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

Percentage Accurate: 93.0% → 98.8%

Time: 10.6s

Alternatives: 15

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: 98.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.3e+102)
   (- x (/ y (/ a (- z t))))
   (if (<= a 3.3e+34)
     (- x (/ 1.0 (/ a (* y (- z t)))))
     (+ x (* y (/ (- t z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e+102) {
		tmp = x - (y / (a / (z - t)));
	} else if (a <= 3.3e+34) {
		tmp = x - (1.0 / (a / (y * (z - t))));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.3d+102)) then
        tmp = x - (y / (a / (z - t)))
    else if (a <= 3.3d+34) then
        tmp = x - (1.0d0 / (a / (y * (z - t))))
    else
        tmp = x + (y * ((t - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e+102) {
		tmp = x - (y / (a / (z - t)));
	} else if (a <= 3.3e+34) {
		tmp = x - (1.0 / (a / (y * (z - t))));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.3e+102:
		tmp = x - (y / (a / (z - t)))
	elif a <= 3.3e+34:
		tmp = x - (1.0 / (a / (y * (z - t))))
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.3e+102)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= 3.3e+34)
		tmp = Float64(x - Float64(1.0 / Float64(a / Float64(y * Float64(z - t)))));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.3e+102)
		tmp = x - (y / (a / (z - t)));
	elseif (a <= 3.3e+34)
		tmp = x - (1.0 / (a / (y * (z - t))));
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.3e+102], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.3e+34], N[(x - N[(1.0 / N[(a / N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.3000000000000001e102

   1. Initial program 87.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -4.3000000000000001e102 < a < 3.29999999999999988e34

   1. Initial program 99.8%

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

      1. associate-/l* 87.7%

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

   3. Simplified 87.7%

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

      1. associate-*r/ 99.8%

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

      2. clear-num 99.8%

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

   6. Applied egg-rr 99.8%

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

   if 3.29999999999999988e34 < a

   1. Initial program 80.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+34}:\\ \;\;\;\;x - \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 51.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-z}{a}\\ \mathbf{if}\;t \leq -1.75 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+37}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z) a))))
   (if (<= t -1.75e+65)
     (* t (/ y a))
     (if (<= t -4.2e-240)
       x
       (if (<= t -2.9e-300)
         t_1
         (if (<= t 8.5e-55)
           x
           (if (<= t 4e+37) t_1 (if (<= t 6.3e+99) x (/ t (/ a y))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-z / a);
	double tmp;
	if (t <= -1.75e+65) {
		tmp = t * (y / a);
	} else if (t <= -4.2e-240) {
		tmp = x;
	} else if (t <= -2.9e-300) {
		tmp = t_1;
	} else if (t <= 8.5e-55) {
		tmp = x;
	} else if (t <= 4e+37) {
		tmp = t_1;
	} else if (t <= 6.3e+99) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (-z / a)
    if (t <= (-1.75d+65)) then
        tmp = t * (y / a)
    else if (t <= (-4.2d-240)) then
        tmp = x
    else if (t <= (-2.9d-300)) then
        tmp = t_1
    else if (t <= 8.5d-55) then
        tmp = x
    else if (t <= 4d+37) then
        tmp = t_1
    else if (t <= 6.3d+99) then
        tmp = x
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-z / a);
	double tmp;
	if (t <= -1.75e+65) {
		tmp = t * (y / a);
	} else if (t <= -4.2e-240) {
		tmp = x;
	} else if (t <= -2.9e-300) {
		tmp = t_1;
	} else if (t <= 8.5e-55) {
		tmp = x;
	} else if (t <= 4e+37) {
		tmp = t_1;
	} else if (t <= 6.3e+99) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-z / a)
	tmp = 0
	if t <= -1.75e+65:
		tmp = t * (y / a)
	elif t <= -4.2e-240:
		tmp = x
	elif t <= -2.9e-300:
		tmp = t_1
	elif t <= 8.5e-55:
		tmp = x
	elif t <= 4e+37:
		tmp = t_1
	elif t <= 6.3e+99:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-z) / a))
	tmp = 0.0
	if (t <= -1.75e+65)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= -4.2e-240)
		tmp = x;
	elseif (t <= -2.9e-300)
		tmp = t_1;
	elseif (t <= 8.5e-55)
		tmp = x;
	elseif (t <= 4e+37)
		tmp = t_1;
	elseif (t <= 6.3e+99)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-z / a);
	tmp = 0.0;
	if (t <= -1.75e+65)
		tmp = t * (y / a);
	elseif (t <= -4.2e-240)
		tmp = x;
	elseif (t <= -2.9e-300)
		tmp = t_1;
	elseif (t <= 8.5e-55)
		tmp = x;
	elseif (t <= 4e+37)
		tmp = t_1;
	elseif (t <= 6.3e+99)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((-z) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.75e+65], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -4.2e-240], x, If[LessEqual[t, -2.9e-300], t$95$1, If[LessEqual[t, 8.5e-55], x, If[LessEqual[t, 4e+37], t$95$1, If[LessEqual[t, 6.3e+99], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.75e65

   1. Initial program 88.9%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

      1. add-cube-cbrt 88.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 88.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 87.9%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 87.9%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 97.0%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in t around inf 61.0%

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

      1. associate-*r/ 68.2%

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

   9. Simplified 68.2%

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

   if -1.75e65 < t < -4.19999999999999987e-240 or -2.89999999999999992e-300 < t < 8.49999999999999968e-55 or 3.99999999999999982e37 < t < 6.2999999999999996e99

   1. Initial program 96.2%

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

      1. associate-/l* 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around inf 61.9%

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

   if -4.19999999999999987e-240 < t < -2.89999999999999992e-300 or 8.49999999999999968e-55 < t < 3.99999999999999982e37

   1. Initial program 96.0%

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

      1. associate-/l* 85.3%

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

   3. Simplified 85.3%

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

   5. Taylor expanded in z around inf 73.6%

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

      1. mul-1-neg 73.6%

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

      2. associate-/l* 62.9%

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

      3. distribute-rgt-neg-in 62.9%

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

      4. distribute-frac-neg2 62.9%

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

   7. Simplified 62.9%

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

   if 6.2999999999999996e99 < t

   1. Initial program 84.4%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

      1. add-cube-cbrt 93.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 93.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 83.8%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 83.8%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 95.1%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 95.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in t around inf 58.3%

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

      1. associate-*r/ 64.6%

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

   9. Simplified 64.6%

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

       1. clear-num 64.6%

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

       2. un-div-inv 64.6%

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

   11. Applied egg-rr 64.6%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.75 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{-55}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+37}:\\ \;\;\;\;y \cdot \frac{-z}{a}\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ t_2 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.85 \cdot 10^{+31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))) (t_2 (* t (/ y a))))
   (if (<= t -1.25e+65)
     t_2
     (if (<= t -2.15e-240)
       x
       (if (<= t -6.5e-306)
         t_1
         (if (<= t 3.2e-78) x (if (<= t 3.85e+31) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double t_2 = t * (y / a);
	double tmp;
	if (t <= -1.25e+65) {
		tmp = t_2;
	} else if (t <= -2.15e-240) {
		tmp = x;
	} else if (t <= -6.5e-306) {
		tmp = t_1;
	} else if (t <= 3.2e-78) {
		tmp = x;
	} else if (t <= 3.85e+31) {
		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 = z * (y / -a)
    t_2 = t * (y / a)
    if (t <= (-1.25d+65)) then
        tmp = t_2
    else if (t <= (-2.15d-240)) then
        tmp = x
    else if (t <= (-6.5d-306)) then
        tmp = t_1
    else if (t <= 3.2d-78) then
        tmp = x
    else if (t <= 3.85d+31) 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 = z * (y / -a);
	double t_2 = t * (y / a);
	double tmp;
	if (t <= -1.25e+65) {
		tmp = t_2;
	} else if (t <= -2.15e-240) {
		tmp = x;
	} else if (t <= -6.5e-306) {
		tmp = t_1;
	} else if (t <= 3.2e-78) {
		tmp = x;
	} else if (t <= 3.85e+31) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	t_2 = t * (y / a)
	tmp = 0
	if t <= -1.25e+65:
		tmp = t_2
	elif t <= -2.15e-240:
		tmp = x
	elif t <= -6.5e-306:
		tmp = t_1
	elif t <= 3.2e-78:
		tmp = x
	elif t <= 3.85e+31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	t_2 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t <= -1.25e+65)
		tmp = t_2;
	elseif (t <= -2.15e-240)
		tmp = x;
	elseif (t <= -6.5e-306)
		tmp = t_1;
	elseif (t <= 3.2e-78)
		tmp = x;
	elseif (t <= 3.85e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	t_2 = t * (y / a);
	tmp = 0.0;
	if (t <= -1.25e+65)
		tmp = t_2;
	elseif (t <= -2.15e-240)
		tmp = x;
	elseif (t <= -6.5e-306)
		tmp = t_1;
	elseif (t <= 3.2e-78)
		tmp = x;
	elseif (t <= 3.85e+31)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+65], t$95$2, If[LessEqual[t, -2.15e-240], x, If[LessEqual[t, -6.5e-306], t$95$1, If[LessEqual[t, 3.2e-78], x, If[LessEqual[t, 3.85e+31], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.24999999999999993e65 or 3.84999999999999984e31 < t

   1. Initial program 87.5%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

      1. add-cube-cbrt 90.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 90.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 86.6%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 86.6%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 96.4%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 96.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in t around inf 56.2%

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

      1. associate-*r/ 62.1%

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

   9. Simplified 62.1%

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

   if -1.24999999999999993e65 < t < -2.15000000000000007e-240 or -6.5000000000000004e-306 < t < 3.2e-78

   1. Initial program 96.5%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf 62.9%

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

   if -2.15000000000000007e-240 < t < -6.5000000000000004e-306 or 3.2e-78 < t < 3.84999999999999984e31

   1. Initial program 96.2%

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

      1. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

      1. add-cube-cbrt 81.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 81.5%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 95.1%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 95.1%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 98.5%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 98.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in z around inf 74.7%

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

      1. associate-*r/ 74.7%

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

      2. *-commutative 74.7%

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

      3. neg-mul-1 74.7%

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

      4. distribute-rgt-neg-out 74.7%

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

      5. associate-*r/ 78.2%

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

   9. Simplified 78.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-240}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-306}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-78}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.85 \cdot 10^{+31}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+65}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= t -3.7e+65)
     t_1
     (if (<= t -5.5e-242)
       x
       (if (<= t -1.8e-302)
         (* z (/ y (- a)))
         (if (<= t 3.2e-77) x (if (<= t 3.6e+31) (/ (* y z) (- a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -3.7e+65) {
		tmp = t_1;
	} else if (t <= -5.5e-242) {
		tmp = x;
	} else if (t <= -1.8e-302) {
		tmp = z * (y / -a);
	} else if (t <= 3.2e-77) {
		tmp = x;
	} else if (t <= 3.6e+31) {
		tmp = (y * z) / -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 = t * (y / a)
    if (t <= (-3.7d+65)) then
        tmp = t_1
    else if (t <= (-5.5d-242)) then
        tmp = x
    else if (t <= (-1.8d-302)) then
        tmp = z * (y / -a)
    else if (t <= 3.2d-77) then
        tmp = x
    else if (t <= 3.6d+31) then
        tmp = (y * z) / -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 = t * (y / a);
	double tmp;
	if (t <= -3.7e+65) {
		tmp = t_1;
	} else if (t <= -5.5e-242) {
		tmp = x;
	} else if (t <= -1.8e-302) {
		tmp = z * (y / -a);
	} else if (t <= 3.2e-77) {
		tmp = x;
	} else if (t <= 3.6e+31) {
		tmp = (y * z) / -a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if t <= -3.7e+65:
		tmp = t_1
	elif t <= -5.5e-242:
		tmp = x
	elif t <= -1.8e-302:
		tmp = z * (y / -a)
	elif t <= 3.2e-77:
		tmp = x
	elif t <= 3.6e+31:
		tmp = (y * z) / -a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t <= -3.7e+65)
		tmp = t_1;
	elseif (t <= -5.5e-242)
		tmp = x;
	elseif (t <= -1.8e-302)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (t <= 3.2e-77)
		tmp = x;
	elseif (t <= 3.6e+31)
		tmp = Float64(Float64(y * z) / Float64(-a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (y / a);
	tmp = 0.0;
	if (t <= -3.7e+65)
		tmp = t_1;
	elseif (t <= -5.5e-242)
		tmp = x;
	elseif (t <= -1.8e-302)
		tmp = z * (y / -a);
	elseif (t <= 3.2e-77)
		tmp = x;
	elseif (t <= 3.6e+31)
		tmp = (y * z) / -a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+65], t$95$1, If[LessEqual[t, -5.5e-242], x, If[LessEqual[t, -1.8e-302], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-77], x, If[LessEqual[t, 3.6e+31], N[(N[(y * z), $MachinePrecision] / (-a)), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -3.69999999999999995e65 or 3.59999999999999996e31 < t

   1. Initial program 87.5%

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

      1. associate-/l* 91.8%

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

   3. Simplified 91.8%

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

      1. add-cube-cbrt 90.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 90.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 86.6%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 86.6%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 96.4%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 96.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in t around inf 56.2%

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

      1. associate-*r/ 62.1%

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

   9. Simplified 62.1%

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

   if -3.69999999999999995e65 < t < -5.4999999999999998e-242 or -1.8e-302 < t < 3.2e-77

   1. Initial program 96.5%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in x around inf 62.9%

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

   if -5.4999999999999998e-242 < t < -1.8e-302

   1. Initial program 92.3%

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

      1. associate-/l* 78.0%

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

   3. Simplified 78.0%

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

      1. add-cube-cbrt 76.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 76.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 91.0%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 91.0%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 98.1%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in z around inf 77.3%

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

      1. associate-*r/ 77.3%

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

      2. *-commutative 77.3%

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

      3. neg-mul-1 77.3%

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

      4. distribute-rgt-neg-out 77.3%

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

      5. associate-*r/ 84.8%

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

   9. Simplified 84.8%

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

   if 3.2e-77 < t < 3.59999999999999996e31

   1. Initial program 99.8%

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

      1. associate-/l* 86.6%

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

   3. Simplified 86.6%

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

   5. Taylor expanded in z around inf 72.2%

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

      1. mul-1-neg 72.2%

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

      2. associate-/l* 58.8%

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

      3. distribute-rgt-neg-in 58.8%

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

      4. distribute-frac-neg2 58.8%

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

   7. Simplified 58.8%

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

      1. *-commutative 58.8%

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

      2. distribute-frac-neg2 58.8%

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

      3. distribute-frac-neg 58.8%

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

      4. associate-*l/ 72.2%

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

   9. Applied egg-rr 72.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+65}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-242}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-302}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-77}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;\frac{y \cdot z}{-a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+115} \lor \neg \left(z \leq 2.1 \cdot 10^{-22} \lor \neg \left(z \leq 7.2 \cdot 10^{+17}\right) \land z \leq 2.7 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4.4e+115)
         (not (or (<= z 2.1e-22) (and (not (<= z 7.2e+17)) (<= z 2.7e+92)))))
   (* (/ y a) (- t z))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -4.4e+115) || !((z <= 2.1e-22) || (!(z <= 7.2e+17) && (z <= 2.7e+92)))) {
		tmp = (y / a) * (t - z);
	} 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 <= (-4.4d+115)) .or. (.not. (z <= 2.1d-22) .or. (.not. (z <= 7.2d+17)) .and. (z <= 2.7d+92))) then
        tmp = (y / a) * (t - z)
    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 <= -4.4e+115) || !((z <= 2.1e-22) || (!(z <= 7.2e+17) && (z <= 2.7e+92)))) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -4.4e+115) or not ((z <= 2.1e-22) or (not (z <= 7.2e+17) and (z <= 2.7e+92))):
		tmp = (y / a) * (t - z)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -4.4e+115) || !((z <= 2.1e-22) || (!(z <= 7.2e+17) && (z <= 2.7e+92))))
		tmp = Float64(Float64(y / a) * Float64(t - z));
	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 <= -4.4e+115) || ~(((z <= 2.1e-22) || (~((z <= 7.2e+17)) && (z <= 2.7e+92)))))
		tmp = (y / a) * (t - z);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -4.4e+115], N[Not[Or[LessEqual[z, 2.1e-22], And[N[Not[LessEqual[z, 7.2e+17]], $MachinePrecision], LessEqual[z, 2.7e+92]]]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.4000000000000001e115 or 2.10000000000000008e-22 < z < 7.2e17 or 2.6999999999999999e92 < z

   1. Initial program 90.3%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

      1. add-cube-cbrt 87.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 87.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 89.2%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 89.2%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 95.9%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 95.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in x around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. associate-/l* 71.3%

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

      3. distribute-lft-neg-in 71.3%

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

      4. div-sub 71.1%

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

      5. distribute-lft-out-- 70.2%

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

      6. distribute-lft-neg-in 70.2%

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

      7. associate-*r/ 71.0%

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

      8. mul-1-neg 71.0%

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

      9. cancel-sign-sub 71.0%

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

      10. *-commutative 71.0%

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

      11. associate-*l/ 72.8%

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

      12. +-commutative 72.8%

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

      13. associate-*r/ 72.7%

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

      14. fma-define 72.7%

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

      15. mul-1-neg 72.7%

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

      16. associate-*r/ 68.2%

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

      17. fma-neg 68.2%

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

      18. *-commutative 68.2%

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

      19. associate-*l/ 72.7%

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

      20. associate-*r/ 77.6%

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

      21. distribute-rgt-out-- 80.6%

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

   9. Simplified 80.6%

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

   if -4.4000000000000001e115 < z < 2.10000000000000008e-22 or 7.2e17 < z < 2.6999999999999999e92

   1. Initial program 93.8%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

      1. add-cube-cbrt 94.3%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 94.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 92.2%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 92.2%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 95.9%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 95.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in z around 0 86.7%

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

      1. mul-1-neg 86.7%

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

      2. associate-*r/ 90.9%

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

      3. distribute-lft-neg-out 90.9%

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

      4. cancel-sign-sub 90.9%

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

   9. Simplified 90.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{+115} \lor \neg \left(z \leq 2.1 \cdot 10^{-22} \lor \neg \left(z \leq 7.2 \cdot 10^{+17}\right) \land z \leq 2.7 \cdot 10^{+92}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+34}:\\ \;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.5e+104)
   (- x (/ y (/ a (- z t))))
   (if (<= a 1.7e+34)
     (- x (* (* y (- z t)) (/ 1.0 a)))
     (+ x (* y (/ (- t z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+104) {
		tmp = x - (y / (a / (z - t)));
	} else if (a <= 1.7e+34) {
		tmp = x - ((y * (z - t)) * (1.0 / a));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.5d+104)) then
        tmp = x - (y / (a / (z - t)))
    else if (a <= 1.7d+34) then
        tmp = x - ((y * (z - t)) * (1.0d0 / a))
    else
        tmp = x + (y * ((t - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.5e+104) {
		tmp = x - (y / (a / (z - t)));
	} else if (a <= 1.7e+34) {
		tmp = x - ((y * (z - t)) * (1.0 / a));
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.5e+104:
		tmp = x - (y / (a / (z - t)))
	elif a <= 1.7e+34:
		tmp = x - ((y * (z - t)) * (1.0 / a))
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.5e+104)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= 1.7e+34)
		tmp = Float64(x - Float64(Float64(y * Float64(z - t)) * Float64(1.0 / a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.5e+104)
		tmp = x - (y / (a / (z - t)));
	elseif (a <= 1.7e+34)
		tmp = x - ((y * (z - t)) * (1.0 / a));
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e+104], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+34], N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] * N[(1.0 / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.49999999999999984e104

   1. Initial program 87.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -1.49999999999999984e104 < a < 1.7e34

   1. Initial program 99.8%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 99.8%

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

   4. Applied egg-rr 99.8%

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

   if 1.7e34 < a

   1. Initial program 80.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+34}:\\ \;\;\;\;x - \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 10^{+34}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -4.3e+102)
   (- x (/ y (/ a (- z t))))
   (if (<= a 1e+34) (- x (/ (* y (- z t)) a)) (+ x (* y (/ (- t z) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e+102) {
		tmp = x - (y / (a / (z - t)));
	} else if (a <= 1e+34) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-4.3d+102)) then
        tmp = x - (y / (a / (z - t)))
    else if (a <= 1d+34) then
        tmp = x - ((y * (z - t)) / a)
    else
        tmp = x + (y * ((t - z) / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -4.3e+102) {
		tmp = x - (y / (a / (z - t)));
	} else if (a <= 1e+34) {
		tmp = x - ((y * (z - t)) / a);
	} else {
		tmp = x + (y * ((t - z) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -4.3e+102:
		tmp = x - (y / (a / (z - t)))
	elif a <= 1e+34:
		tmp = x - ((y * (z - t)) / a)
	else:
		tmp = x + (y * ((t - z) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -4.3e+102)
		tmp = Float64(x - Float64(y / Float64(a / Float64(z - t))));
	elseif (a <= 1e+34)
		tmp = Float64(x - Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(t - z) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -4.3e+102)
		tmp = x - (y / (a / (z - t)));
	elseif (a <= 1e+34)
		tmp = x - ((y * (z - t)) / a);
	else
		tmp = x + (y * ((t - z) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -4.3e+102], N[(x - N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1e+34], N[(x - N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.3000000000000001e102

   1. Initial program 87.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -4.3000000000000001e102 < a < 9.99999999999999946e33

   1. Initial program 99.8%

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

   if 9.99999999999999946e33 < a

   1. Initial program 80.1%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+102}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq 10^{+34}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+40} \lor \neg \left(t \leq 3.7 \cdot 10^{+31}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -2.6e+40) (not (<= t 3.7e+31)))
   (+ x (* t (/ y a)))
   (- x (/ y (/ a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e+40) || !(t <= 3.7e+31)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-2.6d+40)) .or. (.not. (t <= 3.7d+31))) then
        tmp = x + (t * (y / a))
    else
        tmp = x - (y / (a / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -2.6e+40) || !(t <= 3.7e+31)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - (y / (a / z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -2.6e+40) or not (t <= 3.7e+31):
		tmp = x + (t * (y / a))
	else:
		tmp = x - (y / (a / z))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -2.6e+40) || !(t <= 3.7e+31))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(y / Float64(a / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -2.6e+40) || ~((t <= 3.7e+31)))
		tmp = x + (t * (y / a));
	else
		tmp = x - (y / (a / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2.6e+40], N[Not[LessEqual[t, 3.7e+31]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.6000000000000001e40 or 3.6999999999999998e31 < t

   1. Initial program 87.7%

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

      1. associate-/l* 92.5%

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

   3. Simplified 92.5%

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

      1. add-cube-cbrt 91.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 91.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 86.8%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 86.8%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 96.5%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 96.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in z around 0 78.5%

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

      1. mul-1-neg 78.5%

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

      2. associate-*r/ 86.2%

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

      3. distribute-lft-neg-out 86.2%

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

      4. cancel-sign-sub 86.2%

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

   9. Simplified 86.2%

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

   if -2.6000000000000001e40 < t < 3.6999999999999998e31

   1. Initial program 96.9%

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

      1. associate-/l* 93.7%

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

   3. Simplified 93.7%

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

      1. clear-num 93.4%

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

      2. un-div-inv 93.7%

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

   6. Applied egg-rr 93.7%

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

   7. Taylor expanded in z around inf 89.4%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.6 \cdot 10^{+40} \lor \neg \left(t \leq 3.7 \cdot 10^{+31}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-23} \lor \neg \left(t \leq 3.85 \cdot 10^{+31}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.6e-23) (not (<= t 3.85e+31)))
   (+ x (* t (/ y a)))
   (- x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.6e-23) || !(t <= 3.85e+31)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.6d-23)) .or. (.not. (t <= 3.85d+31))) then
        tmp = x + (t * (y / a))
    else
        tmp = x - ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.6e-23) || !(t <= 3.85e+31)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = x - ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.6e-23) or not (t <= 3.85e+31):
		tmp = x + (t * (y / a))
	else:
		tmp = x - ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.6e-23) || !(t <= 3.85e+31))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(x - Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.6e-23) || ~((t <= 3.85e+31)))
		tmp = x + (t * (y / a));
	else
		tmp = x - ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.6e-23], N[Not[LessEqual[t, 3.85e+31]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5999999999999998e-23 or 3.84999999999999984e31 < t

   1. Initial program 87.9%

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

      1. associate-/l* 93.0%

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

   3. Simplified 93.0%

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

      1. add-cube-cbrt 91.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 91.9%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 86.9%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 86.9%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 96.6%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 96.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in z around 0 78.6%

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

      1. mul-1-neg 78.6%

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

      2. associate-*r/ 85.8%

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

      3. distribute-lft-neg-out 85.8%

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

      4. cancel-sign-sub 85.8%

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

   9. Simplified 85.8%

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

   if -3.5999999999999998e-23 < t < 3.84999999999999984e31

   1. Initial program 97.5%

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

      1. associate-/l* 93.2%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in z around inf 93.0%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.6 \cdot 10^{-23} \lor \neg \left(t \leq 3.85 \cdot 10^{+31}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.05e+132) x (if (<= a 2.6e+53) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.05e+132) {
		tmp = x;
	} else if (a <= 2.6e+53) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.05d+132)) then
        tmp = x
    else if (a <= 2.6d+53) then
        tmp = (y / a) * (t - z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.05e+132) {
		tmp = x;
	} else if (a <= 2.6e+53) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.05e+132:
		tmp = x
	elif a <= 2.6e+53:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.05e+132)
		tmp = x;
	elseif (a <= 2.6e+53)
		tmp = Float64(Float64(y / a) * Float64(t - z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.05e+132)
		tmp = x;
	elseif (a <= 2.6e+53)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.05e+132], x, If[LessEqual[a, 2.6e+53], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.04999999999999997e132 or 2.59999999999999998e53 < a

   1. Initial program 83.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 67.9%

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

   if -1.04999999999999997e132 < a < 2.59999999999999998e53

   1. Initial program 98.6%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

      1. add-cube-cbrt 87.6%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 87.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 97.4%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 97.4%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 96.2%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 96.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in x around 0 75.1%

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

      1. mul-1-neg 75.1%

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

      2. associate-/l* 65.6%

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

      3. distribute-lft-neg-in 65.6%

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

      4. div-sub 65.5%

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

      5. distribute-lft-out-- 61.6%

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

      6. distribute-lft-neg-in 61.6%

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

      7. associate-*r/ 65.9%

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

      8. mul-1-neg 65.9%

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

      9. cancel-sign-sub 65.9%

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

      10. *-commutative 65.9%

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

      11. associate-*l/ 71.2%

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

      12. +-commutative 71.2%

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

      13. associate-*r/ 69.3%

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

      14. fma-define 69.3%

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

      15. mul-1-neg 69.3%

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

      16. associate-*r/ 62.6%

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

      17. fma-neg 62.6%

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

      18. *-commutative 62.6%

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

      19. associate-*l/ 69.3%

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

      20. associate-*r/ 67.9%

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

      21. distribute-rgt-out-- 74.6%

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

   9. Simplified 74.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+132}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{+53}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+72} \lor \neg \left(t \leq 1.3 \cdot 10^{+108}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.4e+72) (not (<= t 1.3e+108))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.4e+72) || !(t <= 1.3e+108)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.4d+72)) .or. (.not. (t <= 1.3d+108))) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.4e+72) || !(t <= 1.3e+108)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.4e+72) or not (t <= 1.3e+108):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.4e+72) || !(t <= 1.3e+108))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.4e+72) || ~((t <= 1.3e+108)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.4e+72], N[Not[LessEqual[t, 1.3e+108]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -3.3999999999999998e72 or 1.3000000000000001e108 < t

   1. Initial program 86.7%

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

      1. associate-/l* 91.7%

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

   3. Simplified 91.7%

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

      1. add-cube-cbrt 90.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 90.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 85.9%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 85.9%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 96.1%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 96.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in t around inf 59.7%

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

      1. associate-*r/ 66.4%

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

   9. Simplified 66.4%

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

   if -3.3999999999999998e72 < t < 1.3000000000000001e108

   1. Initial program 96.1%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in x around inf 54.5%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{+72} \lor \neg \left(t \leq 1.3 \cdot 10^{+108}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.3e+68) (* t (/ y a)) (if (<= t 1.55e+105) x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e+68) {
		tmp = t * (y / a);
	} else if (t <= 1.55e+105) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-2.3d+68)) then
        tmp = t * (y / a)
    else if (t <= 1.55d+105) then
        tmp = x
    else
        tmp = t / (a / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.3e+68) {
		tmp = t * (y / a);
	} else if (t <= 1.55e+105) {
		tmp = x;
	} else {
		tmp = t / (a / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.3e+68:
		tmp = t * (y / a)
	elif t <= 1.55e+105:
		tmp = x
	else:
		tmp = t / (a / y)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.3e+68)
		tmp = Float64(t * Float64(y / a));
	elseif (t <= 1.55e+105)
		tmp = x;
	else
		tmp = Float64(t / Float64(a / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.3e+68)
		tmp = t * (y / a);
	elseif (t <= 1.55e+105)
		tmp = x;
	else
		tmp = t / (a / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.3e+68], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.55e+105], x, N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.3e68

   1. Initial program 88.9%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

      1. add-cube-cbrt 88.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 88.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 87.9%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 87.9%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 97.0%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 97.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in t around inf 61.0%

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

      1. associate-*r/ 68.2%

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

   9. Simplified 68.2%

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

   if -2.3e68 < t < 1.55000000000000002e105

   1. Initial program 96.1%

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

      1. associate-/l* 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in x around inf 54.5%

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

   if 1.55000000000000002e105 < t

   1. Initial program 84.4%

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

      1. associate-/l* 94.4%

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

   3. Simplified 94.4%

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

      1. add-cube-cbrt 93.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}} \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}\right) \cdot \sqrt[3]{x - y \cdot \frac{z - t}{a}}} \]

      2. pow3 93.4%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x - y \cdot \frac{z - t}{a}}\right)}^{3}} \]

      3. associate-*r/ 83.8%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\frac{y \cdot \left(z - t\right)}{a}}}\right)}^{3} \]

      4. *-commutative 83.8%

         \[\leadsto {\left(\sqrt[3]{x - \frac{\color{blue}{\left(z - t\right) \cdot y}}{a}}\right)}^{3} \]

      5. associate-/l* 95.1%

         \[\leadsto {\left(\sqrt[3]{x - \color{blue}{\left(z - t\right) \cdot \frac{y}{a}}}\right)}^{3} \]

   6. Applied egg-rr 95.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x - \left(z - t\right) \cdot \frac{y}{a}}\right)}^{3}} \]

   7. Taylor expanded in t around inf 58.3%

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

      1. associate-*r/ 64.6%

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

   9. Simplified 64.6%

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

       1. clear-num 64.6%

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

       2. un-div-inv 64.6%

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

   11. Applied egg-rr 64.6%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+68}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. associate-/l* 93.1%

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

3. Simplified 93.1%

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

5. Final simplification 93.1%

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

Alternative 14: 93.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.4%

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

   1. associate-/l* 93.1%

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

3. Simplified 93.1%

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

   1. clear-num 92.9%

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

   2. un-div-inv 93.5%

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

6. Applied egg-rr 93.5%

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

7. Final simplification 93.5%

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

Alternative 15: 39.9% 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 92.4%

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

   1. associate-/l* 93.1%

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

3. Simplified 93.1%

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

5. Taylor expanded in x around inf 42.2%

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

6. Final simplification 42.2%

   \[\leadsto x \]
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 2024079 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

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

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