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

Percentage Accurate: 92.9% → 97.3%

Time: 7.7s

Alternatives: 10

Speedup: 1.0×

• 24.6% 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: 92.9% 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: 97.3% 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 92.9%

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

   1. *-commutative 92.9%

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

   2. associate-/l* 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 2: 87.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a}\\ t_2 := \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -2 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 10^{+83}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+303}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) a))) (t_2 (/ (* (- z t) y) a)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -2e+75)
       t_2
       (if (<= t_2 1e+83) (- x (/ (* t y) a)) (if (<= t_2 2e+303) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / a);
	double t_2 = ((z - t) * y) / a;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -2e+75) {
		tmp = t_2;
	} else if (t_2 <= 1e+83) {
		tmp = x - ((t * y) / a);
	} else if (t_2 <= 2e+303) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / a);
	double t_2 = ((z - t) * y) / a;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -2e+75) {
		tmp = t_2;
	} else if (t_2 <= 1e+83) {
		tmp = x - ((t * y) / a);
	} else if (t_2 <= 2e+303) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / a)
	t_2 = ((z - t) * y) / a
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -2e+75:
		tmp = t_2
	elif t_2 <= 1e+83:
		tmp = x - ((t * y) / a)
	elif t_2 <= 2e+303:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / a))
	t_2 = Float64(Float64(Float64(z - t) * y) / a)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -2e+75)
		tmp = t_2;
	elseif (t_2 <= 1e+83)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	elseif (t_2 <= 2e+303)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / a);
	t_2 = ((z - t) * y) / a;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -2e+75)
		tmp = t_2;
	elseif (t_2 <= 1e+83)
		tmp = x - ((t * y) / a);
	elseif (t_2 <= 2e+303)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -2e+75], t$95$2, If[LessEqual[t$95$2, 1e+83], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+303], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -inf.0 or 2e303 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 79.8%

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

   2. Taylor expanded in x around 0 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-*l/ 95.5%

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

   4. Applied egg-rr 95.5%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a) < -1.99999999999999985e75 or 1.00000000000000003e83 < (/.f64 (*.f64 y (-.f64 z t)) a) < 2e303

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 90.3%

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

   if -1.99999999999999985e75 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.00000000000000003e83

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 91.5%

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

      1. mul-1-neg 91.5%

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

      2. associate-*l/ 90.6%

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

      3. unsub-neg 90.6%

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

      4. associate-*l/ 91.5%

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

      5. *-commutative 91.5%

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

      6. associate-/l* 90.6%

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

   4. Simplified 90.6%

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

   5. Taylor expanded in y around 0 91.5%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a} \leq -\infty:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a} \leq -2 \cdot 10^{+75}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a} \leq 10^{+83}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a} \leq 2 \cdot 10^{+303}:\\ \;\;\;\;\frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]

Alternative 3: 98.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 2 \cdot 10^{+286}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 2e+286)))
     (* y (/ (- z t) a))
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 2e+286)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 2e+286)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) * y
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 2e+286):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) * y)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 2e+286))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) * y;
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 2e+286)))
		tmp = y * ((z - t) / a);
	else
		tmp = x + (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 2e+286]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -inf.0 or 2.00000000000000007e286 < (*.f64 y (-.f64 z t))

   1. Initial program 71.1%

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

   2. Taylor expanded in x around 0 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*l/ 93.6%

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

   4. Applied egg-rr 93.6%

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

   if -inf.0 < (*.f64 y (-.f64 z t)) < 2.00000000000000007e286

   1. Initial program 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -\infty \lor \neg \left(\left(z - t\right) \cdot y \leq 2 \cdot 10^{+286}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \]

Alternative 4: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-207}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y a))))
   (if (<= z -5.2e+17)
     t_1
     (if (<= z -1.15e-151)
       x
       (if (<= z 1.28e-207) (* (/ y a) (- t)) (if (<= z 3.3e+42) x t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / a);
	double tmp;
	if (z <= -5.2e+17) {
		tmp = t_1;
	} else if (z <= -1.15e-151) {
		tmp = x;
	} else if (z <= 1.28e-207) {
		tmp = (y / a) * -t;
	} else if (z <= 3.3e+42) {
		tmp = x;
	} else {
		tmp = 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 = z * (y / a)
    if (z <= (-5.2d+17)) then
        tmp = t_1
    else if (z <= (-1.15d-151)) then
        tmp = x
    else if (z <= 1.28d-207) then
        tmp = (y / a) * -t
    else if (z <= 3.3d+42) then
        tmp = x
    else
        tmp = 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 = z * (y / a);
	double tmp;
	if (z <= -5.2e+17) {
		tmp = t_1;
	} else if (z <= -1.15e-151) {
		tmp = x;
	} else if (z <= 1.28e-207) {
		tmp = (y / a) * -t;
	} else if (z <= 3.3e+42) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / a)
	tmp = 0
	if z <= -5.2e+17:
		tmp = t_1
	elif z <= -1.15e-151:
		tmp = x
	elif z <= 1.28e-207:
		tmp = (y / a) * -t
	elif z <= 3.3e+42:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / a))
	tmp = 0.0
	if (z <= -5.2e+17)
		tmp = t_1;
	elseif (z <= -1.15e-151)
		tmp = x;
	elseif (z <= 1.28e-207)
		tmp = Float64(Float64(y / a) * Float64(-t));
	elseif (z <= 3.3e+42)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / a);
	tmp = 0.0;
	if (z <= -5.2e+17)
		tmp = t_1;
	elseif (z <= -1.15e-151)
		tmp = x;
	elseif (z <= 1.28e-207)
		tmp = (y / a) * -t;
	elseif (z <= 3.3e+42)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+17], t$95$1, If[LessEqual[z, -1.15e-151], x, If[LessEqual[z, 1.28e-207], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision], If[LessEqual[z, 3.3e+42], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.2e17 or 3.2999999999999999e42 < z

   1. Initial program 88.3%

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

   2. Taylor expanded in x around 0 72.5%

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

   3. Taylor expanded in z around inf 62.6%

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

      1. associate-*l/ 69.2%

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

      2. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -5.2e17 < z < -1.14999999999999998e-151 or 1.2800000000000001e-207 < z < 3.2999999999999999e42

   1. Initial program 96.8%

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

   2. Taylor expanded in x around inf 61.8%

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

   if -1.14999999999999998e-151 < z < 1.2800000000000001e-207

   1. Initial program 96.3%

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

   2. Taylor expanded in x around 0 58.5%

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

   3. Taylor expanded in z around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. associate-*r/ 58.4%

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

      3. distribute-rgt-neg-in 58.4%

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

   5. Simplified 58.4%

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

4. Final simplification 64.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+17}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-151}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-207}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 5: 68.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-68} \lor \neg \left(y \leq 1.3 \cdot 10^{-167}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.9e-68) (not (<= y 1.3e-167))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -2.9e-68) || !(y <= 1.3e-167)) {
		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 <= (-2.9d-68)) .or. (.not. (y <= 1.3d-167))) 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 <= -2.9e-68) || !(y <= 1.3e-167)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.9e-68) or not (y <= 1.3e-167):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -2.9e-68) || !(y <= 1.3e-167))
		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 <= -2.9e-68) || ~((y <= 1.3e-167)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -2.9e-68], N[Not[LessEqual[y, 1.3e-167]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e-68 or 1.2999999999999999e-167 < y

   1. Initial program 89.8%

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

   2. Taylor expanded in x around 0 67.0%

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

      1. *-commutative 67.0%

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

      2. associate-*l/ 73.5%

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

   4. Applied egg-rr 73.5%

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

   if -2.9e-68 < y < 1.2999999999999999e-167

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 65.9%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-68} \lor \neg \left(y \leq 1.3 \cdot 10^{-167}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 6: 76.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+256}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.15e+92)
   (* y (/ (- z t) a))
   (if (<= t 1.02e+256) (+ x (* z (/ y a))) (* (/ y a) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.15e+92) {
		tmp = y * ((z - t) / a);
	} else if (t <= 1.02e+256) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (y / a) * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.15d+92)) then
        tmp = y * ((z - t) / a)
    else if (t <= 1.02d+256) then
        tmp = x + (z * (y / a))
    else
        tmp = (y / a) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.15e+92) {
		tmp = y * ((z - t) / a);
	} else if (t <= 1.02e+256) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (y / a) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.15e+92:
		tmp = y * ((z - t) / a)
	elif t <= 1.02e+256:
		tmp = x + (z * (y / a))
	else:
		tmp = (y / a) * -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.15e+92)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 1.02e+256)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.15e+92)
		tmp = y * ((z - t) / a);
	elseif (t <= 1.02e+256)
		tmp = x + (z * (y / a));
	else
		tmp = (y / a) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.15e+92], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+256], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1499999999999999e92

   1. Initial program 86.6%

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

   2. Taylor expanded in x around 0 69.1%

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

      1. *-commutative 69.1%

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

      2. associate-*l/ 68.8%

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

   4. Applied egg-rr 68.8%

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

   if -2.1499999999999999e92 < t < 1.02e256

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf 81.1%

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

      1. associate-*l/ 45.0%

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

      2. *-commutative 45.0%

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

   4. Simplified 85.3%

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

   if 1.02e256 < t

   1. Initial program 92.5%

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

   2. Taylor expanded in x around 0 70.7%

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

   3. Taylor expanded in z around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. associate-*r/ 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

   5. Simplified 74.8%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.15 \cdot 10^{+92}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+256}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \end{array} \]

Alternative 7: 76.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+256}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.3e+91)
   (* y (/ (- z t) a))
   (if (<= t 1.02e+256) (+ x (/ z (/ a y))) (* (/ y a) (- t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+91) {
		tmp = y * ((z - t) / a);
	} else if (t <= 1.02e+256) {
		tmp = x + (z / (a / y));
	} else {
		tmp = (y / a) * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.3d+91)) then
        tmp = y * ((z - t) / a)
    else if (t <= 1.02d+256) then
        tmp = x + (z / (a / y))
    else
        tmp = (y / a) * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.3e+91) {
		tmp = y * ((z - t) / a);
	} else if (t <= 1.02e+256) {
		tmp = x + (z / (a / y));
	} else {
		tmp = (y / a) * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.3e+91:
		tmp = y * ((z - t) / a)
	elif t <= 1.02e+256:
		tmp = x + (z / (a / y))
	else:
		tmp = (y / a) * -t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.3e+91)
		tmp = Float64(y * Float64(Float64(z - t) / a));
	elseif (t <= 1.02e+256)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	else
		tmp = Float64(Float64(y / a) * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.3e+91)
		tmp = y * ((z - t) / a);
	elseif (t <= 1.02e+256)
		tmp = x + (z / (a / y));
	else
		tmp = (y / a) * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.3e+91], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+256], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * (-t)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3e91

   1. Initial program 86.6%

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

   2. Taylor expanded in x around 0 69.1%

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

      1. *-commutative 69.1%

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

      2. associate-*l/ 68.8%

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

   4. Applied egg-rr 68.8%

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

   if -1.3e91 < t < 1.02e256

   1. Initial program 94.2%

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

   2. Taylor expanded in z around inf 81.1%

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

      1. associate-*l/ 45.0%

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

      2. *-commutative 45.0%

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

   4. Simplified 85.3%

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

      1. clear-num 85.3%

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

      2. un-div-inv 85.8%

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

   6. Applied egg-rr 85.8%

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

   if 1.02e256 < t

   1. Initial program 92.5%

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

   2. Taylor expanded in x around 0 70.7%

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

   3. Taylor expanded in z around 0 70.7%

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

      1. mul-1-neg 70.7%

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

      2. associate-*r/ 74.8%

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

      3. distribute-rgt-neg-in 74.8%

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

   5. Simplified 74.8%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+256}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-t\right)\\ \end{array} \]

Alternative 8: 83.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-51}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -1.16e-63)
   (+ x (/ z (/ a y)))
   (if (<= z 3.3e-51) (- x (/ y (/ a t))) (+ x (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -1.16e-63) {
		tmp = x + (z / (a / y));
	} else if (z <= 3.3e-51) {
		tmp = x - (y / (a / t));
	} else {
		tmp = x + (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 <= (-1.16d-63)) then
        tmp = x + (z / (a / y))
    else if (z <= 3.3d-51) then
        tmp = x - (y / (a / t))
    else
        tmp = x + (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 <= -1.16e-63) {
		tmp = x + (z / (a / y));
	} else if (z <= 3.3e-51) {
		tmp = x - (y / (a / t));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -1.16e-63:
		tmp = x + (z / (a / y))
	elif z <= 3.3e-51:
		tmp = x - (y / (a / t))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -1.16e-63)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (z <= 3.3e-51)
		tmp = Float64(x - Float64(y / Float64(a / t)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -1.16e-63)
		tmp = x + (z / (a / y));
	elseif (z <= 3.3e-51)
		tmp = x - (y / (a / t));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -1.16e-63], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.3e-51], N[(x - N[(y / N[(a / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.16e-63

   1. Initial program 89.1%

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

   2. Taylor expanded in z around inf 78.1%

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

      1. associate-*l/ 61.0%

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

      2. *-commutative 61.0%

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

   4. Simplified 86.7%

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

      1. clear-num 86.7%

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

      2. un-div-inv 86.7%

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

   6. Applied egg-rr 86.7%

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

   if -1.16e-63 < z < 3.29999999999999973e-51

   1. Initial program 96.2%

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

   2. Taylor expanded in z around 0 90.3%

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

      1. mul-1-neg 90.3%

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

      2. associate-*l/ 91.2%

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

      3. unsub-neg 91.2%

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

      4. associate-*l/ 90.3%

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

      5. *-commutative 90.3%

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

      6. associate-/l* 92.0%

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

   4. Simplified 92.0%

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

   if 3.29999999999999973e-51 < z

   1. Initial program 92.9%

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

   2. Taylor expanded in z around inf 83.3%

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

      1. associate-*l/ 58.4%

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

      2. *-commutative 58.4%

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

   4. Simplified 87.6%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-51}:\\ \;\;\;\;x - \frac{y}{\frac{a}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 9: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+15} \lor \neg \left(z \leq 4.2 \cdot 10^{+39}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.05e+15) (not (<= z 4.2e+39))) (* z (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.05e+15) || !(z <= 4.2e+39)) {
		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 <= (-1.05d+15)) .or. (.not. (z <= 4.2d+39))) 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 <= -1.05e+15) || !(z <= 4.2e+39)) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.05e+15) or not (z <= 4.2e+39):
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.05e+15) || !(z <= 4.2e+39))
		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 <= -1.05e+15) || ~((z <= 4.2e+39)))
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.05e+15], N[Not[LessEqual[z, 4.2e+39]], $MachinePrecision]], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.05e15 or 4.1999999999999997e39 < z

   1. Initial program 88.3%

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

   2. Taylor expanded in x around 0 72.5%

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

   3. Taylor expanded in z around inf 62.6%

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

      1. associate-*l/ 69.2%

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

      2. *-commutative 69.2%

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

   5. Simplified 69.2%

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

   if -1.05e15 < z < 4.1999999999999997e39

   1. Initial program 96.6%

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

   2. Taylor expanded in x around inf 53.6%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+15} \lor \neg \left(z \leq 4.2 \cdot 10^{+39}\right):\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 39.8% 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 92.9%

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

2. Taylor expanded in x around inf 38.5%

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

3. Final simplification 38.5%

   \[\leadsto x \]

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 2023314 
(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)))