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

Percentage Accurate: 93.0% → 97.0%

Time: 8.4s

Alternatives: 12

Speedup: 1.0×

• 25.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.0% 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: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-/l* 95.3%

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

3. Simplified 95.3%

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

5. Taylor expanded in y around 0 91.8%

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

   1. associate-*l/ 98.0%

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

   2. *-commutative 98.0%

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

7. Simplified 98.0%

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

   1. clear-num 98.0%

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

   2. un-div-inv 98.4%

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

9. Applied egg-rr 98.4%

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

10. Final simplification 98.4%

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

Alternative 2: 67.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+31} \lor \neg \left(y \leq -2.4 \cdot 10^{-26} \lor \neg \left(y \leq -1.6 \cdot 10^{-156}\right) \land y \leq 3.3 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.8e+31)
         (not
          (or (<= y -2.4e-26) (and (not (<= y -1.6e-156)) (<= y 3.3e-26)))))
   (* y (/ (- t z) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e+31) || !((y <= -2.4e-26) || (!(y <= -1.6e-156) && (y <= 3.3e-26)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.8d+31)) .or. (.not. (y <= (-2.4d-26)) .or. (.not. (y <= (-1.6d-156))) .and. (y <= 3.3d-26))) then
        tmp = y * ((t - z) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.8e+31) || !((y <= -2.4e-26) || (!(y <= -1.6e-156) && (y <= 3.3e-26)))) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.8e+31) or not ((y <= -2.4e-26) or (not (y <= -1.6e-156) and (y <= 3.3e-26))):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.8e+31) || !((y <= -2.4e-26) || (!(y <= -1.6e-156) && (y <= 3.3e-26))))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.8e+31) || ~(((y <= -2.4e-26) || (~((y <= -1.6e-156)) && (y <= 3.3e-26)))))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.8e+31], N[Not[Or[LessEqual[y, -2.4e-26], And[N[Not[LessEqual[y, -1.6e-156]], $MachinePrecision], LessEqual[y, 3.3e-26]]]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999998e31 or -2.4000000000000001e-26 < y < -1.59999999999999991e-156 or 3.2999999999999998e-26 < y

   1. Initial program 87.7%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. distribute-frac-neg2 66.6%

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

      3. sub-neg 66.6%

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

      4. +-commutative 66.6%

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

      5. neg-sub0 66.6%

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(0 - t\right)} + z\right)}{-a} \]

      6. associate--r- 66.6%

         \[\leadsto \frac{y \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}}{-a} \]

      7. neg-sub0 66.6%

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

      8. associate-*r/ 77.0%

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

      9. distribute-neg-frac 77.0%

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

      10. distribute-neg-frac2 77.0%

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

      11. remove-double-neg 77.0%

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

   7. Simplified 77.0%

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

   if -1.79999999999999998e31 < y < -2.4000000000000001e-26 or -1.59999999999999991e-156 < y < 3.2999999999999998e-26

   1. Initial program 99.8%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in x around inf 72.0%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+31} \lor \neg \left(y \leq -2.4 \cdot 10^{-26} \lor \neg \left(y \leq -1.6 \cdot 10^{-156}\right) \land y \leq 3.3 \cdot 10^{-26}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -2.4 \cdot 10^{+60}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-111}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= t -2.4e+60)
     t_1
     (if (<= t 2.25e-237)
       x
       (if (<= t 2.8e-111) (* (/ y a) (- z)) (if (<= t 1.05e+27) x 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 <= -2.4e+60) {
		tmp = t_1;
	} else if (t <= 2.25e-237) {
		tmp = x;
	} else if (t <= 2.8e-111) {
		tmp = (y / a) * -z;
	} else if (t <= 1.05e+27) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (t <= (-2.4d+60)) then
        tmp = t_1
    else if (t <= 2.25d-237) then
        tmp = x
    else if (t <= 2.8d-111) then
        tmp = (y / a) * -z
    else if (t <= 1.05d+27) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -2.4e+60) {
		tmp = t_1;
	} else if (t <= 2.25e-237) {
		tmp = x;
	} else if (t <= 2.8e-111) {
		tmp = (y / a) * -z;
	} else if (t <= 1.05e+27) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if t <= -2.4e+60:
		tmp = t_1
	elif t <= 2.25e-237:
		tmp = x
	elif t <= 2.8e-111:
		tmp = (y / a) * -z
	elif t <= 1.05e+27:
		tmp = x
	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 <= -2.4e+60)
		tmp = t_1;
	elseif (t <= 2.25e-237)
		tmp = x;
	elseif (t <= 2.8e-111)
		tmp = Float64(Float64(y / a) * Float64(-z));
	elseif (t <= 1.05e+27)
		tmp = x;
	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 <= -2.4e+60)
		tmp = t_1;
	elseif (t <= 2.25e-237)
		tmp = x;
	elseif (t <= 2.8e-111)
		tmp = (y / a) * -z;
	elseif (t <= 1.05e+27)
		tmp = x;
	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, -2.4e+60], t$95$1, If[LessEqual[t, 2.25e-237], x, If[LessEqual[t, 2.8e-111], N[(N[(y / a), $MachinePrecision] * (-z)), $MachinePrecision], If[LessEqual[t, 1.05e+27], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4e60 or 1.04999999999999997e27 < t

   1. Initial program 87.6%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in y around 0 87.6%

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

      1. associate-*l/ 98.1%

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

      2. *-commutative 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in t around inf 59.4%

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

      1. associate-*r/ 66.5%

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

   10. Simplified 66.5%

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

   if -2.4e60 < t < 2.25000000000000005e-237 or 2.79999999999999995e-111 < t < 1.04999999999999997e27

   1. Initial program 96.6%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 58.9%

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

   if 2.25000000000000005e-237 < t < 2.79999999999999995e-111

   1. Initial program 87.2%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 87.2%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 52.5%

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

      1. associate-*l/ 65.3%

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

      2. associate-*r* 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-*r/ 65.3%

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

      5. neg-mul-1 65.3%

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

   10. Simplified 65.3%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-237}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-111}:\\ \;\;\;\;\frac{y}{a} \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+27}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -4 \cdot 10^{+59}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-146}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ y a))))
   (if (<= t -4e+59)
     t_1
     (if (<= t 2.6e-238)
       x
       (if (<= t 1.85e-146) (* (/ z a) (- y)) (if (<= t 2.1e+25) x 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 <= -4e+59) {
		tmp = t_1;
	} else if (t <= 2.6e-238) {
		tmp = x;
	} else if (t <= 1.85e-146) {
		tmp = (z / a) * -y;
	} else if (t <= 2.1e+25) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (y / a)
    if (t <= (-4d+59)) then
        tmp = t_1
    else if (t <= 2.6d-238) then
        tmp = x
    else if (t <= 1.85d-146) then
        tmp = (z / a) * -y
    else if (t <= 2.1d+25) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (y / a);
	double tmp;
	if (t <= -4e+59) {
		tmp = t_1;
	} else if (t <= 2.6e-238) {
		tmp = x;
	} else if (t <= 1.85e-146) {
		tmp = (z / a) * -y;
	} else if (t <= 2.1e+25) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (y / a)
	tmp = 0
	if t <= -4e+59:
		tmp = t_1
	elif t <= 2.6e-238:
		tmp = x
	elif t <= 1.85e-146:
		tmp = (z / a) * -y
	elif t <= 2.1e+25:
		tmp = x
	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 <= -4e+59)
		tmp = t_1;
	elseif (t <= 2.6e-238)
		tmp = x;
	elseif (t <= 1.85e-146)
		tmp = Float64(Float64(z / a) * Float64(-y));
	elseif (t <= 2.1e+25)
		tmp = x;
	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 <= -4e+59)
		tmp = t_1;
	elseif (t <= 2.6e-238)
		tmp = x;
	elseif (t <= 1.85e-146)
		tmp = (z / a) * -y;
	elseif (t <= 2.1e+25)
		tmp = x;
	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, -4e+59], t$95$1, If[LessEqual[t, 2.6e-238], x, If[LessEqual[t, 1.85e-146], N[(N[(z / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t, 2.1e+25], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.99999999999999989e59 or 2.0999999999999999e25 < t

   1. Initial program 87.6%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in y around 0 87.6%

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

      1. associate-*l/ 98.1%

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

      2. *-commutative 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in t around inf 59.4%

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

      1. associate-*r/ 66.5%

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

   10. Simplified 66.5%

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

   if -3.99999999999999989e59 < t < 2.6000000000000001e-238 or 1.84999999999999993e-146 < t < 2.0999999999999999e25

   1. Initial program 96.7%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 58.7%

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

   if 2.6000000000000001e-238 < t < 1.84999999999999993e-146

   1. Initial program 84.5%

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

      1. associate-/l* 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 52.9%

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

      1. mul-1-neg 52.9%

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

      2. associate-/l* 68.0%

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

      3. distribute-rgt-neg-in 68.0%

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

      4. distribute-neg-frac2 68.0%

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

   7. Simplified 68.0%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-238}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.85 \cdot 10^{-146}:\\ \;\;\;\;\frac{z}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+25}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+167} \lor \neg \left(y \leq 1.58 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.1e+167) (not (<= y 1.58e+65)))
   (* y (/ (- t z) a))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.1e+167) || !(y <= 1.58e+65)) {
		tmp = y * ((t - z) / 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 ((y <= (-1.1d+167)) .or. (.not. (y <= 1.58d+65))) then
        tmp = y * ((t - z) / 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 ((y <= -1.1e+167) || !(y <= 1.58e+65)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.1e+167) or not (y <= 1.58e+65):
		tmp = y * ((t - z) / a)
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.1e+167) || !(y <= 1.58e+65))
		tmp = Float64(y * Float64(Float64(t - z) / 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 ((y <= -1.1e+167) || ~((y <= 1.58e+65)))
		tmp = y * ((t - z) / a);
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.1e+167], N[Not[LessEqual[y, 1.58e+65]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000002e167 or 1.5800000000000001e65 < y

   1. Initial program 81.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in x around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. distribute-frac-neg2 68.7%

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

      3. sub-neg 68.7%

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

      4. +-commutative 68.7%

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

      5. neg-sub0 68.7%

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(0 - t\right)} + z\right)}{-a} \]

      6. associate--r- 68.7%

         \[\leadsto \frac{y \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}}{-a} \]

      7. neg-sub0 68.7%

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

      8. associate-*r/ 85.0%

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

      9. distribute-neg-frac 85.0%

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

      10. distribute-neg-frac2 85.0%

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

      11. remove-double-neg 85.0%

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

   7. Simplified 85.0%

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

   if -1.10000000000000002e167 < y < 1.5800000000000001e65

   1. Initial program 97.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. mul-1-neg 83.9%

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

      3. distribute-lft-neg-out 83.9%

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

      4. *-commutative 83.9%

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

      5. associate-/l* 81.1%

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

      6. distribute-neg-frac 81.1%

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

      7. distribute-neg-frac2 81.1%

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

   7. Simplified 81.1%

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

      1. *-commutative 81.1%

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

      2. distribute-frac-neg2 81.1%

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

      3. cancel-sign-sub 81.1%

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

      4. add-sqr-sqrt 43.0%

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

      5. sqrt-unprod 60.4%

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

      6. sqr-neg 60.4%

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

      7. sqrt-unprod 23.1%

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

      8. add-sqr-sqrt 50.5%

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

      9. *-commutative 50.5%

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

      10. +-commutative 50.5%

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

      11. *-commutative 50.5%

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

      12. div-inv 50.5%

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

      13. associate-*l* 51.9%

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

      14. add-sqr-sqrt 24.0%

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

      15. sqrt-unprod 61.8%

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

      16. sqr-neg 61.8%

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

      17. sqrt-unprod 45.4%

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

      18. add-sqr-sqrt 85.1%

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

      19. associate-/r/ 85.1%

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

      20. clear-num 85.1%

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

   9. Applied egg-rr 85.1%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+167} \lor \neg \left(y \leq 1.58 \cdot 10^{+65}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 78.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+79} \lor \neg \left(y \leq 1.42 \cdot 10^{+66}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -4e+79) (not (<= y 1.42e+66)))
   (* y (/ (- t z) a))
   (+ x (/ (* t y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -4e+79) || !(y <= 1.42e+66)) {
		tmp = y * ((t - z) / 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 ((y <= (-4d+79)) .or. (.not. (y <= 1.42d+66))) then
        tmp = y * ((t - z) / 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 ((y <= -4e+79) || !(y <= 1.42e+66)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -4e+79) or not (y <= 1.42e+66):
		tmp = y * ((t - z) / a)
	else:
		tmp = x + ((t * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -4e+79) || !(y <= 1.42e+66))
		tmp = Float64(y * Float64(Float64(t - z) / a));
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -4e+79) || ~((y <= 1.42e+66)))
		tmp = y * ((t - z) / a);
	else
		tmp = x + ((t * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -4e+79], N[Not[LessEqual[y, 1.42e+66]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999987e79 or 1.4200000000000001e66 < y

   1. Initial program 80.6%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in x around 0 67.1%

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

      1. mul-1-neg 67.1%

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

      2. distribute-frac-neg2 67.1%

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

      3. sub-neg 67.1%

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

      4. +-commutative 67.1%

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

      5. neg-sub0 67.1%

         \[\leadsto \frac{y \cdot \left(\color{blue}{\left(0 - t\right)} + z\right)}{-a} \]

      6. associate--r- 67.1%

         \[\leadsto \frac{y \cdot \color{blue}{\left(0 - \left(t - z\right)\right)}}{-a} \]

      7. neg-sub0 67.1%

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

      8. associate-*r/ 83.6%

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

      9. distribute-neg-frac 83.6%

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

      10. distribute-neg-frac2 83.6%

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

      11. remove-double-neg 83.6%

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

   7. Simplified 83.6%

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

   if -3.99999999999999987e79 < y < 1.4200000000000001e66

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. distribute-frac-neg2 99.8%

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

      3. +-commutative 99.8%

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

      4. associate-/l* 92.1%

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

      5. fma-define 92.1%

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

      6. distribute-frac-neg2 92.1%

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

      7. distribute-neg-frac 92.1%

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

      8. sub-neg 92.1%

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

      9. distribute-neg-in 92.1%

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

      10. remove-double-neg 92.1%

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

      11. +-commutative 92.1%

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

      12. sub-neg 92.1%

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

   3. Simplified 92.1%

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

   5. Taylor expanded in z around 0 86.1%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+79} \lor \neg \left(y \leq 1.42 \cdot 10^{+66}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-23}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+67}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6e-23)
   (+ x (* t (/ y a)))
   (if (<= t 3e+67) (- x (* z (/ y a))) (+ x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6e-23) {
		tmp = x + (t * (y / a));
	} else if (t <= 3e+67) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + (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 <= (-6d-23)) then
        tmp = x + (t * (y / a))
    else if (t <= 3d+67) then
        tmp = x - (z * (y / a))
    else
        tmp = x + (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 <= -6e-23) {
		tmp = x + (t * (y / a));
	} else if (t <= 3e+67) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6e-23:
		tmp = x + (t * (y / a))
	elif t <= 3e+67:
		tmp = x - (z * (y / a))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6e-23)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (t <= 3e+67)
		tmp = Float64(x - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6e-23)
		tmp = x + (t * (y / a));
	elseif (t <= 3e+67)
		tmp = x - (z * (y / a));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6e-23], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+67], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.00000000000000006e-23

   1. Initial program 90.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. mul-1-neg 81.3%

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

      3. distribute-lft-neg-out 81.3%

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

      4. *-commutative 81.3%

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

      5. associate-/l* 82.4%

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

      6. distribute-neg-frac 82.4%

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

      7. distribute-neg-frac2 82.4%

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

   7. Simplified 82.4%

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

      1. *-commutative 82.4%

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

      2. distribute-frac-neg2 82.4%

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

      3. cancel-sign-sub 82.4%

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

      4. add-sqr-sqrt 43.2%

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

      5. sqrt-unprod 42.5%

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

      6. sqr-neg 42.5%

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

      7. sqrt-unprod 7.3%

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

      8. add-sqr-sqrt 25.8%

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

      9. *-commutative 25.8%

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

      10. +-commutative 25.8%

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

      11. *-commutative 25.8%

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

      12. div-inv 25.8%

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

      13. associate-*l* 27.2%

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

      14. add-sqr-sqrt 8.6%

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

      15. sqrt-unprod 43.9%

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

      16. sqr-neg 43.9%

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

      17. sqrt-unprod 46.0%

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

      18. add-sqr-sqrt 86.5%

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

      19. associate-/r/ 86.6%

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

      20. clear-num 86.6%

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

   9. Applied egg-rr 86.6%

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

   if -6.00000000000000006e-23 < t < 3.0000000000000001e67

   1. Initial program 94.3%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in y around 0 94.3%

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

      1. associate-*l/ 98.6%

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

      2. *-commutative 98.6%

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

   7. Simplified 98.6%

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

      1. clear-num 98.5%

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

      2. un-div-inv 99.2%

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

   9. Applied egg-rr 99.2%

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

   10. Taylor expanded in z around inf 87.1%

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

       1. *-commutative 87.1%

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

       2. associate-*r/ 92.6%

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

   12. Simplified 92.6%

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

   if 3.0000000000000001e67 < t

   1. Initial program 86.2%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 84.4%

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

      1. associate-*r/ 84.4%

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

      2. mul-1-neg 84.4%

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

      3. distribute-lft-neg-out 84.4%

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

      4. *-commutative 84.4%

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

      5. associate-/l* 89.7%

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

      6. distribute-neg-frac 89.7%

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

      7. distribute-neg-frac2 89.7%

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

   7. Simplified 89.7%

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

      1. *-commutative 89.7%

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

      2. distribute-frac-neg2 89.7%

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

      3. cancel-sign-sub 89.7%

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

      4. add-sqr-sqrt 54.2%

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

      5. sqrt-unprod 54.9%

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

      6. sqr-neg 54.9%

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

      7. sqrt-unprod 8.5%

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

      8. add-sqr-sqrt 23.4%

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

      9. *-commutative 23.4%

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

      10. +-commutative 23.4%

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

      11. *-commutative 23.4%

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

      12. div-inv 23.4%

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

      13. associate-*l* 26.4%

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

      14. add-sqr-sqrt 9.6%

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

      15. sqrt-unprod 58.1%

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

      16. sqr-neg 58.1%

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

      17. sqrt-unprod 58.4%

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

      18. add-sqr-sqrt 95.9%

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

      19. associate-/r/ 95.8%

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

      20. clear-num 95.9%

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

   9. Applied egg-rr 95.9%

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

       1. clear-num 95.8%

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

       2. div-inv 95.9%

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

   11. Applied egg-rr 95.9%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6 \cdot 10^{-23}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+67}:\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.22 \cdot 10^{-23}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -2.22e-23)
   (+ x (* t (/ y a)))
   (if (<= t 3e+56) (- x (* y (/ z a))) (+ x (/ t (/ a y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2.22e-23) {
		tmp = x + (t * (y / a));
	} else if (t <= 3e+56) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (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 <= (-2.22d-23)) then
        tmp = x + (t * (y / a))
    else if (t <= 3d+56) then
        tmp = x - (y * (z / a))
    else
        tmp = x + (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 <= -2.22e-23) {
		tmp = x + (t * (y / a));
	} else if (t <= 3e+56) {
		tmp = x - (y * (z / a));
	} else {
		tmp = x + (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2.22e-23:
		tmp = x + (t * (y / a))
	elif t <= 3e+56:
		tmp = x - (y * (z / a))
	else:
		tmp = x + (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2.22e-23)
		tmp = Float64(x + Float64(t * Float64(y / a)));
	elseif (t <= 3e+56)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x + Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2.22e-23)
		tmp = x + (t * (y / a));
	elseif (t <= 3e+56)
		tmp = x - (y * (z / a));
	else
		tmp = x + (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2.22e-23], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e+56], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.22e-23

   1. Initial program 90.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 0 81.3%

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

      1. associate-*r/ 81.3%

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

      2. mul-1-neg 81.3%

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

      3. distribute-lft-neg-out 81.3%

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

      4. *-commutative 81.3%

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

      5. associate-/l* 82.4%

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

      6. distribute-neg-frac 82.4%

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

      7. distribute-neg-frac2 82.4%

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

   7. Simplified 82.4%

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

      1. *-commutative 82.4%

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

      2. distribute-frac-neg2 82.4%

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

      3. cancel-sign-sub 82.4%

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

      4. add-sqr-sqrt 43.2%

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

      5. sqrt-unprod 42.5%

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

      6. sqr-neg 42.5%

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

      7. sqrt-unprod 7.3%

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

      8. add-sqr-sqrt 25.8%

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

      9. *-commutative 25.8%

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

      10. +-commutative 25.8%

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

      11. *-commutative 25.8%

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

      12. div-inv 25.8%

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

      13. associate-*l* 27.2%

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

      14. add-sqr-sqrt 8.6%

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

      15. sqrt-unprod 43.9%

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

      16. sqr-neg 43.9%

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

      17. sqrt-unprod 46.0%

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

      18. add-sqr-sqrt 86.5%

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

      19. associate-/r/ 86.6%

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

      20. clear-num 86.6%

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

   9. Applied egg-rr 86.6%

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

   if -2.22e-23 < t < 3.00000000000000006e56

   1. Initial program 94.3%

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

      1. associate-/l* 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in z around inf 87.1%

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

      1. associate-/l* 91.2%

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

   7. Simplified 91.2%

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

   if 3.00000000000000006e56 < t

   1. Initial program 86.2%

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

      1. associate-/l* 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in z around 0 84.4%

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

      1. associate-*r/ 84.4%

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

      2. mul-1-neg 84.4%

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

      3. distribute-lft-neg-out 84.4%

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

      4. *-commutative 84.4%

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

      5. associate-/l* 89.7%

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

      6. distribute-neg-frac 89.7%

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

      7. distribute-neg-frac2 89.7%

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

   7. Simplified 89.7%

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

      1. *-commutative 89.7%

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

      2. distribute-frac-neg2 89.7%

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

      3. cancel-sign-sub 89.7%

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

      4. add-sqr-sqrt 54.2%

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

      5. sqrt-unprod 54.9%

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

      6. sqr-neg 54.9%

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

      7. sqrt-unprod 8.5%

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

      8. add-sqr-sqrt 23.4%

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

      9. *-commutative 23.4%

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

      10. +-commutative 23.4%

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

      11. *-commutative 23.4%

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

      12. div-inv 23.4%

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

      13. associate-*l* 26.4%

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

      14. add-sqr-sqrt 9.6%

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

      15. sqrt-unprod 58.1%

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

      16. sqr-neg 58.1%

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

      17. sqrt-unprod 58.4%

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

      18. add-sqr-sqrt 95.9%

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

      19. associate-/r/ 95.8%

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

      20. clear-num 95.9%

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

   9. Applied egg-rr 95.9%

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

       1. clear-num 95.8%

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

       2. div-inv 95.9%

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

   11. Applied egg-rr 95.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.22 \cdot 10^{-23}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+56}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+67} \lor \neg \left(t \leq 8 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5e+67) (not (<= t 8e+26))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5e+67) || !(t <= 8e+26)) {
		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 <= (-5d+67)) .or. (.not. (t <= 8d+26))) 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 <= -5e+67) || !(t <= 8e+26)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5e+67) or not (t <= 8e+26):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5e+67) || !(t <= 8e+26))
		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 <= -5e+67) || ~((t <= 8e+26)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5e+67], N[Not[LessEqual[t, 8e+26]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -4.99999999999999976e67 or 8.00000000000000038e26 < t

   1. Initial program 87.6%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in y around 0 87.6%

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

      1. associate-*l/ 98.1%

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

      2. *-commutative 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in t around inf 59.4%

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

      1. associate-*r/ 66.5%

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

   10. Simplified 66.5%

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

   if -4.99999999999999976e67 < t < 8.00000000000000038e26

   1. Initial program 95.2%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 55.3%

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

4. Final simplification 60.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+67} \lor \neg \left(t \leq 8 \cdot 10^{+26}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (t - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-/l* 95.3%

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

3. Simplified 95.3%

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

5. Taylor expanded in y around 0 91.8%

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

   1. associate-*l/ 98.0%

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

   2. *-commutative 98.0%

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

7. Simplified 98.0%

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

8. Final simplification 98.0%

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

Alternative 11: 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 91.8%

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

   1. associate-/l* 95.3%

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

3. Simplified 95.3%

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

5. Final simplification 95.3%

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

Alternative 12: 38.7% 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 91.8%

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

   1. associate-/l* 95.3%

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

3. Simplified 95.3%

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

5. Taylor expanded in x around inf 40.5%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer target: 99.0% 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 2024100 
(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)))