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

Percentage Accurate: 92.8% → 97.2%

Time: 11.1s

Alternatives: 12

Speedup: 1.0×

• 24.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.8% 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: 97.2% 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 93.1%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. Taylor expanded in y around 0 93.1%

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

   1. associate-*l/ 97.1%

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

   2. *-commutative 97.1%

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

7. Simplified 97.1%

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

   1. clear-num 97.0%

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

   2. un-div-inv 97.1%

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

9. Applied egg-rr 97.1%

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

10. Final simplification 97.1%

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

Alternative 2: 83.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -2000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 10^{-70}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* t (/ y a)))))
   (if (<= t -2000.0)
     t_1
     (if (<= t -2.7e-50)
       (* y (/ (- t z) a))
       (if (<= t 1e-70) (- x (* y (/ z a))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (t * (y / a));
	double tmp;
	if (t <= -2000.0) {
		tmp = t_1;
	} else if (t <= -2.7e-50) {
		tmp = y * ((t - z) / a);
	} else if (t <= 1e-70) {
		tmp = x - (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 = x + (t * (y / a))
    if (t <= (-2000.0d0)) then
        tmp = t_1
    else if (t <= (-2.7d-50)) then
        tmp = y * ((t - z) / a)
    else if (t <= 1d-70) then
        tmp = x - (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 = x + (t * (y / a));
	double tmp;
	if (t <= -2000.0) {
		tmp = t_1;
	} else if (t <= -2.7e-50) {
		tmp = y * ((t - z) / a);
	} else if (t <= 1e-70) {
		tmp = x - (y * (z / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (t * (y / a))
	tmp = 0
	if t <= -2000.0:
		tmp = t_1
	elif t <= -2.7e-50:
		tmp = y * ((t - z) / a)
	elif t <= 1e-70:
		tmp = x - (y * (z / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(t * Float64(y / a)))
	tmp = 0.0
	if (t <= -2000.0)
		tmp = t_1;
	elseif (t <= -2.7e-50)
		tmp = Float64(y * Float64(Float64(t - z) / a));
	elseif (t <= 1e-70)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (t * (y / a));
	tmp = 0.0;
	if (t <= -2000.0)
		tmp = t_1;
	elseif (t <= -2.7e-50)
		tmp = y * ((t - z) / a);
	elseif (t <= 1e-70)
		tmp = x - (y * (z / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2000.0], t$95$1, If[LessEqual[t, -2.7e-50], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-70], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2e3 or 9.99999999999999996e-71 < t

   1. Initial program 92.0%

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

      1. associate-/l* 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in y around 0 92.0%

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

      1. associate-*l/ 97.7%

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

      2. *-commutative 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in z around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. associate-/l* 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. *-commutative 85.8%

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

   10. Simplified 85.8%

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

       1. *-commutative 85.8%

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

       2. cancel-sign-sub 85.8%

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

       3. associate-*r/ 81.3%

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

       4. +-commutative 81.3%

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

       5. associate-*r/ 85.8%

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

   12. Applied egg-rr 85.8%

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

   if -2e3 < t < -2.7e-50

   1. Initial program 100.0%

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

      1. associate-/l* 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in x around 0 96.9%

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

      1. associate-*r/ 96.9%

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

      2. neg-mul-1 96.9%

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

      3. distribute-rgt-neg-in 96.9%

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

      4. sub-neg 96.9%

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

      5. distribute-neg-in 96.9%

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

      6. remove-double-neg 96.9%

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

      7. +-commutative 96.9%

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

      8. sub-neg 96.9%

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

      9. associate-*r/ 96.3%

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

   7. Simplified 96.3%

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

   if -2.7e-50 < t < 9.99999999999999996e-71

   1. Initial program 94.1%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in z around inf 89.3%

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

      1. associate-/l* 88.2%

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

   7. Simplified 88.2%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2000:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-50}:\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{elif}\;t \leq 10^{-70}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-206} \lor \neg \left(y \leq 9 \cdot 10^{-235}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.8e-206) (not (<= y 9e-235)))
   (+ x (* 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 <= -1.8e-206) || !(y <= 9e-235)) {
		tmp = x + (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 <= (-1.8d-206)) .or. (.not. (y <= 9d-235))) then
        tmp = x + (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 <= -1.8e-206) || !(y <= 9e-235)) {
		tmp = x + (y * ((t - z) / a));
	} else {
		tmp = x + ((t * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.8e-206) or not (y <= 9e-235):
		tmp = x + (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 <= -1.8e-206) || !(y <= 9e-235))
		tmp = Float64(x + 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 <= -1.8e-206) || ~((y <= 9e-235)))
		tmp = x + (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, -1.8e-206], N[Not[LessEqual[y, 9e-235]], $MachinePrecision]], N[(x + N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999997e-206 or 8.9999999999999996e-235 < y

   1. Initial program 92.1%

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

      1. associate-/l* 97.5%

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

   3. Simplified 97.5%

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

   if -1.79999999999999997e-206 < y < 8.9999999999999996e-235

   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* 63.4%

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

      5. fma-define 63.4%

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

      6. distribute-frac-neg2 63.4%

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

      7. distribute-neg-frac 63.4%

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

      8. sub-neg 63.4%

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

      9. distribute-neg-in 63.4%

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

      10. remove-double-neg 63.4%

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

      11. +-commutative 63.4%

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

      12. sub-neg 63.4%

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

   3. Simplified 63.4%

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

   5. Taylor expanded in z around 0 91.2%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-206} \lor \neg \left(y \leq 9 \cdot 10^{-235}\right):\\ \;\;\;\;x + y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-49} \lor \neg \left(z \leq 1.8 \cdot 10^{+105}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -6.8e-49) (not (<= z 1.8e+105)))
   (- x (* z (/ y a)))
   (+ x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e-49) || !(z <= 1.8e+105)) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-6.8d-49)) .or. (.not. (z <= 1.8d+105))) then
        tmp = x - (z * (y / a))
    else
        tmp = x + (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -6.8e-49) || !(z <= 1.8e+105)) {
		tmp = x - (z * (y / a));
	} else {
		tmp = x + (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -6.8e-49) or not (z <= 1.8e+105):
		tmp = x - (z * (y / a))
	else:
		tmp = x + (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -6.8e-49) || !(z <= 1.8e+105))
		tmp = Float64(x - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -6.8e-49) || ~((z <= 1.8e+105)))
		tmp = x - (z * (y / a));
	else
		tmp = x + (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -6.8e-49], N[Not[LessEqual[z, 1.8e+105]], $MachinePrecision]], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.8000000000000001e-49 or 1.7999999999999999e105 < z

   1. Initial program 91.2%

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

      1. associate-/l* 92.0%

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

   3. Simplified 92.0%

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

   5. Taylor expanded in y around 0 91.2%

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

      1. associate-*l/ 98.5%

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

      2. *-commutative 98.5%

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

   7. Simplified 98.5%

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

   8. Taylor expanded in z around inf 81.5%

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

      1. *-commutative 81.5%

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

      2. associate-*r/ 86.0%

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

   10. Simplified 86.0%

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

   if -6.8000000000000001e-49 < z < 1.7999999999999999e105

   1. Initial program 94.5%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around 0 94.5%

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

      1. associate-*l/ 96.0%

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

      2. *-commutative 96.0%

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

   7. Simplified 96.0%

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

   8. Taylor expanded in z around 0 85.1%

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

      1. mul-1-neg 85.1%

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

      2. associate-/l* 88.3%

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

      3. distribute-lft-neg-out 88.3%

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

      4. *-commutative 88.3%

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

   10. Simplified 88.3%

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

       1. *-commutative 88.3%

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

       2. cancel-sign-sub 88.3%

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

       3. associate-*r/ 85.1%

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

       4. +-commutative 85.1%

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

       5. associate-*r/ 88.3%

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

   12. Applied egg-rr 88.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-49} \lor \neg \left(z \leq 1.8 \cdot 10^{+105}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-155} \lor \neg \left(x \leq 2 \cdot 10^{+30}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= x -1.6e-155) (not (<= x 2e+30)))
   (+ x (* t (/ y a)))
   (* (/ y a) (- t z))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x <= -1.6e-155) || !(x <= 2e+30)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = (y / a) * (t - 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 ((x <= (-1.6d-155)) .or. (.not. (x <= 2d+30))) then
        tmp = x + (t * (y / a))
    else
        tmp = (y / a) * (t - 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 ((x <= -1.6e-155) || !(x <= 2e+30)) {
		tmp = x + (t * (y / a));
	} else {
		tmp = (y / a) * (t - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (x <= -1.6e-155) or not (x <= 2e+30):
		tmp = x + (t * (y / a))
	else:
		tmp = (y / a) * (t - z)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((x <= -1.6e-155) || !(x <= 2e+30))
		tmp = Float64(x + Float64(t * Float64(y / a)));
	else
		tmp = Float64(Float64(y / a) * Float64(t - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x <= -1.6e-155) || ~((x <= 2e+30)))
		tmp = x + (t * (y / a));
	else
		tmp = (y / a) * (t - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[x, -1.6e-155], N[Not[LessEqual[x, 2e+30]], $MachinePrecision]], N[(x + N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.60000000000000006e-155 or 2e30 < x

   1. Initial program 93.2%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 y around 0 93.2%

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

      1. associate-*l/ 98.7%

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

      2. *-commutative 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in z around 0 80.4%

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

      1. mul-1-neg 80.4%

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

      2. associate-/l* 85.2%

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

      3. distribute-lft-neg-out 85.2%

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

      4. *-commutative 85.2%

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

   10. Simplified 85.2%

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

       1. *-commutative 85.2%

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

       2. cancel-sign-sub 85.2%

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

       3. associate-*r/ 80.4%

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

       4. +-commutative 80.4%

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

       5. associate-*r/ 85.2%

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

   12. Applied egg-rr 85.2%

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

   if -1.60000000000000006e-155 < x < 2e30

   1. Initial program 92.9%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in y around 0 92.9%

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

      1. associate-*l/ 95.0%

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

      2. *-commutative 95.0%

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

   7. Simplified 95.0%

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

   8. Taylor expanded in x around 0 78.9%

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

      1. mul-1-neg 78.9%

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

      2. *-commutative 78.9%

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

      3. associate-*r/ 81.5%

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

      4. *-commutative 81.5%

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

      5. sub-neg 81.5%

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

      6. +-commutative 81.5%

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

      7. distribute-rgt-out 75.1%

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

      8. distribute-lft-neg-out 75.1%

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

      9. associate-/l* 73.6%

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

      10. mul-1-neg 73.6%

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

      11. distribute-neg-in 73.6%

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

      12. mul-1-neg 73.6%

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

      13. remove-double-neg 73.6%

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

      14. sub-neg 73.6%

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

      15. associate-/l* 75.1%

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

      16. distribute-rgt-out-- 81.5%

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

   10. Simplified 81.5%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-155} \lor \neg \left(x \leq 2 \cdot 10^{+30}\right):\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+16} \lor \neg \left(y \leq 5.2 \cdot 10^{+156}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.7e+16) (not (<= y 5.2e+156)))
   (* 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 <= -1.7e+16) || !(y <= 5.2e+156)) {
		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 <= (-1.7d+16)) .or. (.not. (y <= 5.2d+156))) 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 <= -1.7e+16) || !(y <= 5.2e+156)) {
		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 <= -1.7e+16) or not (y <= 5.2e+156):
		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 <= -1.7e+16) || !(y <= 5.2e+156))
		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 <= -1.7e+16) || ~((y <= 5.2e+156)))
		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, -1.7e+16], N[Not[LessEqual[y, 5.2e+156]], $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 < -1.7e16 or 5.20000000000000037e156 < y

   1. Initial program 84.1%

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

      1. associate-/l* 98.6%

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

   3. Simplified 98.6%

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

   5. Taylor expanded in x around 0 75.1%

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

      1. associate-*r/ 75.1%

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

      2. neg-mul-1 75.1%

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

      3. distribute-rgt-neg-in 75.1%

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

      4. sub-neg 75.1%

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

      5. distribute-neg-in 75.1%

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

      6. remove-double-neg 75.1%

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

      7. +-commutative 75.1%

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

      8. sub-neg 75.1%

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

      9. associate-*r/ 85.6%

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

   7. Simplified 85.6%

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

   if -1.7e16 < y < 5.20000000000000037e156

   1. Initial program 99.1%

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

      1. sub-neg 99.1%

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

      2. distribute-frac-neg2 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-/l* 89.2%

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

      5. fma-define 89.2%

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

      6. distribute-frac-neg2 89.2%

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

      7. distribute-neg-frac 89.2%

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

      8. sub-neg 89.2%

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

      9. distribute-neg-in 89.2%

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

      10. remove-double-neg 89.2%

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

      11. +-commutative 89.2%

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

      12. sub-neg 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in z around 0 79.9%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+16} \lor \neg \left(y \leq 5.2 \cdot 10^{+156}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-43} \lor \neg \left(y \leq 1.45 \cdot 10^{-152}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -3.9e-43) (not (<= y 1.45e-152))) (* y (/ (- t z) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -3.9e-43) || !(y <= 1.45e-152)) {
		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 <= (-3.9d-43)) .or. (.not. (y <= 1.45d-152))) 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 <= -3.9e-43) || !(y <= 1.45e-152)) {
		tmp = y * ((t - z) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -3.9e-43) or not (y <= 1.45e-152):
		tmp = y * ((t - z) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -3.9e-43) || !(y <= 1.45e-152))
		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 <= -3.9e-43) || ~((y <= 1.45e-152)))
		tmp = y * ((t - z) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -3.9e-43], N[Not[LessEqual[y, 1.45e-152]], $MachinePrecision]], N[(y * N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.9e-43 or 1.4500000000000001e-152 < y

   1. Initial program 90.2%

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

      1. associate-/l* 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in x around 0 70.4%

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

      1. associate-*r/ 70.4%

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

      2. neg-mul-1 70.4%

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

      3. distribute-rgt-neg-in 70.4%

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

      4. sub-neg 70.4%

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

      5. distribute-neg-in 70.4%

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

      6. remove-double-neg 70.4%

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

      7. +-commutative 70.4%

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

      8. sub-neg 70.4%

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

      9. associate-*r/ 76.5%

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

   7. Simplified 76.5%

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

   if -3.9e-43 < y < 1.4500000000000001e-152

   1. Initial program 99.8%

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

      1. associate-/l* 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in x around inf 59.7%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-43} \lor \neg \left(y \leq 1.45 \cdot 10^{-152}\right):\\ \;\;\;\;y \cdot \frac{t - z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.6 \cdot 10^{+38}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.35 \cdot 10^{+215}:\\ \;\;\;\;\frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -8.6e+38) x (if (<= a 2.35e+215) (* (/ y a) (- t z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -8.6e+38) {
		tmp = x;
	} else if (a <= 2.35e+215) {
		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 <= (-8.6d+38)) then
        tmp = x
    else if (a <= 2.35d+215) 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 <= -8.6e+38) {
		tmp = x;
	} else if (a <= 2.35e+215) {
		tmp = (y / a) * (t - z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -8.6e+38:
		tmp = x
	elif a <= 2.35e+215:
		tmp = (y / a) * (t - z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -8.6e+38)
		tmp = x;
	elseif (a <= 2.35e+215)
		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 <= -8.6e+38)
		tmp = x;
	elseif (a <= 2.35e+215)
		tmp = (y / a) * (t - z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -8.6e+38], x, If[LessEqual[a, 2.35e+215], N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -8.5999999999999994e38 or 2.3500000000000001e215 < a

   1. Initial program 81.2%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf 62.9%

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

   if -8.5999999999999994e38 < a < 2.3500000000000001e215

   1. Initial program 98.7%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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 98.7%

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

      1. associate-*l/ 96.6%

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

      2. *-commutative 96.6%

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

   7. Simplified 96.6%

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

   8. Taylor expanded in x around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. *-commutative 79.3%

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

      3. associate-*r/ 77.2%

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

      4. *-commutative 77.2%

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

      5. sub-neg 77.2%

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

      6. +-commutative 77.2%

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

      7. distribute-rgt-out 66.7%

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

      8. distribute-lft-neg-out 66.7%

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

      9. associate-/l* 67.4%

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

      10. mul-1-neg 67.4%

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

      11. distribute-neg-in 67.4%

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

      12. mul-1-neg 67.4%

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

      13. remove-double-neg 67.4%

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

      14. sub-neg 67.4%

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

      15. associate-/l* 66.7%

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

      16. distribute-rgt-out-- 77.2%

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

   10. Simplified 77.2%

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

Alternative 9: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -22000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{+80}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -22000.0) x (if (<= a 1.4e+80) (/ t (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -22000.0) {
		tmp = x;
	} else if (a <= 1.4e+80) {
		tmp = t / (a / y);
	} 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 <= (-22000.0d0)) then
        tmp = x
    else if (a <= 1.4d+80) then
        tmp = t / (a / y)
    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 <= -22000.0) {
		tmp = x;
	} else if (a <= 1.4e+80) {
		tmp = t / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -22000.0:
		tmp = x
	elif a <= 1.4e+80:
		tmp = t / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -22000.0)
		tmp = x;
	elseif (a <= 1.4e+80)
		tmp = Float64(t / Float64(a / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -22000.0)
		tmp = x;
	elseif (a <= 1.4e+80)
		tmp = t / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -22000.0], x, If[LessEqual[a, 1.4e+80], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -22000 or 1.39999999999999992e80 < a

   1. Initial program 84.5%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around inf 56.6%

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

   if -22000 < a < 1.39999999999999992e80

   1. Initial program 99.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around inf 58.1%

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

      1. associate-/l* 58.7%

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

   7. Simplified 58.7%

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

      1. clear-num 58.7%

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

      2. div-inv 58.8%

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

   9. Applied egg-rr 58.8%

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

Alternative 10: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -16000:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -16000.0) x (if (<= a 3.8e+80) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -16000.0) {
		tmp = x;
	} else if (a <= 3.8e+80) {
		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 (a <= (-16000.0d0)) then
        tmp = x
    else if (a <= 3.8d+80) 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 (a <= -16000.0) {
		tmp = x;
	} else if (a <= 3.8e+80) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -16000.0:
		tmp = x
	elif a <= 3.8e+80:
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -16000.0)
		tmp = x;
	elseif (a <= 3.8e+80)
		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 (a <= -16000.0)
		tmp = x;
	elseif (a <= 3.8e+80)
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -16000.0], x, If[LessEqual[a, 3.8e+80], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -16000 or 3.79999999999999997e80 < a

   1. Initial program 84.5%

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

      1. associate-/l* 98.7%

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

   3. Simplified 98.7%

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

   5. Taylor expanded in x around inf 56.6%

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

   if -16000 < a < 3.79999999999999997e80

   1. Initial program 99.8%

      \[x - \frac{y \cdot \left(z - t\right)}{a} \]
   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. Taylor expanded in t around inf 58.1%

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

      1. associate-/l* 58.7%

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

   7. Simplified 58.7%

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

Alternative 11: 97.1% 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 93.1%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. Taylor expanded in y around 0 93.1%

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

   1. associate-*l/ 97.1%

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

   2. *-commutative 97.1%

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

7. Simplified 97.1%

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

8. Final simplification 97.1%

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

Alternative 12: 39.2% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.1%

   \[x - \frac{y \cdot \left(z - t\right)}{a} \]
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. Taylor expanded in x around inf 34.1%

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

Developer Target 1: 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 2024172 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t)))))))

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