y / a) * -t
	elif z <= 1.2e+20:
		tmp = x
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -2e+73)
		tmp = Float64(z / Float64(a / y));
	elseif (z <= -3.9e-227)
		tmp = x;
	elseif (z <= -2.8e-278)
		tmp = Float64(Float64(y / a) * Float64(-t));
	elseif (z <= 1.2e+20)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -2e+73)
		tmp = z / (a / y);
	elseif (z <= -3.9e-227)
		tmp = x;
	elseif (z <= -2.8e-278)
		tmp = (y / a) * -t;
	elseif (z <= 1.2e+20)
		tmp = x;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -2e+73], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-227], x, If[LessEqual[z, -2.8e-278], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[z, 1.2e+20], x, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.99999999999999997e73

   1. Initial program 87.7%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 72.3%

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

   5. Taylor expanded in z around inf 71.5%

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

      1. associate-*l/ 67.5%

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

      2. associate-/l* 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -1.99999999999999997e73 < z < -3.8999999999999999e-227 or -2.80000000000000008e-278 < z < 1.2e20

   1. Initial program 96.6%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in x around inf 53.5%

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

   if -3.8999999999999999e-227 < z < -2.80000000000000008e-278

   1. Initial program 100.0%

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

      1. associate-*l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 67.5%

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

   5. Taylor expanded in z around 0 67.5%

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

      1. mul-1-neg 67.5%

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

      2. distribute-frac-neg 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in t around 0 78.1%

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

      1. mul-1-neg 78.1%

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

      2. associate-*l/ 78.1%

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

      3. *-commutative 78.1%

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

      4. distribute-rgt-neg-in 78.1%

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

      5. distribute-neg-frac 78.1%

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

   10. Simplified 78.1%

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

   if 1.2e20 < z

   1. Initial program 91.5%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around inf 57.3%

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

   5. Taylor expanded in z around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. clear-num 48.8%

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

      3. un-div-inv 50.3%

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

   7. Applied egg-rr 50.3%

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

      1. associate-/r/ 53.8%

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

   9. Applied egg-rr 53.8%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+73}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-227}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-278}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 4: 69.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-93} \lor \neg \left(y \leq 5.4 \cdot 10^{-78}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.9e-93) (not (<= y 5.4e-78))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.9e-93) || !(y <= 5.4e-78)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-5.9d-93)) .or. (.not. (y <= 5.4d-78))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -5.9e-93) || !(y <= 5.4e-78)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -5.9e-93) or not (y <= 5.4e-78):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -5.9e-93) || !(y <= 5.4e-78))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -5.9e-93) || ~((y <= 5.4e-78)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -5.9e-93], N[Not[LessEqual[y, 5.4e-78]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -5.9e-93 or 5.39999999999999987e-78 < y

   1. Initial program 91.0%

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

      1. associate-*l/ 94.4%

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

   3. Simplified 94.4%

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

   4. Taylor expanded in y around inf 71.0%

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

   5. Taylor expanded in z around 0 71.0%

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

      1. mul-1-neg 71.0%

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

      2. distribute-frac-neg 71.0%

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

      3. +-commutative 71.0%

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

      4. distribute-frac-neg 71.0%

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

      5. sub-neg 71.0%

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

      6. div-sub 72.2%

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

   7. Simplified 72.2%

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

   if -5.9e-93 < y < 5.39999999999999987e-78

   1. Initial program 99.9%

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

      1. associate-*l/ 96.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 72.0%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{-93} \lor \neg \left(y \leq 5.4 \cdot 10^{-78}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 77.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9000000000000 \lor \neg \left(x \leq 1.55 \cdot 10^{-43}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -9000000000000.0) (not (<= x 1.55e-43)))
   (+ x (* z (/ y a)))
   (* y (/ (- z t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -9000000000000.0) || !(x <= 1.55e-43)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y * ((z - 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 ((x <= (-9000000000000.0d0)) .or. (.not. (x <= 1.55d-43))) then
        tmp = x + (z * (y / a))
    else
        tmp = y * ((z - 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 ((x <= -9000000000000.0) || !(x <= 1.55e-43)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -9000000000000.0) or not (x <= 1.55e-43):
		tmp = x + (z * (y / a))
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -9000000000000.0) || !(x <= 1.55e-43))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(y * Float64(Float64(z - t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -9000000000000.0) || ~((x <= 1.55e-43)))
		tmp = x + (z * (y / a));
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -9000000000000.0], N[Not[LessEqual[x, 1.55e-43]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9e12 or 1.55e-43 < x

   1. Initial program 93.3%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in t around 0 83.2%

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

      1. associate-*l/ 86.1%

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

      2. *-commutative 86.1%

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

   6. Simplified 86.1%

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

   if -9e12 < x < 1.55e-43

   1. Initial program 94.9%

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

      1. associate-*l/ 93.4%

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

   3. Simplified 93.4%

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

   4. Taylor expanded in y around inf 79.2%

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

   5. Taylor expanded in z around 0 79.2%

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

      1. mul-1-neg 79.2%

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

      2. distribute-frac-neg 79.2%

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

      3. +-commutative 79.2%

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

      4. distribute-frac-neg 79.2%

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

      5. sub-neg 79.2%

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

      6. div-sub 81.0%

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

   7. Simplified 81.0%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9000000000000 \lor \neg \left(x \leq 1.55 \cdot 10^{-43}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 6: 85.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4600000000 \lor \neg \left(z \leq 2.8 \cdot 10^{-7}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4600000000.0) (not (<= z 2.8e-7)))
   (+ x (* z (/ y a)))
   (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4600000000.0) || !(z <= 2.8e-7)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-4600000000.0d0)) .or. (.not. (z <= 2.8d-7))) then
        tmp = x + (z * (y / a))
    else
        tmp = x - (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4600000000.0) || !(z <= 2.8e-7)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4600000000.0) or not (z <= 2.8e-7):
		tmp = x + (z * (y / a))
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4600000000.0) || !(z <= 2.8e-7))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4600000000.0) || ~((z <= 2.8e-7)))
		tmp = x + (z * (y / a));
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4600000000.0], N[Not[LessEqual[z, 2.8e-7]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.6e9 or 2.80000000000000019e-7 < z

   1. Initial program 91.6%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around 0 81.3%

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

      1. associate-*l/ 87.3%

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

      2. *-commutative 87.3%

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

   6. Simplified 87.3%

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

   if -4.6e9 < z < 2.80000000000000019e-7

   1. Initial program 96.3%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in z around 0 89.7%

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

      1. mul-1-neg 89.7%

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

      2. associate-*l/ 89.4%

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

      3. distribute-rgt-neg-out 89.4%

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

      4. +-commutative 89.4%

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

      5. *-commutative 89.4%

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

      6. distribute-lft-neg-out 89.4%

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

      7. unsub-neg 89.4%

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

   6. Simplified 89.4%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4600000000 \lor \neg \left(z \leq 2.8 \cdot 10^{-7}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 84.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+14} \lor \neg \left(z \leq 9.6 \cdot 10^{-7}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.35e+14) (not (<= z 9.6e-7)))
   (+ x (* z (/ y a)))
   (- x (/ (* y t) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.35e+14) || !(z <= 9.6e-7)) {
		tmp = x + (z * (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) :: tmp
    if ((z <= (-2.35d+14)) .or. (.not. (z <= 9.6d-7))) then
        tmp = x + (z * (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 tmp;
	if ((z <= -2.35e+14) || !(z <= 9.6e-7)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - ((y * t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.35e+14) or not (z <= 9.6e-7):
		tmp = x + (z * (y / a))
	else:
		tmp = x - ((y * t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.35e+14) || !(z <= 9.6e-7))
		tmp = Float64(x + Float64(z * 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)
	tmp = 0.0;
	if ((z <= -2.35e+14) || ~((z <= 9.6e-7)))
		tmp = x + (z * (y / a));
	else
		tmp = x - ((y * t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.35e+14], N[Not[LessEqual[z, 9.6e-7]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.35e14 or 9.59999999999999914e-7 < z

   1. Initial program 91.6%

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

      1. associate-*l/ 96.9%

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

   3. Simplified 96.9%

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

   4. Taylor expanded in t around 0 81.3%

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

      1. associate-*l/ 87.3%

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

      2. *-commutative 87.3%

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

   6. Simplified 87.3%

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

   if -2.35e14 < z < 9.59999999999999914e-7

   1. Initial program 96.3%

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

      1. associate-*l/ 93.6%

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

   3. Simplified 93.6%

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

      1. *-commutative 93.6%

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

      2. clear-num 93.3%

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

      3. un-div-inv 93.6%

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

   5. Applied egg-rr 93.6%

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

   6. Taylor expanded in z around 0 89.7%

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

      1. +-commutative 89.7%

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

      2. mul-1-neg 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-/l* 89.3%

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

      5. unsub-neg 89.3%

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

      6. associate-/l* 89.7%

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

      7. *-commutative 89.7%

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

   8. Simplified 89.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{+14} \lor \neg \left(z \leq 9.6 \cdot 10^{-7}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \end{array} \]

Alternative 8: 95.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.4 \cdot 10^{-205}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 2.4e-205) (+ x (* (- z t) (/ y a))) (+ x (/ y (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.4e-205) {
		tmp = x + ((z - t) * (y / a));
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= 2.4d-205) then
        tmp = x + ((z - t) * (y / a))
    else
        tmp = x + (y / (a / (z - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 2.4e-205) {
		tmp = x + ((z - t) * (y / a));
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 2.4e-205:
		tmp = x + ((z - t) * (y / a))
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 2.4e-205)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= 2.4e-205)
		tmp = x + ((z - t) * (y / a));
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 2.4e-205], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.4000000000000002e-205

   1. Initial program 94.6%

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

      1. associate-*l/ 98.5%

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

   3. Simplified 98.5%

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

   if 2.4000000000000002e-205 < t

   1. Initial program 93.3%

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

      1. associate-*l/ 91.1%

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

   3. Simplified 91.1%

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

      1. associate-/r/ 97.5%

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

   5. Applied egg-rr 97.5%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.4 \cdot 10^{-205}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]

Alternative 9: 50.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+75} \lor \neg \left(z \leq 1.8 \cdot 10^{+20}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.75e+75) (not (<= z 1.8e+20))) (* z (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2.75e+75) || !(z <= 1.8e+20)) {
		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 ((z <= (-2.75d+75)) .or. (.not. (z <= 1.8d+20))) 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 ((z <= -2.75e+75) || !(z <= 1.8e+20)) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -2.75e+75) or not (z <= 1.8e+20):
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2.75e+75) || !(z <= 1.8e+20))
		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 ((z <= -2.75e+75) || ~((z <= 1.8e+20)))
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2.75e+75], N[Not[LessEqual[z, 1.8e+20]], $MachinePrecision]], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.75e75 or 1.8e20 < z

   1. Initial program 89.8%

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

      1. associate-*l/ 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in y around inf 64.0%

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

   5. Taylor expanded in z around inf 58.9%

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

      1. *-commutative 58.9%

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

      2. clear-num 58.9%

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

      3. un-div-inv 60.6%

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

   7. Applied egg-rr 60.6%

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

      1. associate-/r/ 63.5%

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

   9. Applied egg-rr 63.5%

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

   if -2.75e75 < z < 1.8e20

   1. Initial program 96.8%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around inf 51.7%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+75} \lor \neg \left(z \leq 1.8 \cdot 10^{+20}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.05e+70) (/ z (/ a y)) (if (<= z 1.75e+20) x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+70) {
		tmp = z / (a / y);
	} else if (z <= 1.75e+20) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= (-1.05d+70)) then
        tmp = z / (a / y)
    else if (z <= 1.75d+20) then
        tmp = x
    else
        tmp = z * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.05e+70) {
		tmp = z / (a / y);
	} else if (z <= 1.75e+20) {
		tmp = x;
	} else {
		tmp = z * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.05e+70:
		tmp = z / (a / y)
	elif z <= 1.75e+20:
		tmp = x
	else:
		tmp = z * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.05e+70)
		tmp = Float64(z / Float64(a / y));
	elseif (z <= 1.75e+20)
		tmp = x;
	else
		tmp = Float64(z * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.05e+70)
		tmp = z / (a / y);
	elseif (z <= 1.75e+20)
		tmp = x;
	else
		tmp = z * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.05e+70], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+20], x, N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.05000000000000004e70

   1. Initial program 87.7%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in y around inf 72.3%

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

   5. Taylor expanded in z around inf 71.5%

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

      1. associate-*l/ 67.5%

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

      2. associate-/l* 75.5%

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

   7. Applied egg-rr 75.5%

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

   if -1.05000000000000004e70 < z < 1.75e20

   1. Initial program 96.8%

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

      1. associate-*l/ 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in x around inf 51.7%

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

   if 1.75e20 < z

   1. Initial program 91.5%

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

      1. associate-*l/ 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around inf 57.3%

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

   5. Taylor expanded in z around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. clear-num 48.8%

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

      3. un-div-inv 50.3%

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

   7. Applied egg-rr 50.3%

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

      1. associate-/r/ 53.8%

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

   9. Applied egg-rr 53.8%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+70}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 11: 97.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / 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/ 95.2%

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

3. Simplified 95.2%

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

4. Final simplification 95.2%

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

Alternative 12: 38.9% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 94.0%

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

   1. associate-*l/ 95.2%

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

3. Simplified 95.2%

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

4. Taylor expanded in x around inf 41.5%

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

5. Final simplification 41.5%

   \[\leadsto x \]

Developer target: 99.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023274 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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