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

Percentage Accurate: 93.5% → 96.9%

Time: 7.5s

Alternatives: 12

Speedup: 1.0×

• 24.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.5% 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: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

   1. *-commutative 96.5%

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

   2. clear-num 96.5%

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

   3. un-div-inv 96.9%

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

5. Applied egg-rr 96.9%

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

6. Final simplification 96.9%

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

Alternative 2: 72.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot y}{a}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+133}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+209}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+242}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z y) a))))
   (if (<= t -1.2e+133)
     (/ (- y) (/ a t))
     (if (<= t 4.2e+108)
       t_1
       (if (<= t 2.95e+209)
         (* (/ t a) (- y))
         (if (<= t 6.2e+242) t_1 (/ (* t (- y)) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((z * y) / a);
	double tmp;
	if (t <= -1.2e+133) {
		tmp = -y / (a / t);
	} else if (t <= 4.2e+108) {
		tmp = t_1;
	} else if (t <= 2.95e+209) {
		tmp = (t / a) * -y;
	} else if (t <= 6.2e+242) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = x + ((z * y) / a)
    if (t <= (-1.2d+133)) then
        tmp = -y / (a / t)
    else if (t <= 4.2d+108) then
        tmp = t_1
    else if (t <= 2.95d+209) then
        tmp = (t / a) * -y
    else if (t <= 6.2d+242) then
        tmp = t_1
    else
        tmp = (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 t_1 = x + ((z * y) / a);
	double tmp;
	if (t <= -1.2e+133) {
		tmp = -y / (a / t);
	} else if (t <= 4.2e+108) {
		tmp = t_1;
	} else if (t <= 2.95e+209) {
		tmp = (t / a) * -y;
	} else if (t <= 6.2e+242) {
		tmp = t_1;
	} else {
		tmp = (t * -y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((z * y) / a)
	tmp = 0
	if t <= -1.2e+133:
		tmp = -y / (a / t)
	elif t <= 4.2e+108:
		tmp = t_1
	elif t <= 2.95e+209:
		tmp = (t / a) * -y
	elif t <= 6.2e+242:
		tmp = t_1
	else:
		tmp = (t * -y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(z * y) / a))
	tmp = 0.0
	if (t <= -1.2e+133)
		tmp = Float64(Float64(-y) / Float64(a / t));
	elseif (t <= 4.2e+108)
		tmp = t_1;
	elseif (t <= 2.95e+209)
		tmp = Float64(Float64(t / a) * Float64(-y));
	elseif (t <= 6.2e+242)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * Float64(-y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((z * y) / a);
	tmp = 0.0;
	if (t <= -1.2e+133)
		tmp = -y / (a / t);
	elseif (t <= 4.2e+108)
		tmp = t_1;
	elseif (t <= 2.95e+209)
		tmp = (t / a) * -y;
	elseif (t <= 6.2e+242)
		tmp = t_1;
	else
		tmp = (t * -y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+133], N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e+108], t$95$1, If[LessEqual[t, 2.95e+209], N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t, 6.2e+242], t$95$1, N[(N[(t * (-y)), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1999999999999999e133

   1. Initial program 84.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. associate-*r/ 94.9%

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

   6. Simplified 94.9%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 5.5%

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

      3. sqr-neg 5.5%

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

      4. sqrt-unprod 20.3%

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

      5. add-sqr-sqrt 20.3%

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

      6. div-inv 20.3%

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

      7. associate-*r* 17.5%

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

      8. *-commutative 17.5%

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

      9. div-inv 17.5%

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

      10. associate-/l* 20.2%

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

      11. add-sqr-sqrt 20.2%

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

      12. sqrt-unprod 5.8%

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

      13. sqr-neg 5.8%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 94.9%

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

   8. Applied egg-rr 94.9%

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

   9. Taylor expanded in x around 0 66.9%

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

       1. mul-1-neg 66.9%

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

       2. associate-*l/ 74.5%

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

       3. distribute-rgt-neg-in 74.5%

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

   11. Simplified 74.5%

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

       1. distribute-rgt-neg-out 74.5%

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

       2. clear-num 74.4%

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

       3. associate-*l/ 74.5%

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

       4. *-un-lft-identity 74.5%

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

   13. Applied egg-rr 74.5%

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

   if -1.1999999999999999e133 < t < 4.20000000000000019e108 or 2.9499999999999999e209 < t < 6.2000000000000002e242

   1. Initial program 94.7%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in z around inf 79.2%

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

   if 4.20000000000000019e108 < t < 2.9499999999999999e209

   1. Initial program 91.6%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 91.6%

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

      1. mul-1-neg 91.6%

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

      2. unsub-neg 91.6%

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

      3. associate-*r/ 95.7%

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

   6. Simplified 95.7%

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

      1. add-sqr-sqrt 95.5%

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

      2. sqrt-unprod 57.8%

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

      3. sqr-neg 57.8%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 31.0%

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

      6. div-inv 31.0%

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

      7. associate-*r* 30.9%

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

      8. *-commutative 30.9%

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

      9. div-inv 30.9%

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

      10. associate-/l* 30.9%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 58.1%

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

      13. sqr-neg 58.1%

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

      14. sqrt-unprod 95.7%

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

      15. add-sqr-sqrt 95.9%

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

   8. Applied egg-rr 95.9%

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

   9. Taylor expanded in x around 0 62.0%

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

       1. mul-1-neg 62.0%

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

       2. associate-*l/ 66.5%

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

       3. distribute-rgt-neg-in 66.5%

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

   11. Simplified 66.5%

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

   if 6.2000000000000002e242 < t

   1. Initial program 93.1%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 79.6%

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

   5. Taylor expanded in a around 0 86.0%

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

   6. Taylor expanded in z around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. distribute-lft-neg-out 86.0%

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

      3. *-commutative 86.0%

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

   8. Simplified 86.0%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+133}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{elif}\;t \leq 2.95 \cdot 10^{+209}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+242}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \]

Alternative 3: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;t \leq -1.2 \cdot 10^{+133}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+139}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+242}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= t -1.2e+133)
     (/ (- y) (/ a t))
     (if (<= t 4.5e+108)
       t_1
       (if (<= t 4.1e+139)
         (* (/ t a) (- y))
         (if (<= t 7.8e+242) t_1 (/ (* t (- y)) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -1.2e+133) {
		tmp = -y / (a / t);
	} else if (t <= 4.5e+108) {
		tmp = t_1;
	} else if (t <= 4.1e+139) {
		tmp = (t / a) * -y;
	} else if (t <= 7.8e+242) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (t <= (-1.2d+133)) then
        tmp = -y / (a / t)
    else if (t <= 4.5d+108) then
        tmp = t_1
    else if (t <= 4.1d+139) then
        tmp = (t / a) * -y
    else if (t <= 7.8d+242) then
        tmp = t_1
    else
        tmp = (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 t_1 = x + (z * (y / a));
	double tmp;
	if (t <= -1.2e+133) {
		tmp = -y / (a / t);
	} else if (t <= 4.5e+108) {
		tmp = t_1;
	} else if (t <= 4.1e+139) {
		tmp = (t / a) * -y;
	} else if (t <= 7.8e+242) {
		tmp = t_1;
	} else {
		tmp = (t * -y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if t <= -1.2e+133:
		tmp = -y / (a / t)
	elif t <= 4.5e+108:
		tmp = t_1
	elif t <= 4.1e+139:
		tmp = (t / a) * -y
	elif t <= 7.8e+242:
		tmp = t_1
	else:
		tmp = (t * -y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (t <= -1.2e+133)
		tmp = Float64(Float64(-y) / Float64(a / t));
	elseif (t <= 4.5e+108)
		tmp = t_1;
	elseif (t <= 4.1e+139)
		tmp = Float64(Float64(t / a) * Float64(-y));
	elseif (t <= 7.8e+242)
		tmp = t_1;
	else
		tmp = Float64(Float64(t * Float64(-y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (t <= -1.2e+133)
		tmp = -y / (a / t);
	elseif (t <= 4.5e+108)
		tmp = t_1;
	elseif (t <= 4.1e+139)
		tmp = (t / a) * -y;
	elseif (t <= 7.8e+242)
		tmp = t_1;
	else
		tmp = (t * -y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.2e+133], N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+108], t$95$1, If[LessEqual[t, 4.1e+139], N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t, 7.8e+242], t$95$1, N[(N[(t * (-y)), $MachinePrecision] / a), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.1999999999999999e133

   1. Initial program 84.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. associate-*r/ 94.9%

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

   6. Simplified 94.9%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 5.5%

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

      3. sqr-neg 5.5%

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

      4. sqrt-unprod 20.3%

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

      5. add-sqr-sqrt 20.3%

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

      6. div-inv 20.3%

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

      7. associate-*r* 17.5%

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

      8. *-commutative 17.5%

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

      9. div-inv 17.5%

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

      10. associate-/l* 20.2%

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

      11. add-sqr-sqrt 20.2%

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

      12. sqrt-unprod 5.8%

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

      13. sqr-neg 5.8%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 94.9%

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

   8. Applied egg-rr 94.9%

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

   9. Taylor expanded in x around 0 66.9%

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

       1. mul-1-neg 66.9%

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

       2. associate-*l/ 74.5%

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

       3. distribute-rgt-neg-in 74.5%

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

   11. Simplified 74.5%

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

       1. distribute-rgt-neg-out 74.5%

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

       2. clear-num 74.4%

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

       3. associate-*l/ 74.5%

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

       4. *-un-lft-identity 74.5%

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

   13. Applied egg-rr 74.5%

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

   if -1.1999999999999999e133 < t < 4.5e108 or 4.1000000000000002e139 < t < 7.8000000000000003e242

   1. Initial program 95.0%

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

      1. associate-*l/ 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in t around 0 77.1%

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

      1. +-commutative 77.1%

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

      2. associate-*l/ 80.6%

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

      3. *-commutative 80.6%

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

   6. Simplified 80.6%

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

   if 4.5e108 < t < 4.1000000000000002e139

   1. Initial program 82.7%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

      3. associate-*r/ 99.6%

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

   6. Simplified 99.6%

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

      1. add-sqr-sqrt 99.6%

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

      2. sqrt-unprod 99.6%

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

      3. sqr-neg 99.6%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 18.5%

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

      6. div-inv 18.5%

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

      7. associate-*r* 18.4%

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

      8. *-commutative 18.4%

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

      9. div-inv 18.4%

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

      10. associate-/l* 18.5%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 99.9%

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

      13. sqr-neg 99.9%

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

      14. sqrt-unprod 99.7%

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

      15. add-sqr-sqrt 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x around 0 65.0%

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

       1. mul-1-neg 65.0%

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

       2. associate-*l/ 82.3%

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

       3. distribute-rgt-neg-in 82.3%

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

   11. Simplified 82.3%

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

   if 7.8000000000000003e242 < t

   1. Initial program 93.1%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 79.6%

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

   5. Taylor expanded in a around 0 86.0%

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

   6. Taylor expanded in z around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. distribute-lft-neg-out 86.0%

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

      3. *-commutative 86.0%

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

   8. Simplified 86.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+133}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+139}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+242}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \]

Alternative 4: 74.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+140}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+244}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.5e+133)
   (/ (- y) (/ a t))
   (if (<= t 4.5e+108)
     (+ x (/ z (/ a y)))
     (if (<= t 2.8e+140)
       (* (/ t a) (- y))
       (if (<= t 4.1e+244) (+ x (* z (/ y a))) (/ (* t (- y)) a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.5e+133) {
		tmp = -y / (a / t);
	} else if (t <= 4.5e+108) {
		tmp = x + (z / (a / y));
	} else if (t <= 2.8e+140) {
		tmp = (t / a) * -y;
	} else if (t <= 4.1e+244) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (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 (t <= (-1.5d+133)) then
        tmp = -y / (a / t)
    else if (t <= 4.5d+108) then
        tmp = x + (z / (a / y))
    else if (t <= 2.8d+140) then
        tmp = (t / a) * -y
    else if (t <= 4.1d+244) then
        tmp = x + (z * (y / a))
    else
        tmp = (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 (t <= -1.5e+133) {
		tmp = -y / (a / t);
	} else if (t <= 4.5e+108) {
		tmp = x + (z / (a / y));
	} else if (t <= 2.8e+140) {
		tmp = (t / a) * -y;
	} else if (t <= 4.1e+244) {
		tmp = x + (z * (y / a));
	} else {
		tmp = (t * -y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.5e+133:
		tmp = -y / (a / t)
	elif t <= 4.5e+108:
		tmp = x + (z / (a / y))
	elif t <= 2.8e+140:
		tmp = (t / a) * -y
	elif t <= 4.1e+244:
		tmp = x + (z * (y / a))
	else:
		tmp = (t * -y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.5e+133)
		tmp = Float64(Float64(-y) / Float64(a / t));
	elseif (t <= 4.5e+108)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (t <= 2.8e+140)
		tmp = Float64(Float64(t / a) * Float64(-y));
	elseif (t <= 4.1e+244)
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(Float64(t * Float64(-y)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.5e+133)
		tmp = -y / (a / t);
	elseif (t <= 4.5e+108)
		tmp = x + (z / (a / y));
	elseif (t <= 2.8e+140)
		tmp = (t / a) * -y;
	elseif (t <= 4.1e+244)
		tmp = x + (z * (y / a));
	else
		tmp = (t * -y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.5e+133], N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+108], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e+140], N[(N[(t / a), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[t, 4.1e+244], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * (-y)), $MachinePrecision] / a), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.50000000000000003e133

   1. Initial program 84.9%

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

      1. associate-*l/ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in z around 0 84.9%

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

      1. mul-1-neg 84.9%

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

      2. unsub-neg 84.9%

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

      3. associate-*r/ 94.9%

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

   6. Simplified 94.9%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 5.5%

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

      3. sqr-neg 5.5%

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

      4. sqrt-unprod 20.3%

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

      5. add-sqr-sqrt 20.3%

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

      6. div-inv 20.3%

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

      7. associate-*r* 17.5%

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

      8. *-commutative 17.5%

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

      9. div-inv 17.5%

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

      10. associate-/l* 20.2%

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

      11. add-sqr-sqrt 20.2%

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

      12. sqrt-unprod 5.8%

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

      13. sqr-neg 5.8%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 94.9%

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

   8. Applied egg-rr 94.9%

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

   9. Taylor expanded in x around 0 66.9%

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

       1. mul-1-neg 66.9%

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

       2. associate-*l/ 74.5%

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

       3. distribute-rgt-neg-in 74.5%

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

   11. Simplified 74.5%

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

       1. distribute-rgt-neg-out 74.5%

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

       2. clear-num 74.4%

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

       3. associate-*l/ 74.5%

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

       4. *-un-lft-identity 74.5%

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

   13. Applied egg-rr 74.5%

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

   if -1.50000000000000003e133 < t < 4.5e108

   1. Initial program 95.1%

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

      1. associate-*l/ 96.6%

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

   3. Simplified 96.6%

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

   4. Taylor expanded in t around 0 79.1%

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

      1. +-commutative 79.1%

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

      2. associate-*l/ 82.4%

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

      3. *-commutative 82.4%

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

   6. Simplified 82.4%

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

      1. clear-num 82.4%

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

      2. div-inv 82.9%

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

   8. Applied egg-rr 82.9%

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

   if 4.5e108 < t < 2.79999999999999983e140

   1. Initial program 82.7%

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

      1. associate-*l/ 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 82.7%

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

      1. mul-1-neg 82.7%

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

      2. unsub-neg 82.7%

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

      3. associate-*r/ 99.6%

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

   6. Simplified 99.6%

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

      1. add-sqr-sqrt 99.6%

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

      2. sqrt-unprod 99.6%

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

      3. sqr-neg 99.6%

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

      4. sqrt-unprod 0.0%

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

      5. add-sqr-sqrt 18.5%

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

      6. div-inv 18.5%

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

      7. associate-*r* 18.4%

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

      8. *-commutative 18.4%

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

      9. div-inv 18.4%

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

      10. associate-/l* 18.5%

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

      11. add-sqr-sqrt 0.0%

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

      12. sqrt-unprod 99.9%

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

      13. sqr-neg 99.9%

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

      14. sqrt-unprod 99.7%

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

      15. add-sqr-sqrt 99.9%

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

   8. Applied egg-rr 99.9%

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

   9. Taylor expanded in x around 0 65.0%

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

       1. mul-1-neg 65.0%

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

       2. associate-*l/ 82.3%

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

       3. distribute-rgt-neg-in 82.3%

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

   11. Simplified 82.3%

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

   if 2.79999999999999983e140 < t < 4.09999999999999993e244

   1. Initial program 94.4%

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

      1. associate-*l/ 94.7%

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

   3. Simplified 94.7%

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

   4. Taylor expanded in t around 0 57.7%

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

      1. +-commutative 57.7%

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

      2. associate-*l/ 63.0%

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

      3. *-commutative 63.0%

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

   6. Simplified 63.0%

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

   if 4.09999999999999993e244 < t

   1. Initial program 93.1%

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

      1. associate-*l/ 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around inf 79.6%

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

   5. Taylor expanded in a around 0 86.0%

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

   6. Taylor expanded in z around 0 86.0%

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

      1. mul-1-neg 86.0%

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

      2. distribute-lft-neg-out 86.0%

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

      3. *-commutative 86.0%

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

   8. Simplified 86.0%

      \[\leadsto \frac{\color{blue}{y \cdot \left(-t\right)}}{a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+133}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+108}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+140}:\\ \;\;\;\;\frac{t}{a} \cdot \left(-y\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+244}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \left(-y\right)}{a}\\ \end{array} \]

Alternative 5: 49.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;y \leq -1.22 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ a y))))
   (if (<= y -1.22e+51)
     t_1
     (if (<= y 7.2e-60) x (if (<= y 6.2e+85) t_1 (/ (- y) (/ a t)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a / y);
	double tmp;
	if (y <= -1.22e+51) {
		tmp = t_1;
	} else if (y <= 7.2e-60) {
		tmp = x;
	} else if (y <= 6.2e+85) {
		tmp = t_1;
	} else {
		tmp = -y / (a / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z / (a / y)
    if (y <= (-1.22d+51)) then
        tmp = t_1
    else if (y <= 7.2d-60) then
        tmp = x
    else if (y <= 6.2d+85) then
        tmp = t_1
    else
        tmp = -y / (a / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a / y);
	double tmp;
	if (y <= -1.22e+51) {
		tmp = t_1;
	} else if (y <= 7.2e-60) {
		tmp = x;
	} else if (y <= 6.2e+85) {
		tmp = t_1;
	} else {
		tmp = -y / (a / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a / y)
	tmp = 0
	if y <= -1.22e+51:
		tmp = t_1
	elif y <= 7.2e-60:
		tmp = x
	elif y <= 6.2e+85:
		tmp = t_1
	else:
		tmp = -y / (a / t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a / y))
	tmp = 0.0
	if (y <= -1.22e+51)
		tmp = t_1;
	elseif (y <= 7.2e-60)
		tmp = x;
	elseif (y <= 6.2e+85)
		tmp = t_1;
	else
		tmp = Float64(Float64(-y) / Float64(a / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a / y);
	tmp = 0.0;
	if (y <= -1.22e+51)
		tmp = t_1;
	elseif (y <= 7.2e-60)
		tmp = x;
	elseif (y <= 6.2e+85)
		tmp = t_1;
	else
		tmp = -y / (a / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.22e+51], t$95$1, If[LessEqual[y, 7.2e-60], x, If[LessEqual[y, 6.2e+85], t$95$1, N[((-y) / N[(a / t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.22000000000000005e51 or 7.2e-60 < y < 6.20000000000000023e85

   1. Initial program 93.1%

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

      1. associate-*l/ 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in y around inf 73.4%

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

   5. Taylor expanded in z around inf 49.1%

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

   6. Taylor expanded in y around 0 47.9%

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

      1. *-commutative 47.9%

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

      2. associate-/l* 51.4%

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

   8. Simplified 51.4%

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

   if -1.22000000000000005e51 < y < 7.2e-60

   1. Initial program 98.4%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 56.2%

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

   if 6.20000000000000023e85 < y

   1. Initial program 79.7%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

      3. associate-*r/ 76.9%

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

   6. Simplified 76.9%

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

      1. add-sqr-sqrt 31.3%

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

      2. sqrt-unprod 35.7%

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

      3. sqr-neg 35.7%

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

      4. sqrt-unprod 8.4%

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

      5. add-sqr-sqrt 14.5%

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

      6. div-inv 14.5%

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

      7. associate-*r* 12.5%

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

      8. *-commutative 12.5%

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

      9. div-inv 12.5%

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

      10. associate-/l* 14.5%

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

      11. add-sqr-sqrt 8.3%

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

      12. sqrt-unprod 35.8%

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

      13. sqr-neg 35.8%

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

      14. sqrt-unprod 29.5%

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

      15. add-sqr-sqrt 76.9%

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

   8. Applied egg-rr 76.9%

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

   9. Taylor expanded in x around 0 56.4%

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

       1. mul-1-neg 56.4%

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

       2. associate-*l/ 65.5%

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

       3. distribute-rgt-neg-in 65.5%

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

   11. Simplified 65.5%

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

       1. distribute-rgt-neg-out 65.5%

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

       2. clear-num 65.5%

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

       3. associate-*l/ 65.5%

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

       4. *-un-lft-identity 65.5%

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

   13. Applied egg-rr 65.5%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+51}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{+85}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{a}{t}}\\ \end{array} \]

Alternative 6: 49.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{a}{y}}\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+57}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ a y))))
   (if (<= y -1.15e+51)
     t_1
     (if (<= y 1.1e-59) x (if (<= y 9.5e+57) t_1 (* t (/ y (- a))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a / y);
	double tmp;
	if (y <= -1.15e+51) {
		tmp = t_1;
	} else if (y <= 1.1e-59) {
		tmp = x;
	} else if (y <= 9.5e+57) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = z / (a / y)
    if (y <= (-1.15d+51)) then
        tmp = t_1
    else if (y <= 1.1d-59) then
        tmp = x
    else if (y <= 9.5d+57) then
        tmp = t_1
    else
        tmp = 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 t_1 = z / (a / y);
	double tmp;
	if (y <= -1.15e+51) {
		tmp = t_1;
	} else if (y <= 1.1e-59) {
		tmp = x;
	} else if (y <= 9.5e+57) {
		tmp = t_1;
	} else {
		tmp = t * (y / -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a / y)
	tmp = 0
	if y <= -1.15e+51:
		tmp = t_1
	elif y <= 1.1e-59:
		tmp = x
	elif y <= 9.5e+57:
		tmp = t_1
	else:
		tmp = t * (y / -a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a / y))
	tmp = 0.0
	if (y <= -1.15e+51)
		tmp = t_1;
	elseif (y <= 1.1e-59)
		tmp = x;
	elseif (y <= 9.5e+57)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(y / Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a / y);
	tmp = 0.0;
	if (y <= -1.15e+51)
		tmp = t_1;
	elseif (y <= 1.1e-59)
		tmp = x;
	elseif (y <= 9.5e+57)
		tmp = t_1;
	else
		tmp = t * (y / -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+51], t$95$1, If[LessEqual[y, 1.1e-59], x, If[LessEqual[y, 9.5e+57], t$95$1, N[(t * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.15000000000000003e51 or 1.0999999999999999e-59 < y < 9.4999999999999997e57

   1. Initial program 93.7%

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

      1. associate-*l/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around inf 74.1%

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

   5. Taylor expanded in z around inf 49.5%

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

   6. Taylor expanded in y around 0 49.4%

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

      1. *-commutative 49.4%

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

      2. associate-/l* 51.9%

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

   8. Simplified 51.9%

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

   if -1.15000000000000003e51 < y < 1.0999999999999999e-59

   1. Initial program 98.4%

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

      1. associate-*l/ 95.9%

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

   3. Simplified 95.9%

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

   4. Taylor expanded in x around inf 56.2%

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

   if 9.4999999999999997e57 < y

   1. Initial program 80.5%

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

      1. associate-*l/ 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in z around 0 66.6%

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

      1. mul-1-neg 66.6%

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

      2. unsub-neg 66.6%

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

      3. associate-*r/ 76.2%

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

   6. Simplified 76.2%

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

      1. add-sqr-sqrt 30.9%

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

      2. sqrt-unprod 36.6%

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

      3. sqr-neg 36.6%

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

      4. sqrt-unprod 9.1%

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

      5. add-sqr-sqrt 14.6%

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

      6. div-inv 14.6%

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

      7. associate-*r* 12.9%

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

      8. *-commutative 12.9%

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

      9. div-inv 12.9%

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

      10. associate-/l* 14.7%

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

      11. add-sqr-sqrt 9.1%

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

      12. sqrt-unprod 35.1%

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

      13. sqr-neg 35.1%

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

      14. sqrt-unprod 27.8%

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

      15. add-sqr-sqrt 74.6%

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

   8. Applied egg-rr 74.6%

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

   9. Taylor expanded in x around 0 55.4%

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

       1. mul-1-neg 55.4%

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

       2. associate-*l/ 62.2%

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

       3. distribute-rgt-neg-in 62.2%

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

   11. Simplified 62.2%

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

   12. Taylor expanded in t around 0 55.4%

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

       1. associate-*r/ 55.4%

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

       2. *-commutative 55.4%

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

       3. neg-mul-1 55.4%

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

       4. distribute-rgt-neg-out 55.4%

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

       5. associate-/l* 61.7%

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

       6. *-lft-identity 61.7%

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

       7. neg-mul-1 61.7%

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

       8. times-frac 61.7%

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

       9. metadata-eval 61.7%

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

       10. neg-mul-1 61.7%

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

       11. distribute-frac-neg 61.7%

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

       12. associate-/r/ 63.4%

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

       13. *-commutative 63.4%

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

   14. Simplified 63.4%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+51}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-59}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+57}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{-a}\\ \end{array} \]

Alternative 7: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -880000000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-29}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= z -880000000000.0)
   (+ x (/ z (/ a y)))
   (if (<= z 6.2e-29) (- x (* t (/ y a))) (+ x (* z (/ y a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -880000000000.0) {
		tmp = x + (z / (a / y));
	} else if (z <= 6.2e-29) {
		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 (z <= (-880000000000.0d0)) then
        tmp = x + (z / (a / y))
    else if (z <= 6.2d-29) 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 (z <= -880000000000.0) {
		tmp = x + (z / (a / y));
	} else if (z <= 6.2e-29) {
		tmp = x - (t * (y / a));
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -880000000000.0:
		tmp = x + (z / (a / y))
	elif z <= 6.2e-29:
		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 (z <= -880000000000.0)
		tmp = Float64(x + Float64(z / Float64(a / y)));
	elseif (z <= 6.2e-29)
		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 (z <= -880000000000.0)
		tmp = x + (z / (a / y));
	elseif (z <= 6.2e-29)
		tmp = x - (t * (y / a));
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -880000000000.0], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e-29], 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 3 regimes

2. if z < -8.8e11

   1. Initial program 94.3%

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

      1. associate-*l/ 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in t around 0 83.0%

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

      1. +-commutative 83.0%

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

      2. associate-*l/ 84.3%

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

      3. *-commutative 84.3%

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

   6. Simplified 84.3%

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

      1. clear-num 84.3%

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

      2. div-inv 84.4%

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

   8. Applied egg-rr 84.4%

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

   if -8.8e11 < z < 6.20000000000000052e-29

   1. Initial program 95.5%

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

      1. associate-*l/ 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in z around 0 90.9%

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

      1. mul-1-neg 90.9%

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

      2. unsub-neg 90.9%

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

      3. associate-*r/ 91.6%

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

   6. Simplified 91.6%

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

   if 6.20000000000000052e-29 < z

   1. Initial program 88.7%

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

      1. associate-*l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 77.6%

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

      1. +-commutative 77.6%

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

      2. associate-*l/ 84.3%

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

      3. *-commutative 84.3%

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

   6. Simplified 84.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -880000000000:\\ \;\;\;\;x + \frac{z}{\frac{a}{y}}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-29}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]

Alternative 8: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.4e-73) x (if (<= a 2.1e+82) (* y (/ z a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.4e-73) {
		tmp = x;
	} else if (a <= 2.1e+82) {
		tmp = y * (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 (a <= (-1.4d-73)) then
        tmp = x
    else if (a <= 2.1d+82) then
        tmp = y * (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 (a <= -1.4e-73) {
		tmp = x;
	} else if (a <= 2.1e+82) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.4e-73:
		tmp = x
	elif a <= 2.1e+82:
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.4e-73)
		tmp = x;
	elseif (a <= 2.1e+82)
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.4e-73)
		tmp = x;
	elseif (a <= 2.1e+82)
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.4e-73], x, If[LessEqual[a, 2.1e+82], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.40000000000000006e-73 or 2.1e82 < a

   1. Initial program 87.3%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around inf 56.7%

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

   if -1.40000000000000006e-73 < a < 2.1e82

   1. Initial program 99.2%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 77.4%

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

   5. Taylor expanded in z around inf 48.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{-73}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+82}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 47.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e-69) x (if (<= a 7.8e+81) (/ y (/ a z)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e-69) {
		tmp = x;
	} else if (a <= 7.8e+81) {
		tmp = y / (a / 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 <= (-3.9d-69)) then
        tmp = x
    else if (a <= 7.8d+81) then
        tmp = y / (a / 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 <= -3.9e-69) {
		tmp = x;
	} else if (a <= 7.8e+81) {
		tmp = y / (a / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e-69:
		tmp = x
	elif a <= 7.8e+81:
		tmp = y / (a / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.9e-69)
		tmp = x;
	elseif (a <= 7.8e+81)
		tmp = Float64(y / Float64(a / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.9e-69)
		tmp = x;
	elseif (a <= 7.8e+81)
		tmp = y / (a / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.9e-69], x, If[LessEqual[a, 7.8e+81], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.89999999999999981e-69 or 7.8000000000000002e81 < a

   1. Initial program 87.3%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around inf 56.7%

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

   if -3.89999999999999981e-69 < a < 7.8000000000000002e81

   1. Initial program 99.2%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 77.4%

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

   5. Taylor expanded in z around inf 48.5%

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

   6. Taylor expanded in y around 0 52.3%

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

      1. associate-/l* 48.7%

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

   8. Simplified 48.7%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 7.8 \cdot 10^{+81}:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 49.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+81}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.65e-69) x (if (<= a 8.6e+81) (/ z (/ a y)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.65e-69) {
		tmp = x;
	} else if (a <= 8.6e+81) {
		tmp = z / (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 <= (-1.65d-69)) then
        tmp = x
    else if (a <= 8.6d+81) then
        tmp = z / (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 <= -1.65e-69) {
		tmp = x;
	} else if (a <= 8.6e+81) {
		tmp = z / (a / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.65e-69:
		tmp = x
	elif a <= 8.6e+81:
		tmp = z / (a / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.65e-69)
		tmp = x;
	elseif (a <= 8.6e+81)
		tmp = Float64(z / 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 <= -1.65e-69)
		tmp = x;
	elseif (a <= 8.6e+81)
		tmp = z / (a / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.65e-69], x, If[LessEqual[a, 8.6e+81], N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -1.65e-69 or 8.6000000000000003e81 < a

   1. Initial program 87.3%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in x around inf 56.7%

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

   if -1.65e-69 < a < 8.6000000000000003e81

   1. Initial program 99.2%

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

      1. associate-*l/ 96.7%

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

   3. Simplified 96.7%

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

   4. Taylor expanded in y around inf 77.4%

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

   5. Taylor expanded in z around inf 48.5%

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

   6. Taylor expanded in y around 0 52.3%

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

      1. *-commutative 52.3%

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

      2. associate-/l* 55.5%

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

   8. Simplified 55.5%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.65 \cdot 10^{-69}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+81}:\\ \;\;\;\;\frac{z}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 96.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

4. Final simplification 96.5%

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

Alternative 12: 39.8% 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 92.9%

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

   1. associate-*l/ 96.5%

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

3. Simplified 96.5%

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

4. Taylor expanded in x around inf 36.4%

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

5. Final simplification 36.4%

   \[\leadsto x \]

Developer target: 99.2% accurate, 0.7× 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 2023297 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

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

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