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

Percentage Accurate: 92.9% → 99.6%

Time: 9.5s

Alternatives: 12

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+261} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+273}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -2e+261) (not (<= t_1 5e+273)))
     (+ x (/ y (/ a (- z t))))
     (+ x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -2e+261) || !(t_1 <= 5e+273)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z - t)
    if ((t_1 <= (-2d+261)) .or. (.not. (t_1 <= 5d+273))) then
        tmp = x + (y / (a / (z - t)))
    else
        tmp = x + (t_1 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -2e+261) || !(t_1 <= 5e+273)) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if (t_1 <= -2e+261) or not (t_1 <= 5e+273):
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x + (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -2e+261) || !(t_1 <= 5e+273))
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if ((t_1 <= -2e+261) || ~((t_1 <= 5e+273)))
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x + (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e+261], N[Not[LessEqual[t$95$1, 5e+273]], $MachinePrecision]], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -1.9999999999999999e261 or 4.99999999999999961e273 < (*.f64 y (-.f64 z t))

   1. Initial program 72.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -1.9999999999999999e261 < (*.f64 y (-.f64 z t)) < 4.99999999999999961e273

   1. Initial program 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -2 \cdot 10^{+261} \lor \neg \left(y \cdot \left(z - t\right) \leq 5 \cdot 10^{+273}\right):\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 75.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-184}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+114}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y) a))))
   (if (<= t -5e+218)
     t_1
     (if (<= t -1.85e+146)
       (+ x (/ (* y z) a))
       (if (<= t -2.3e+108)
         t_1
         (if (<= t 1.8e-184)
           (+ x (* y (/ z a)))
           (if (<= t 1.05e+114) (+ x (* z (/ y a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (t <= -5e+218) {
		tmp = t_1;
	} else if (t <= -1.85e+146) {
		tmp = x + ((y * z) / a);
	} else if (t <= -2.3e+108) {
		tmp = t_1;
	} else if (t <= 1.8e-184) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.05e+114) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (-y / a)
    if (t <= (-5d+218)) then
        tmp = t_1
    else if (t <= (-1.85d+146)) then
        tmp = x + ((y * z) / a)
    else if (t <= (-2.3d+108)) then
        tmp = t_1
    else if (t <= 1.8d-184) then
        tmp = x + (y * (z / a))
    else if (t <= 1.05d+114) then
        tmp = x + (z * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (t <= -5e+218) {
		tmp = t_1;
	} else if (t <= -1.85e+146) {
		tmp = x + ((y * z) / a);
	} else if (t <= -2.3e+108) {
		tmp = t_1;
	} else if (t <= 1.8e-184) {
		tmp = x + (y * (z / a));
	} else if (t <= 1.05e+114) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-y / a)
	tmp = 0
	if t <= -5e+218:
		tmp = t_1
	elif t <= -1.85e+146:
		tmp = x + ((y * z) / a)
	elif t <= -2.3e+108:
		tmp = t_1
	elif t <= 1.8e-184:
		tmp = x + (y * (z / a))
	elif t <= 1.05e+114:
		tmp = x + (z * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (t <= -5e+218)
		tmp = t_1;
	elseif (t <= -1.85e+146)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= -2.3e+108)
		tmp = t_1;
	elseif (t <= 1.8e-184)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t <= 1.05e+114)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-y / a);
	tmp = 0.0;
	if (t <= -5e+218)
		tmp = t_1;
	elseif (t <= -1.85e+146)
		tmp = x + ((y * z) / a);
	elseif (t <= -2.3e+108)
		tmp = t_1;
	elseif (t <= 1.8e-184)
		tmp = x + (y * (z / a));
	elseif (t <= 1.05e+114)
		tmp = x + (z * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+218], t$95$1, If[LessEqual[t, -1.85e+146], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.3e+108], t$95$1, If[LessEqual[t, 1.8e-184], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+114], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.99999999999999983e218 or -1.85000000000000002e146 < t < -2.2999999999999999e108 or 1.05e114 < t

   1. Initial program 79.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 79.6%

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

      1. associate-*l/ 96.7%

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

      2. *-commutative 96.7%

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

   7. Simplified 96.7%

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

   8. Taylor expanded in z around 0 77.8%

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

      1. associate-*r/ 93.2%

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

      2. neg-mul-1 93.2%

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

      3. distribute-lft-neg-in 93.2%

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

      4. cancel-sign-sub-inv 93.2%

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

   10. Simplified 93.2%

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

       1. *-commutative 93.2%

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

       2. add-sqr-sqrt 47.6%

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

       3. sqrt-unprod 42.9%

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

       4. sqr-neg 42.9%

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

       5. sqrt-unprod 5.7%

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

       6. add-sqr-sqrt 13.5%

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

       7. associate-/r/ 13.4%

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

       8. add-sqr-sqrt 5.6%

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

       9. sqrt-unprod 42.8%

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

       10. sqr-neg 42.8%

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

       11. sqrt-unprod 45.4%

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

       12. add-sqr-sqrt 91.1%

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

   12. Applied egg-rr 91.1%

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

   13. Taylor expanded in x around 0 63.7%

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

       1. mul-1-neg 63.7%

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

       2. associate-*r/ 80.5%

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

       3. *-commutative 80.5%

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

       4. distribute-rgt-neg-out 80.5%

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

   15. Simplified 80.5%

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

   if -4.99999999999999983e218 < t < -1.85000000000000002e146

   1. Initial program 99.7%

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

      1. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in z around inf 83.5%

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

   if -2.2999999999999999e108 < t < 1.8000000000000001e-184

   1. Initial program 94.5%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-/l* 81.7%

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

   7. Simplified 81.7%

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

   if 1.8000000000000001e-184 < t < 1.05e114

   1. Initial program 94.2%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 77.0%

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

   7. Simplified 77.0%

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

      1. clear-num 76.4%

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

      2. un-div-inv 77.3%

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

   9. Applied egg-rr 77.3%

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

       1. associate-/r/ 82.1%

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

   11. Applied egg-rr 82.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+218}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-184}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+114}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-184}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+113}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y) a))))
   (if (<= t -5e+218)
     t_1
     (if (<= t -2.4e+146)
       (+ x (/ (* y z) a))
       (if (<= t -1.05e+108)
         t_1
         (if (<= t 7e-184)
           (+ x (/ y (/ a z)))
           (if (<= t 7.5e+113) (+ x (* z (/ y a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (t <= -5e+218) {
		tmp = t_1;
	} else if (t <= -2.4e+146) {
		tmp = x + ((y * z) / a);
	} else if (t <= -1.05e+108) {
		tmp = t_1;
	} else if (t <= 7e-184) {
		tmp = x + (y / (a / z));
	} else if (t <= 7.5e+113) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (-y / a)
    if (t <= (-5d+218)) then
        tmp = t_1
    else if (t <= (-2.4d+146)) then
        tmp = x + ((y * z) / a)
    else if (t <= (-1.05d+108)) then
        tmp = t_1
    else if (t <= 7d-184) then
        tmp = x + (y / (a / z))
    else if (t <= 7.5d+113) then
        tmp = x + (z * (y / a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (t <= -5e+218) {
		tmp = t_1;
	} else if (t <= -2.4e+146) {
		tmp = x + ((y * z) / a);
	} else if (t <= -1.05e+108) {
		tmp = t_1;
	} else if (t <= 7e-184) {
		tmp = x + (y / (a / z));
	} else if (t <= 7.5e+113) {
		tmp = x + (z * (y / a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-y / a)
	tmp = 0
	if t <= -5e+218:
		tmp = t_1
	elif t <= -2.4e+146:
		tmp = x + ((y * z) / a)
	elif t <= -1.05e+108:
		tmp = t_1
	elif t <= 7e-184:
		tmp = x + (y / (a / z))
	elif t <= 7.5e+113:
		tmp = x + (z * (y / a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (t <= -5e+218)
		tmp = t_1;
	elseif (t <= -2.4e+146)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t <= -1.05e+108)
		tmp = t_1;
	elseif (t <= 7e-184)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 7.5e+113)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-y / a);
	tmp = 0.0;
	if (t <= -5e+218)
		tmp = t_1;
	elseif (t <= -2.4e+146)
		tmp = x + ((y * z) / a);
	elseif (t <= -1.05e+108)
		tmp = t_1;
	elseif (t <= 7e-184)
		tmp = x + (y / (a / z));
	elseif (t <= 7.5e+113)
		tmp = x + (z * (y / a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5e+218], t$95$1, If[LessEqual[t, -2.4e+146], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.05e+108], t$95$1, If[LessEqual[t, 7e-184], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e+113], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.99999999999999983e218 or -2.4000000000000002e146 < t < -1.05000000000000005e108 or 7.5000000000000001e113 < t

   1. Initial program 79.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 79.6%

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

      1. associate-*l/ 96.7%

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

      2. *-commutative 96.7%

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

   7. Simplified 96.7%

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

   8. Taylor expanded in z around 0 77.8%

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

      1. associate-*r/ 93.2%

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

      2. neg-mul-1 93.2%

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

      3. distribute-lft-neg-in 93.2%

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

      4. cancel-sign-sub-inv 93.2%

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

   10. Simplified 93.2%

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

       1. *-commutative 93.2%

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

       2. add-sqr-sqrt 47.6%

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

       3. sqrt-unprod 42.9%

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

       4. sqr-neg 42.9%

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

       5. sqrt-unprod 5.7%

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

       6. add-sqr-sqrt 13.5%

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

       7. associate-/r/ 13.4%

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

       8. add-sqr-sqrt 5.6%

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

       9. sqrt-unprod 42.8%

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

       10. sqr-neg 42.8%

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

       11. sqrt-unprod 45.4%

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

       12. add-sqr-sqrt 91.1%

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

   12. Applied egg-rr 91.1%

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

   13. Taylor expanded in x around 0 63.7%

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

       1. mul-1-neg 63.7%

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

       2. associate-*r/ 80.5%

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

       3. *-commutative 80.5%

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

       4. distribute-rgt-neg-out 80.5%

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

   15. Simplified 80.5%

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

   if -4.99999999999999983e218 < t < -2.4000000000000002e146

   1. Initial program 99.7%

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

      1. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in z around inf 83.5%

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

   if -1.05000000000000005e108 < t < 6.99999999999999962e-184

   1. Initial program 94.5%

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

      1. associate-/l* 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in t around 0 80.2%

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

      1. +-commutative 80.2%

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

      2. associate-/l* 81.7%

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

   7. Simplified 81.7%

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

      1. clear-num 81.7%

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

      2. un-div-inv 81.7%

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

   9. Applied egg-rr 81.7%

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

   if 6.99999999999999962e-184 < t < 7.5000000000000001e113

   1. Initial program 94.2%

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

      1. associate-/l* 93.3%

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

   3. Simplified 93.3%

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

   5. Taylor expanded in t around 0 77.9%

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

      1. +-commutative 77.9%

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

      2. associate-/l* 77.0%

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

   7. Simplified 77.0%

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

      1. clear-num 76.4%

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

      2. un-div-inv 77.3%

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

   9. Applied egg-rr 77.3%

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

       1. associate-/r/ 82.1%

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

   11. Applied egg-rr 82.1%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+218}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-184}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{+113}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \frac{-y}{a}\\ \mathbf{if}\;t \leq -5 \cdot 10^{+218}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+106} \lor \neg \left(t \leq 5.8 \cdot 10^{+113}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (/ (- y) a))))
   (if (<= t -5e+218)
     t_1
     (if (<= t -2.3e+146)
       (+ x (/ (* y z) a))
       (if (or (<= t -2.7e+106) (not (<= t 5.8e+113)))
         t_1
         (+ x (* y (/ z a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (t <= -5e+218) {
		tmp = t_1;
	} else if (t <= -2.3e+146) {
		tmp = x + ((y * z) / a);
	} else if ((t <= -2.7e+106) || !(t <= 5.8e+113)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (-y / a)
    if (t <= (-5d+218)) then
        tmp = t_1
    else if (t <= (-2.3d+146)) then
        tmp = x + ((y * z) / a)
    else if ((t <= (-2.7d+106)) .or. (.not. (t <= 5.8d+113))) then
        tmp = t_1
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * (-y / a);
	double tmp;
	if (t <= -5e+218) {
		tmp = t_1;
	} else if (t <= -2.3e+146) {
		tmp = x + ((y * z) / a);
	} else if ((t <= -2.7e+106) || !(t <= 5.8e+113)) {
		tmp = t_1;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * (-y / a)
	tmp = 0
	if t <= -5e+218:
		tmp = t_1
	elif t <= -2.3e+146:
		tmp = x + ((y * z) / a)
	elif (t <= -2.7e+106) or not (t <= 5.8e+113):
		tmp = t_1
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(Float64(-y) / a))
	tmp = 0.0
	if (t <= -5e+218)
		tmp = t_1;
	elseif (t <= -2.3e+146)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif ((t <= -2.7e+106) || !(t <= 5.8e+113))
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * (-y / a);
	tmp = 0.0;
	if (t <= -5e+218)
		tmp = t_1;
	elseif (t <= -2.3e+146)
		tmp = x + ((y * z) / a);
	elseif ((t <= -2.7e+106) || ~((t <= 5.8e+113)))
		tmp = t_1;
	else
		tmp = x + (y * (z / a));
	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, -5e+218], t$95$1, If[LessEqual[t, -2.3e+146], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, -2.7e+106], N[Not[LessEqual[t, 5.8e+113]], $MachinePrecision]], t$95$1, N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.99999999999999983e218 or -2.3e146 < t < -2.70000000000000006e106 or 5.79999999999999968e113 < t

   1. Initial program 79.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 79.6%

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

      1. associate-*l/ 96.7%

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

      2. *-commutative 96.7%

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

   7. Simplified 96.7%

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

   8. Taylor expanded in z around 0 77.8%

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

      1. associate-*r/ 93.2%

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

      2. neg-mul-1 93.2%

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

      3. distribute-lft-neg-in 93.2%

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

      4. cancel-sign-sub-inv 93.2%

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

   10. Simplified 93.2%

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

       1. *-commutative 93.2%

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

       2. add-sqr-sqrt 47.6%

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

       3. sqrt-unprod 42.9%

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

       4. sqr-neg 42.9%

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

       5. sqrt-unprod 5.7%

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

       6. add-sqr-sqrt 13.5%

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

       7. associate-/r/ 13.4%

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

       8. add-sqr-sqrt 5.6%

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

       9. sqrt-unprod 42.8%

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

       10. sqr-neg 42.8%

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

       11. sqrt-unprod 45.4%

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

       12. add-sqr-sqrt 91.1%

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

   12. Applied egg-rr 91.1%

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

   13. Taylor expanded in x around 0 63.7%

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

       1. mul-1-neg 63.7%

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

       2. associate-*r/ 80.5%

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

       3. *-commutative 80.5%

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

       4. distribute-rgt-neg-out 80.5%

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

   15. Simplified 80.5%

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

   if -4.99999999999999983e218 < t < -2.3e146

   1. Initial program 99.7%

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

      1. associate-/l* 84.6%

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

   3. Simplified 84.6%

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

   5. Taylor expanded in z around inf 83.5%

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

   if -2.70000000000000006e106 < t < 5.79999999999999968e113

   1. Initial program 94.4%

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

      1. associate-/l* 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around 0 79.4%

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

      1. +-commutative 79.4%

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

      2. associate-/l* 80.1%

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

   7. Simplified 80.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5 \cdot 10^{+218}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{+146}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+106} \lor \neg \left(t \leq 5.8 \cdot 10^{+113}\right):\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+219} \lor \neg \left(t \leq 10^{+114}\right):\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.9e+219) (not (<= t 1e+114)))
   (* t (/ (- y) a))
   (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.9e+219) || !(t <= 1e+114)) {
		tmp = t * (-y / a);
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.9d+219)) .or. (.not. (t <= 1d+114))) then
        tmp = t * (-y / a)
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.9e+219) || !(t <= 1e+114)) {
		tmp = t * (-y / a);
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.9e+219) or not (t <= 1e+114):
		tmp = t * (-y / a)
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.9e+219) || !(t <= 1e+114))
		tmp = Float64(t * Float64(Float64(-y) / a));
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.9e+219) || ~((t <= 1e+114)))
		tmp = t * (-y / a);
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.9e+219], N[Not[LessEqual[t, 1e+114]], $MachinePrecision]], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.89999999999999998e219 or 1e114 < t

   1. Initial program 81.7%

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

      1. associate-/l* 94.3%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in y around 0 81.7%

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

      1. associate-*l/ 96.5%

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

      2. *-commutative 96.5%

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

   7. Simplified 96.5%

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

   8. Taylor expanded in z around 0 79.8%

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

      1. associate-*r/ 92.7%

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

      2. neg-mul-1 92.7%

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

      3. distribute-lft-neg-in 92.7%

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

      4. cancel-sign-sub-inv 92.7%

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

   10. Simplified 92.7%

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

       1. *-commutative 92.7%

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

       2. add-sqr-sqrt 47.5%

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

       3. sqrt-unprod 44.2%

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

       4. sqr-neg 44.2%

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

       5. sqrt-unprod 6.1%

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

       6. add-sqr-sqrt 14.5%

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

       7. associate-/r/ 14.5%

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

       8. add-sqr-sqrt 6.0%

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

       9. sqrt-unprod 44.0%

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

       10. sqr-neg 44.0%

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

       11. sqrt-unprod 46.9%

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

       12. add-sqr-sqrt 92.2%

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

   12. Applied egg-rr 92.2%

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

   13. Taylor expanded in x around 0 64.6%

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

       1. mul-1-neg 64.6%

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

       2. associate-*r/ 79.0%

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

       3. *-commutative 79.0%

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

       4. distribute-rgt-neg-out 79.0%

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

   15. Simplified 79.0%

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

   if -1.89999999999999998e219 < t < 1e114

   1. Initial program 93.9%

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

      1. associate-/l* 94.5%

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

   3. Simplified 94.5%

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

   5. Taylor expanded in z around inf 78.1%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+219} \lor \neg \left(t \leq 10^{+114}\right):\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+43} \lor \neg \left(t \leq 1.3 \cdot 10^{+90}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.2e+43) (not (<= t 1.3e+90)))
   (- x (* t (/ y a)))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+43) || !(t <= 1.3e+90)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.2d+43)) .or. (.not. (t <= 1.3d+90))) then
        tmp = x - (t * (y / a))
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.2e+43) || !(t <= 1.3e+90)) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.2e+43) or not (t <= 1.3e+90):
		tmp = x - (t * (y / a))
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.2e+43) || !(t <= 1.3e+90))
		tmp = Float64(x - Float64(t * Float64(y / a)));
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.2e+43) || ~((t <= 1.3e+90)))
		tmp = x - (t * (y / a));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.2e+43], N[Not[LessEqual[t, 1.3e+90]], $MachinePrecision]], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.20000000000000012e43 or 1.2999999999999999e90 < t

   1. Initial program 83.4%

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

      1. associate-/l* 93.6%

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

   3. Simplified 93.6%

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

   5. Taylor expanded in y around 0 83.4%

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

      1. associate-*l/ 96.1%

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

      2. *-commutative 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in z around 0 77.9%

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

      1. associate-*r/ 88.5%

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

      2. neg-mul-1 88.5%

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

      3. distribute-lft-neg-in 88.5%

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

      4. cancel-sign-sub-inv 88.5%

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

   10. Simplified 88.5%

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

   if -1.20000000000000012e43 < t < 1.2999999999999999e90

   1. Initial program 95.8%

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

      1. associate-/l* 94.9%

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

   3. Simplified 94.9%

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

   5. Taylor expanded in t around 0 83.3%

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

      1. +-commutative 83.3%

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

      2. associate-/l* 83.0%

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

   7. Simplified 83.0%

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

      1. clear-num 82.8%

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

      2. un-div-inv 83.1%

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

   9. Applied egg-rr 83.1%

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

       1. associate-/r/ 84.5%

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

   11. Applied egg-rr 84.5%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+43} \lor \neg \left(t \leq 1.3 \cdot 10^{+90}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+75} \lor \neg \left(y \leq 11.8\right):\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.45e+75) (not (<= y 11.8))) (* (/ t a) (- y)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.45e+75) || !(y <= 11.8)) {
		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 ((y <= (-1.45d+75)) .or. (.not. (y <= 11.8d0))) 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 ((y <= -1.45e+75) || !(y <= 11.8)) {
		tmp = (t / a) * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.45e+75) or not (y <= 11.8):
		tmp = (t / a) * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.45e+75) || !(y <= 11.8))
		tmp = Float64(Float64(t / a) * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.45e+75) || ~((y <= 11.8)))
		tmp = (t / a) * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.45e+75], N[Not[LessEqual[y, 11.8]], $MachinePrecision]], N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.4499999999999999e75 or 11.800000000000001 < y

   1. Initial program 84.6%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in y around 0 84.6%

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

      1. associate-*l/ 94.0%

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

      2. *-commutative 94.0%

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

   7. Simplified 94.0%

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

   8. Taylor expanded in z around 0 54.0%

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

      1. associate-*r/ 60.4%

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

      2. neg-mul-1 60.4%

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

      3. distribute-lft-neg-in 60.4%

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

      4. cancel-sign-sub-inv 60.4%

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

   10. Simplified 60.4%

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

       1. *-commutative 60.4%

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

       2. add-sqr-sqrt 32.3%

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

       3. sqrt-unprod 38.5%

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

       4. sqr-neg 38.5%

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

       5. sqrt-unprod 9.9%

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

       6. add-sqr-sqrt 20.1%

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

       7. associate-/r/ 17.2%

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

       8. add-sqr-sqrt 8.5%

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

       9. sqrt-unprod 38.5%

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

       10. sqr-neg 38.5%

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

       11. sqrt-unprod 31.5%

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

       12. add-sqr-sqrt 61.2%

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

   12. Applied egg-rr 61.2%

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

   13. Taylor expanded in x around 0 40.8%

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

       1. mul-1-neg 40.8%

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

       2. associate-*l/ 48.0%

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

       3. distribute-lft-neg-in 48.0%

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

       4. *-commutative 48.0%

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

       5. distribute-neg-frac2 48.0%

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

   15. Simplified 48.0%

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

   if -1.4499999999999999e75 < y < 11.800000000000001

   1. Initial program 98.2%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in x around inf 54.6%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+75} \lor \neg \left(y \leq 11.8\right):\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 9:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -2.65e+76) (* t (/ (- y) a)) (if (<= y 9.0) x (* (/ t a) (- y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.65e+76) {
		tmp = t * (-y / a);
	} else if (y <= 9.0) {
		tmp = x;
	} else {
		tmp = (t / a) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-2.65d+76)) then
        tmp = t * (-y / a)
    else if (y <= 9.0d0) then
        tmp = x
    else
        tmp = (t / a) * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -2.65e+76) {
		tmp = t * (-y / a);
	} else if (y <= 9.0) {
		tmp = x;
	} else {
		tmp = (t / a) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -2.65e+76:
		tmp = t * (-y / a)
	elif y <= 9.0:
		tmp = x
	else:
		tmp = (t / a) * -y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -2.65e+76)
		tmp = Float64(t * Float64(Float64(-y) / a));
	elseif (y <= 9.0)
		tmp = x;
	else
		tmp = Float64(Float64(t / a) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -2.65e+76)
		tmp = t * (-y / a);
	elseif (y <= 9.0)
		tmp = x;
	else
		tmp = (t / a) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -2.65e+76], N[(t * N[((-y) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.0], x, N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.65000000000000008e76

   1. Initial program 83.6%

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

      1. associate-/l* 96.3%

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

   3. Simplified 96.3%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. associate-*l/ 90.0%

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

      2. *-commutative 90.0%

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

   7. Simplified 90.0%

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

   8. Taylor expanded in z around 0 51.7%

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

      1. associate-*r/ 59.6%

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

      2. neg-mul-1 59.6%

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

      3. distribute-lft-neg-in 59.6%

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

      4. cancel-sign-sub-inv 59.6%

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

   10. Simplified 59.6%

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

       1. *-commutative 59.6%

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

       2. add-sqr-sqrt 36.1%

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

       3. sqrt-unprod 35.3%

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

       4. sqr-neg 35.3%

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

       5. sqrt-unprod 5.8%

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

       6. add-sqr-sqrt 13.7%

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

       7. associate-/r/ 12.1%

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

       8. add-sqr-sqrt 5.9%

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

       9. sqrt-unprod 36.9%

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

       10. sqr-neg 36.9%

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

       11. sqrt-unprod 32.7%

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

       12. add-sqr-sqrt 59.6%

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

   12. Applied egg-rr 59.6%

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

   13. Taylor expanded in x around 0 43.2%

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

       1. mul-1-neg 43.2%

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

       2. associate-*r/ 51.2%

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

       3. *-commutative 51.2%

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

       4. distribute-rgt-neg-out 51.2%

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

   15. Simplified 51.2%

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

   if -2.65000000000000008e76 < y < 9

   1. Initial program 98.2%

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

      1. associate-/l* 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in x around inf 54.6%

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

   if 9 < y

   1. Initial program 85.4%

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

      1. associate-/l* 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in y around 0 85.4%

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

      1. associate-*l/ 97.3%

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

      2. *-commutative 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in z around 0 55.8%

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

      1. associate-*r/ 61.1%

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

      2. neg-mul-1 61.1%

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

      3. distribute-lft-neg-in 61.1%

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

      4. cancel-sign-sub-inv 61.1%

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

   10. Simplified 61.1%

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

       1. *-commutative 61.1%

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

       2. add-sqr-sqrt 29.2%

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

       3. sqrt-unprod 41.1%

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

       4. sqr-neg 41.1%

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

       5. sqrt-unprod 13.3%

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

       6. add-sqr-sqrt 25.3%

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

       7. associate-/r/ 21.2%

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

       8. add-sqr-sqrt 10.6%

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

       9. sqrt-unprod 39.8%

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

       10. sqr-neg 39.8%

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

       11. sqrt-unprod 30.5%

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

       12. add-sqr-sqrt 62.5%

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

   12. Applied egg-rr 62.5%

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

   13. Taylor expanded in x around 0 38.9%

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

       1. mul-1-neg 38.9%

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

       2. associate-*l/ 45.6%

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

       3. distribute-lft-neg-in 45.6%

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

       4. *-commutative 45.6%

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

       5. distribute-neg-frac2 45.6%

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

   15. Simplified 45.6%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+76}:\\ \;\;\;\;t \cdot \frac{-y}{a}\\ \mathbf{elif}\;y \leq 9:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+159}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -5e+159) (+ x (* y (/ (- z t) a))) (+ x (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -5e+159) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + ((z - 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 <= (-5d+159)) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = x + ((z - 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 <= -5e+159) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -5e+159:
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = x + ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -5e+159)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -5e+159)
		tmp = x + (y * ((z - t) / a));
	else
		tmp = x + ((z - t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -5e+159], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.00000000000000003e159

   1. Initial program 80.5%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

   if -5.00000000000000003e159 < y

   1. Initial program 93.4%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around 0 93.4%

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

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+159}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+159}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.2e+159) (+ x (/ y (/ a (- z t)))) (+ x (* (- z t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -3.2e+159) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + ((z - 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 <= (-3.2d+159)) then
        tmp = x + (y / (a / (z - t)))
    else
        tmp = x + ((z - 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 <= -3.2e+159) {
		tmp = x + (y / (a / (z - t)));
	} else {
		tmp = x + ((z - t) * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -3.2e+159:
		tmp = x + (y / (a / (z - t)))
	else:
		tmp = x + ((z - t) * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -3.2e+159)
		tmp = Float64(x + Float64(y / Float64(a / Float64(z - t))));
	else
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -3.2e+159)
		tmp = x + (y / (a / (z - t)));
	else
		tmp = x + ((z - t) * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -3.2e+159], N[(x + N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.19999999999999985e159

   1. Initial program 80.5%

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

      1. associate-/l* 97.1%

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

   3. Simplified 97.1%

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

      1. clear-num 97.0%

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

      2. un-div-inv 97.3%

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

   6. Applied egg-rr 97.3%

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

   if -3.19999999999999985e159 < y

   1. Initial program 93.4%

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

      1. associate-/l* 94.0%

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

   3. Simplified 94.0%

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

   5. Taylor expanded in y around 0 93.4%

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

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+159}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 93.0% accurate, 1.0× speedup

Math

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

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(y * Float64(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[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.5%

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

   1. associate-/l* 94.5%

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

3. Simplified 94.5%

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

5. Final simplification 94.5%

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

Alternative 12: 38.8% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

   1. associate-/l* 94.5%

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

3. Simplified 94.5%

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

5. Taylor expanded in x around inf 34.8%

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

6. Final simplification 34.8%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.2% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))