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

Percentage Accurate: 93.2% → 99.5%

Time: 10.5s

Alternatives: 9

Speedup: 1.0×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.2% 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: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z - t\right) \cdot y\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+194} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+209}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z t) y)))
   (if (or (<= t_1 -5e+194) (not (<= t_1 4e+209)))
     (+ x (/ y (/ a (- z t))))
     (+ 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 <= -5e+194) || !(t_1 <= 4e+209)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z - t) * y
    if ((t_1 <= (-5d+194)) .or. (.not. (t_1 <= 4d+209))) then
        tmp = x + (y / (a / (z - t)))
    else
        tmp = x + (t_1 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) * y;
	double tmp;
	if ((t_1 <= -5e+194) || !(t_1 <= 4e+209)) {
		tmp = x + (y / (a / (z - t)));
	} 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 <= -5e+194) or not (t_1 <= 4e+209):
		tmp = x + (y / (a / (z - t)))
	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 <= -5e+194) || !(t_1 <= 4e+209))
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	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 <= -5e+194) || ~((t_1 <= 4e+209)))
		tmp = x + (y / (a / (z - t)));
	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, -5e+194], N[Not[LessEqual[t$95$1, 4e+209]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $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)) < -4.99999999999999989e194 or 4.0000000000000003e209 < (*.f64 y (-.f64 z t))

   1. Initial program 80.9%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -4.99999999999999989e194 < (*.f64 y (-.f64 z t)) < 4.0000000000000003e209

   1. Initial program 98.9%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(z - t\right) \cdot y \leq -5 \cdot 10^{+194} \lor \neg \left(\left(z - t\right) \cdot y \leq 4 \cdot 10^{+209}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ t_2 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+164}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-224}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.35 \cdot 10^{+61}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y a)))) (t_2 (+ x (* z (/ y a)))))
   (if (<= z -1.3e+164)
     t_2
     (if (<= z -1.5e-144)
       t_1
       (if (<= z 6.4e-224)
         (- x (* y (/ t a)))
         (if (<= z 4.35e+61) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / a));
	double t_2 = x + (z * (y / a));
	double tmp;
	if (z <= -1.3e+164) {
		tmp = t_2;
	} else if (z <= -1.5e-144) {
		tmp = t_1;
	} else if (z <= 6.4e-224) {
		tmp = x - (y * (t / a));
	} else if (z <= 4.35e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = x - (t * (y / a))
    t_2 = x + (z * (y / a))
    if (z <= (-1.3d+164)) then
        tmp = t_2
    else if (z <= (-1.5d-144)) then
        tmp = t_1
    else if (z <= 6.4d-224) then
        tmp = x - (y * (t / a))
    else if (z <= 4.35d+61) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / a));
	double t_2 = x + (z * (y / a));
	double tmp;
	if (z <= -1.3e+164) {
		tmp = t_2;
	} else if (z <= -1.5e-144) {
		tmp = t_1;
	} else if (z <= 6.4e-224) {
		tmp = x - (y * (t / a));
	} else if (z <= 4.35e+61) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / a))
	t_2 = x + (z * (y / a))
	tmp = 0
	if z <= -1.3e+164:
		tmp = t_2
	elif z <= -1.5e-144:
		tmp = t_1
	elif z <= 6.4e-224:
		tmp = x - (y * (t / a))
	elif z <= 4.35e+61:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / a)))
	t_2 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (z <= -1.3e+164)
		tmp = t_2;
	elseif (z <= -1.5e-144)
		tmp = t_1;
	elseif (z <= 6.4e-224)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	elseif (z <= 4.35e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / a));
	t_2 = x + (z * (y / a));
	tmp = 0.0;
	if (z <= -1.3e+164)
		tmp = t_2;
	elseif (z <= -1.5e-144)
		tmp = t_1;
	elseif (z <= 6.4e-224)
		tmp = x - (y * (t / a));
	elseif (z <= 4.35e+61)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+164], t$95$2, If[LessEqual[z, -1.5e-144], t$95$1, If[LessEqual[z, 6.4e-224], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.35e+61], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e164 or 4.3500000000000001e61 < z

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 86.4%

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

      1. +-commutative 86.4%

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

      2. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

      1. associate-/r/ 93.5%

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

   9. Applied egg-rr 93.5%

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

   if -1.3e164 < z < -1.4999999999999999e-144 or 6.3999999999999997e-224 < z < 4.3500000000000001e61

   1. Initial program 93.6%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around 0 74.7%

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

      1. associate-*r/ 74.7%

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

      2. neg-mul-1 74.7%

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

   7. Simplified 74.7%

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

      1. associate-/r/ 85.1%

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

      2. add-sqr-sqrt 40.8%

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

      3. sqrt-unprod 52.3%

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

      4. sqr-neg 52.3%

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

      5. sqrt-unprod 23.8%

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

      6. add-sqr-sqrt 43.9%

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

      7. frac-2neg 43.9%

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

      8. distribute-frac-neg 43.9%

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

      9. cancel-sign-sub-inv 43.9%

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

      10. *-commutative 43.9%

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

      11. add-sqr-sqrt 20.1%

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

      12. sqrt-unprod 54.5%

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

      13. sqr-neg 54.5%

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

      14. sqrt-unprod 44.2%

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

      15. add-sqr-sqrt 85.1%

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

   9. Applied egg-rr 85.1%

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

   if -1.4999999999999999e-144 < z < 6.3999999999999997e-224

   1. Initial program 95.3%

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

      1. *-commutative 95.3%

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

      2. associate-/l* 90.8%

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

   3. Simplified 90.8%

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

   5. Taylor expanded in z around 0 92.4%

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

      1. mul-1-neg 92.4%

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

      2. associate-*r/ 88.0%

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

      3. unsub-neg 88.0%

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

      4. associate-*r/ 92.4%

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

      5. associate-/l* 88.1%

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

      6. associate-/r/ 95.5%

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

   7. Simplified 95.5%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+164}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-144}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-224}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.35 \cdot 10^{+61}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-254}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+63}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= z -3.3e+162)
     t_1
     (if (<= z -6.6e-254)
       (- x (* t (/ y a)))
       (if (<= z 3.05e+63) (- x (/ (* t y) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (z <= -3.3e+162) {
		tmp = t_1;
	} else if (z <= -6.6e-254) {
		tmp = x - (t * (y / a));
	} else if (z <= 3.05e+63) {
		tmp = x - ((t * y) / a);
	} 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 = x + (z * (y / a))
    if (z <= (-3.3d+162)) then
        tmp = t_1
    else if (z <= (-6.6d-254)) then
        tmp = x - (t * (y / a))
    else if (z <= 3.05d+63) then
        tmp = x - ((t * y) / a)
    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 = x + (z * (y / a));
	double tmp;
	if (z <= -3.3e+162) {
		tmp = t_1;
	} else if (z <= -6.6e-254) {
		tmp = x - (t * (y / a));
	} else if (z <= 3.05e+63) {
		tmp = x - ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if z <= -3.3e+162:
		tmp = t_1
	elif z <= -6.6e-254:
		tmp = x - (t * (y / a))
	elif z <= 3.05e+63:
		tmp = x - ((t * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (z <= -3.3e+162)
		tmp = t_1;
	elseif (z <= -6.6e-254)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (z <= 3.05e+63)
		tmp = Float64(x - Float64(Float64(t * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (z <= -3.3e+162)
		tmp = t_1;
	elseif (z <= -6.6e-254)
		tmp = x - (t * (y / a));
	elseif (z <= 3.05e+63)
		tmp = x - ((t * y) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+162], t$95$1, If[LessEqual[z, -6.6e-254], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.05e+63], N[(x - N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.29999999999999987e162 or 3.04999999999999984e63 < z

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 86.4%

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

      1. +-commutative 86.4%

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

      2. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

      1. associate-/r/ 93.5%

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

   9. Applied egg-rr 93.5%

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

   if -3.29999999999999987e162 < z < -6.60000000000000033e-254

   1. Initial program 91.6%

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

      1. associate-/l* 91.1%

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

   3. Simplified 91.1%

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

   5. Taylor expanded in z around 0 76.5%

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

      1. associate-*r/ 76.5%

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

      2. neg-mul-1 76.5%

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

   7. Simplified 76.5%

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

      1. associate-/r/ 85.1%

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

      2. add-sqr-sqrt 42.1%

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

      3. sqrt-unprod 52.7%

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

      4. sqr-neg 52.7%

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

      5. sqrt-unprod 23.3%

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

      6. add-sqr-sqrt 40.4%

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

      7. frac-2neg 40.4%

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

      8. distribute-frac-neg 40.4%

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

      9. cancel-sign-sub-inv 40.4%

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

      10. *-commutative 40.4%

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

      11. add-sqr-sqrt 17.1%

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

      12. sqrt-unprod 48.6%

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

      13. sqr-neg 48.6%

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

      14. sqrt-unprod 42.9%

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

      15. add-sqr-sqrt 85.1%

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

   9. Applied egg-rr 85.1%

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

   if -6.60000000000000033e-254 < z < 3.04999999999999984e63

   1. Initial program 97.5%

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

      1. +-commutative 97.5%

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

      2. associate-*r/ 94.0%

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

      3. fma-udef 94.0%

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

   3. Simplified 94.0%

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

      1. fma-udef 94.0%

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

      2. associate-*r/ 97.5%

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

      3. div-inv 97.4%

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

      4. div-inv 97.5%

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

      5. *-commutative 97.5%

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

      6. associate-*r/ 93.5%

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

   6. Applied egg-rr 93.5%

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

   7. Taylor expanded in z around 0 92.7%

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

      1. mul-1-neg 92.7%

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

      2. associate-*l/ 89.2%

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

      3. distribute-lft-neg-in 89.2%

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

      4. cancel-sign-sub-inv 89.2%

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

      5. associate-*l/ 92.7%

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

   9. Simplified 92.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+162}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-254}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 3.05 \cdot 10^{+63}:\\ \;\;\;\;x - \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+162} \lor \neg \left(z \leq 1.26 \cdot 10^{+63}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -3.3e+162) (not (<= z 1.26e+63)))
   (+ 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 <= -3.3e+162) || !(z <= 1.26e+63)) {
		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 <= (-3.3d+162)) .or. (.not. (z <= 1.26d+63))) 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 <= -3.3e+162) || !(z <= 1.26e+63)) {
		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 <= -3.3e+162) or not (z <= 1.26e+63):
		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 <= -3.3e+162) || !(z <= 1.26e+63))
		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 <= -3.3e+162) || ~((z <= 1.26e+63)))
		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, -3.3e+162], N[Not[LessEqual[z, 1.26e+63]], $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 < -3.29999999999999987e162 or 1.26e63 < z

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 86.4%

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

      1. +-commutative 86.4%

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

      2. associate-/l* 79.0%

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

   7. Simplified 79.0%

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

      1. associate-/r/ 93.5%

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

   9. Applied egg-rr 93.5%

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

   if -3.29999999999999987e162 < z < 1.26e63

   1. Initial program 94.2%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in z around 0 82.1%

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

      1. associate-*r/ 82.1%

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

      2. neg-mul-1 82.1%

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

   7. Simplified 82.1%

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

      1. associate-/r/ 86.2%

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

      2. add-sqr-sqrt 40.8%

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

      3. sqrt-unprod 55.1%

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

      4. sqr-neg 55.1%

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

      5. sqrt-unprod 24.3%

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

      6. add-sqr-sqrt 44.0%

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

      7. frac-2neg 44.0%

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

      8. distribute-frac-neg 44.0%

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

      9. cancel-sign-sub-inv 44.0%

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

      10. *-commutative 44.0%

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

      11. add-sqr-sqrt 19.7%

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

      12. sqrt-unprod 54.9%

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

      13. sqr-neg 54.9%

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

      14. sqrt-unprod 45.2%

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

      15. add-sqr-sqrt 86.2%

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

   9. Applied egg-rr 86.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+162} \lor \neg \left(z \leq 1.26 \cdot 10^{+63}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+207}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -9.2e+207) (+ x (/ (* z y) a)) (+ x (/ y (/ a (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -9.2e+207) {
		tmp = x + ((z * 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 (z <= (-9.2d+207)) then
        tmp = x + ((z * 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 (z <= -9.2e+207) {
		tmp = x + ((z * y) / a);
	} else {
		tmp = x + (y / (a / (z - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -9.2e+207:
		tmp = x + ((z * y) / a)
	else:
		tmp = x + (y / (a / (z - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -9.2e+207)
		tmp = Float64(x + Float64(Float64(z * 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 (z <= -9.2e+207)
		tmp = x + ((z * y) / a);
	else
		tmp = x + (y / (a / (z - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -9.2e+207], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.19999999999999979e207

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.9%

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

   if -9.19999999999999979e207 < z

   1. Initial program 92.8%

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

      1. associate-/l* 91.6%

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

   3. Simplified 91.6%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.2 \cdot 10^{+207}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. *-commutative 93.4%

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

   2. associate-/l* 96.7%

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

3. Simplified 96.7%

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

5. Final simplification 96.7%

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

Alternative 7: 67.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. *-commutative 93.4%

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

   2. associate-/l* 96.7%

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

3. Simplified 96.7%

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

5. Taylor expanded in z around inf 66.4%

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

6. Final simplification 66.4%

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

Alternative 8: 70.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. *-commutative 93.4%

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

   2. associate-/l* 96.7%

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

3. Simplified 96.7%

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

5. Taylor expanded in t around 0 66.4%

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

   1. +-commutative 66.4%

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

   2. associate-/l* 64.0%

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

7. Simplified 64.0%

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

   1. associate-/r/ 68.8%

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

9. Applied egg-rr 68.8%

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

10. Final simplification 68.8%

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

Alternative 9: 39.3% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. *-commutative 93.4%

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

   2. associate-/l* 96.7%

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

3. Simplified 96.7%

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

5. Taylor expanded in x around inf 38.3%

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

6. Final simplification 38.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024027 
(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)))