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

Percentage Accurate: 93.0% → 97.8%

Time: 11.5s

Alternatives: 15

Speedup: 0.6×

• 25.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -3.3e-74) (+ 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 <= -3.3e-74) {
		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 <= (-3.3d-74)) 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 <= -3.3e-74) {
		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 <= -3.3e-74:
		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 <= -3.3e-74)
		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 <= -3.3e-74)
		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, -3.3e-74], 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 < -3.29999999999999996e-74

   1. Initial program 88.3%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -3.29999999999999996e-74 < y

   1. Initial program 95.0%

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

      1. associate-/l* 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in y around 0 95.0%

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

      1. *-commutative 95.0%

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

      2. associate-*r/ 98.6%

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

   7. Simplified 98.6%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-74}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 84.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z - t}}\\ t_2 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{+91}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{+247}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a (- z t)))) (t_2 (/ (* y (- z t)) a)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -5e+91) t_2 (if (<= t_2 1e+247) (- x (/ t (/ a y))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (z - t));
	double t_2 = (y * (z - t)) / a;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -5e+91) {
		tmp = t_2;
	} else if (t_2 <= 1e+247) {
		tmp = x - (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (z - t));
	double t_2 = (y * (z - t)) / a;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -5e+91) {
		tmp = t_2;
	} else if (t_2 <= 1e+247) {
		tmp = x - (t / (a / y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / (z - t))
	t_2 = (y * (z - t)) / a
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -5e+91:
		tmp = t_2
	elif t_2 <= 1e+247:
		tmp = x - (t / (a / y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / Float64(z - t)))
	t_2 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -5e+91)
		tmp = t_2;
	elseif (t_2 <= 1e+247)
		tmp = Float64(x - Float64(t / Float64(a / y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / (z - t));
	t_2 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -5e+91)
		tmp = t_2;
	elseif (t_2 <= 1e+247)
		tmp = x - (t / (a / y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -5e+91], t$95$2, If[LessEqual[t$95$2, 1e+247], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -inf.0 or 9.99999999999999952e246 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 82.9%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in a around 0 82.7%

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

   6. Taylor expanded in a around 0 82.9%

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

      1. associate-*r/ 97.3%

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

      2. *-commutative 97.3%

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

   8. Applied egg-rr 97.3%

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

      1. *-commutative 97.3%

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

      2. clear-num 97.3%

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

      3. un-div-inv 97.4%

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

   10. Applied egg-rr 97.4%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a) < -5.0000000000000002e91

   1. Initial program 99.7%

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

      1. associate-/l* 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in a around 0 96.4%

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

   6. Taylor expanded in a around 0 83.5%

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

   if -5.0000000000000002e91 < (/.f64 (*.f64 y (-.f64 z t)) a) < 9.99999999999999952e246

   1. Initial program 99.7%

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

      1. associate-/l* 92.3%

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

   3. Simplified 92.3%

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

   5. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in z around 0 88.0%

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

      1. associate-*l/ 82.3%

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

      2. *-commutative 82.3%

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

      3. neg-mul-1 82.3%

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

      4. sub-neg 82.3%

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

      5. *-commutative 82.3%

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

      6. associate-*l/ 88.0%

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

      7. associate-*r/ 86.1%

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

   10. Simplified 86.1%

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

       1. clear-num 85.5%

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

       2. un-div-inv 86.4%

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

   12. Applied egg-rr 86.4%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq -5 \cdot 10^{+91}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 10^{+247}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{\frac{a}{z - t}}\\ t_2 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -1 \cdot 10^{+106}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 10^{+247}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (/ a (- z t)))) (t_2 (/ (* y (- z t)) a)))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e+106) t_2 (if (<= t_2 1e+247) (- x (/ (* y t) a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (z - t));
	double t_2 = (y * (z - t)) / a;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e+106) {
		tmp = t_2;
	} else if (t_2 <= 1e+247) {
		tmp = x - ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a / (z - t));
	double t_2 = (y * (z - t)) / a;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e+106) {
		tmp = t_2;
	} else if (t_2 <= 1e+247) {
		tmp = x - ((y * t) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a / (z - t))
	t_2 = (y * (z - t)) / a
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e+106:
		tmp = t_2
	elif t_2 <= 1e+247:
		tmp = x - ((y * t) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a / Float64(z - t)))
	t_2 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e+106)
		tmp = t_2;
	elseif (t_2 <= 1e+247)
		tmp = Float64(x - Float64(Float64(y * t) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a / (z - t));
	t_2 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e+106)
		tmp = t_2;
	elseif (t_2 <= 1e+247)
		tmp = x - ((y * t) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e+106], t$95$2, If[LessEqual[t$95$2, 1e+247], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -inf.0 or 9.99999999999999952e246 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 82.9%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in a around 0 82.7%

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

   6. Taylor expanded in a around 0 82.9%

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

      1. associate-*r/ 97.3%

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

      2. *-commutative 97.3%

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

   8. Applied egg-rr 97.3%

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

      1. *-commutative 97.3%

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

      2. clear-num 97.3%

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

      3. un-div-inv 97.4%

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

   10. Applied egg-rr 97.4%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a) < -1.00000000000000009e106

   1. Initial program 99.6%

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

      1. associate-/l* 67.4%

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

   3. Simplified 67.4%

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

   5. Taylor expanded in a around 0 96.2%

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

   6. Taylor expanded in a around 0 82.9%

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

   if -1.00000000000000009e106 < (/.f64 (*.f64 y (-.f64 z t)) a) < 9.99999999999999952e246

   1. Initial program 99.7%

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

      1. associate-/l* 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in z around 0 88.1%

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

      1. +-commutative 88.1%

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

      2. associate-*r/ 88.1%

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

      3. mul-1-neg 88.1%

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

      4. distribute-lft-neg-out 88.1%

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

      5. *-commutative 88.1%

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

   7. Simplified 88.1%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -\infty:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq -1 \cdot 10^{+106}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 10^{+247}:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-\frac{y}{a}\right)\\ t_2 := z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-272}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* t (- (/ y a)))) (t_2 (* z (/ y a))))
   (if (<= z -3.2e+23)
     t_2
     (if (<= z -1.35e-108)
       t_1
       (if (<= z -6e-272)
         x
         (if (<= z 1.8e-171)
           (* y (/ (- t) a))
           (if (<= z 7.8e-10) x (if (<= z 6.8e+86) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = t * -(y / a);
	double t_2 = z * (y / a);
	double tmp;
	if (z <= -3.2e+23) {
		tmp = t_2;
	} else if (z <= -1.35e-108) {
		tmp = t_1;
	} else if (z <= -6e-272) {
		tmp = x;
	} else if (z <= 1.8e-171) {
		tmp = y * (-t / a);
	} else if (z <= 7.8e-10) {
		tmp = x;
	} else if (z <= 6.8e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * -(y / a)
    t_2 = z * (y / a)
    if (z <= (-3.2d+23)) then
        tmp = t_2
    else if (z <= (-1.35d-108)) then
        tmp = t_1
    else if (z <= (-6d-272)) then
        tmp = x
    else if (z <= 1.8d-171) then
        tmp = y * (-t / a)
    else if (z <= 7.8d-10) then
        tmp = x
    else if (z <= 6.8d+86) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = t * -(y / a);
	double t_2 = z * (y / a);
	double tmp;
	if (z <= -3.2e+23) {
		tmp = t_2;
	} else if (z <= -1.35e-108) {
		tmp = t_1;
	} else if (z <= -6e-272) {
		tmp = x;
	} else if (z <= 1.8e-171) {
		tmp = y * (-t / a);
	} else if (z <= 7.8e-10) {
		tmp = x;
	} else if (z <= 6.8e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = t * -(y / a)
	t_2 = z * (y / a)
	tmp = 0
	if z <= -3.2e+23:
		tmp = t_2
	elif z <= -1.35e-108:
		tmp = t_1
	elif z <= -6e-272:
		tmp = x
	elif z <= 1.8e-171:
		tmp = y * (-t / a)
	elif z <= 7.8e-10:
		tmp = x
	elif z <= 6.8e+86:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(t * Float64(-Float64(y / a)))
	t_2 = Float64(z * Float64(y / a))
	tmp = 0.0
	if (z <= -3.2e+23)
		tmp = t_2;
	elseif (z <= -1.35e-108)
		tmp = t_1;
	elseif (z <= -6e-272)
		tmp = x;
	elseif (z <= 1.8e-171)
		tmp = Float64(y * Float64(Float64(-t) / a));
	elseif (z <= 7.8e-10)
		tmp = x;
	elseif (z <= 6.8e+86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = t * -(y / a);
	t_2 = z * (y / a);
	tmp = 0.0;
	if (z <= -3.2e+23)
		tmp = t_2;
	elseif (z <= -1.35e-108)
		tmp = t_1;
	elseif (z <= -6e-272)
		tmp = x;
	elseif (z <= 1.8e-171)
		tmp = y * (-t / a);
	elseif (z <= 7.8e-10)
		tmp = x;
	elseif (z <= 6.8e+86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(t * (-N[(y / a), $MachinePrecision])), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+23], t$95$2, If[LessEqual[z, -1.35e-108], t$95$1, If[LessEqual[z, -6e-272], x, If[LessEqual[z, 1.8e-171], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e-10], x, If[LessEqual[z, 6.8e+86], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.2e23 or 6.7999999999999995e86 < z

   1. Initial program 91.5%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in a around 0 84.9%

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

   6. Taylor expanded in z around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. associate-/l* 62.3%

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

   8. Applied egg-rr 62.3%

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

   if -3.2e23 < z < -1.35000000000000002e-108 or 7.7999999999999999e-10 < z < 6.7999999999999995e86

   1. Initial program 92.4%

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

      1. associate-/l* 90.4%

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

   3. Simplified 90.4%

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

   5. Taylor expanded in y around 0 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*r/ 97.2%

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

   7. Simplified 97.2%

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

   8. Taylor expanded in z around 0 71.6%

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

      1. associate-*l/ 69.6%

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

      2. *-commutative 69.6%

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

      3. neg-mul-1 69.6%

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

      4. sub-neg 69.6%

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

      5. *-commutative 69.6%

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

      6. associate-*l/ 71.6%

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

      7. associate-*r/ 81.8%

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

   10. Simplified 81.8%

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

   11. Taylor expanded in x around 0 49.8%

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

       1. associate-*r/ 49.8%

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

       2. neg-mul-1 49.8%

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

       3. distribute-rgt-neg-in 49.8%

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

       4. associate-/l* 60.0%

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

   13. Simplified 60.0%

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

   if -1.35000000000000002e-108 < z < -6.0000000000000006e-272 or 1.80000000000000002e-171 < z < 7.7999999999999999e-10

   1. Initial program 94.5%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf 56.7%

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

   if -6.0000000000000006e-272 < z < 1.80000000000000002e-171

   1. Initial program 95.4%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in a around 0 79.1%

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

   6. Taylor expanded in t around inf 59.2%

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

      1. mul-1-neg 59.2%

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

      2. *-commutative 59.2%

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

      3. distribute-rgt-neg-in 59.2%

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

   8. Simplified 59.2%

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

      1. frac-2neg 59.2%

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

      2. distribute-frac-neg 59.2%

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

      3. add-sqr-sqrt 20.4%

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

      4. sqrt-unprod 16.3%

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

      5. sqr-neg 16.3%

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

      6. sqrt-unprod 0.9%

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

      7. add-sqr-sqrt 1.3%

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

      8. remove-double-neg 1.3%

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

      9. distribute-rgt-neg-out 1.3%

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

      10. frac-2neg 1.3%

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

      11. associate-/l* 1.3%

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

      12. add-sqr-sqrt 0.5%

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

      13. sqrt-unprod 35.3%

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

      14. sqr-neg 35.3%

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

      15. sqrt-unprod 43.0%

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

      16. add-sqr-sqrt 63.5%

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

   10. Applied egg-rr 63.5%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+23}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-272}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(-\frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-t}{a}\\ t_2 := z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{-21}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- t) a))) (t_2 (* z (/ y a))))
   (if (<= z -1.16e-21)
     t_2
     (if (<= z -1.55e-108)
       t_1
       (if (<= z -2.5e-271)
         x
         (if (<= z 6.2e-171) t_1 (if (<= z 4.6e-10) x t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-t / a);
	double t_2 = z * (y / a);
	double tmp;
	if (z <= -1.16e-21) {
		tmp = t_2;
	} else if (z <= -1.55e-108) {
		tmp = t_1;
	} else if (z <= -2.5e-271) {
		tmp = x;
	} else if (z <= 6.2e-171) {
		tmp = t_1;
	} else if (z <= 4.6e-10) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (-t / a)
    t_2 = z * (y / a)
    if (z <= (-1.16d-21)) then
        tmp = t_2
    else if (z <= (-1.55d-108)) then
        tmp = t_1
    else if (z <= (-2.5d-271)) then
        tmp = x
    else if (z <= 6.2d-171) then
        tmp = t_1
    else if (z <= 4.6d-10) then
        tmp = x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (-t / a);
	double t_2 = z * (y / a);
	double tmp;
	if (z <= -1.16e-21) {
		tmp = t_2;
	} else if (z <= -1.55e-108) {
		tmp = t_1;
	} else if (z <= -2.5e-271) {
		tmp = x;
	} else if (z <= 6.2e-171) {
		tmp = t_1;
	} else if (z <= 4.6e-10) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (-t / a)
	t_2 = z * (y / a)
	tmp = 0
	if z <= -1.16e-21:
		tmp = t_2
	elif z <= -1.55e-108:
		tmp = t_1
	elif z <= -2.5e-271:
		tmp = x
	elif z <= 6.2e-171:
		tmp = t_1
	elif z <= 4.6e-10:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(-t) / a))
	t_2 = Float64(z * Float64(y / a))
	tmp = 0.0
	if (z <= -1.16e-21)
		tmp = t_2;
	elseif (z <= -1.55e-108)
		tmp = t_1;
	elseif (z <= -2.5e-271)
		tmp = x;
	elseif (z <= 6.2e-171)
		tmp = t_1;
	elseif (z <= 4.6e-10)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (-t / a);
	t_2 = z * (y / a);
	tmp = 0.0;
	if (z <= -1.16e-21)
		tmp = t_2;
	elseif (z <= -1.55e-108)
		tmp = t_1;
	elseif (z <= -2.5e-271)
		tmp = x;
	elseif (z <= 6.2e-171)
		tmp = t_1;
	elseif (z <= 4.6e-10)
		tmp = x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.16e-21], t$95$2, If[LessEqual[z, -1.55e-108], t$95$1, If[LessEqual[z, -2.5e-271], x, If[LessEqual[z, 6.2e-171], t$95$1, If[LessEqual[z, 4.6e-10], x, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1600000000000001e-21 or 4.60000000000000014e-10 < z

   1. Initial program 91.0%

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

      1. associate-/l* 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in a around 0 84.2%

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

   6. Taylor expanded in z around inf 53.7%

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

      1. *-commutative 53.7%

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

      2. associate-/l* 57.6%

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

   8. Applied egg-rr 57.6%

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

   if -1.1600000000000001e-21 < z < -1.55000000000000007e-108 or -2.5000000000000001e-271 < z < 6.2000000000000001e-171

   1. Initial program 95.7%

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

      1. associate-/l* 96.9%

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

   3. Simplified 96.9%

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

   5. Taylor expanded in a around 0 84.0%

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

   6. Taylor expanded in t around inf 59.7%

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

      1. mul-1-neg 59.7%

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

      2. *-commutative 59.7%

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

      3. distribute-rgt-neg-in 59.7%

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

   8. Simplified 59.7%

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

      1. frac-2neg 59.7%

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

      2. distribute-frac-neg 59.7%

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

      3. add-sqr-sqrt 19.3%

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

      4. sqrt-unprod 13.8%

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

      5. sqr-neg 13.8%

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

      6. sqrt-unprod 0.8%

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

      7. add-sqr-sqrt 1.4%

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

      8. remove-double-neg 1.4%

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

      9. distribute-rgt-neg-out 1.4%

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

      10. frac-2neg 1.4%

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

      11. associate-/l* 1.4%

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

      12. add-sqr-sqrt 0.7%

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

      13. sqrt-unprod 32.4%

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

      14. sqr-neg 32.4%

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

      15. sqrt-unprod 40.0%

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

      16. add-sqr-sqrt 60.9%

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

   10. Applied egg-rr 60.9%

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

   if -1.55000000000000007e-108 < z < -2.5000000000000001e-271 or 6.2000000000000001e-171 < z < 4.60000000000000014e-10

   1. Initial program 94.5%

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

      1. associate-/l* 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf 56.7%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{-21}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-108}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-271}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-171}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - t \cdot \frac{y}{a}\\ t_2 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-73}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* t (/ y a)))) (t_2 (+ x (* z (/ y a)))))
   (if (<= z -4.8e+23)
     t_2
     (if (<= z -5.5e-73)
       t_1
       (if (<= z 6e-16) (- x (* y (/ t a))) (if (<= z 3.8e+86) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / a));
	double t_2 = x + (z * (y / a));
	double tmp;
	if (z <= -4.8e+23) {
		tmp = t_2;
	} else if (z <= -5.5e-73) {
		tmp = t_1;
	} else if (z <= 6e-16) {
		tmp = x - (y * (t / a));
	} else if (z <= 3.8e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - (t * (y / a))
    t_2 = x + (z * (y / a))
    if (z <= (-4.8d+23)) then
        tmp = t_2
    else if (z <= (-5.5d-73)) then
        tmp = t_1
    else if (z <= 6d-16) then
        tmp = x - (y * (t / a))
    else if (z <= 3.8d+86) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (t * (y / a));
	double t_2 = x + (z * (y / a));
	double tmp;
	if (z <= -4.8e+23) {
		tmp = t_2;
	} else if (z <= -5.5e-73) {
		tmp = t_1;
	} else if (z <= 6e-16) {
		tmp = x - (y * (t / a));
	} else if (z <= 3.8e+86) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - (t * (y / a))
	t_2 = x + (z * (y / a))
	tmp = 0
	if z <= -4.8e+23:
		tmp = t_2
	elif z <= -5.5e-73:
		tmp = t_1
	elif z <= 6e-16:
		tmp = x - (y * (t / a))
	elif z <= 3.8e+86:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(t * Float64(y / a)))
	t_2 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (z <= -4.8e+23)
		tmp = t_2;
	elseif (z <= -5.5e-73)
		tmp = t_1;
	elseif (z <= 6e-16)
		tmp = Float64(x - Float64(y * Float64(t / a)));
	elseif (z <= 3.8e+86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - (t * (y / a));
	t_2 = x + (z * (y / a));
	tmp = 0.0;
	if (z <= -4.8e+23)
		tmp = t_2;
	elseif (z <= -5.5e-73)
		tmp = t_1;
	elseif (z <= 6e-16)
		tmp = x - (y * (t / a));
	elseif (z <= 3.8e+86)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+23], t$95$2, If[LessEqual[z, -5.5e-73], t$95$1, If[LessEqual[z, 6e-16], N[(x - N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+86], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8e23 or 3.79999999999999978e86 < z

   1. Initial program 91.5%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in y around 0 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*r/ 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in z around inf 84.9%

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

      1. associate-*l/ 90.5%

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

      2. *-commutative 90.5%

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

   10. Simplified 90.5%

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

   if -4.8e23 < z < -5.50000000000000006e-73 or 5.99999999999999987e-16 < z < 3.79999999999999978e86

   1. Initial program 93.1%

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

      1. associate-/l* 88.6%

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

   3. Simplified 88.6%

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

   5. Taylor expanded in y around 0 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*r/ 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in z around 0 70.4%

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

      1. associate-*l/ 65.8%

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

      2. *-commutative 65.8%

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

      3. neg-mul-1 65.8%

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

      4. sub-neg 65.8%

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

      5. *-commutative 65.8%

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

      6. associate-*l/ 70.4%

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

      7. associate-*r/ 82.6%

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

   10. Simplified 82.6%

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

   if -5.50000000000000006e-73 < z < 5.99999999999999987e-16

   1. Initial program 94.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 z around 0 88.5%

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

      1. mul-1-neg 88.5%

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

      2. unsub-neg 88.5%

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

      3. *-commutative 88.5%

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

      4. associate-/l* 93.4%

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

   7. Simplified 93.4%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-73}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-16}:\\ \;\;\;\;x - y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+86}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 93.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-164} \lor \neg \left(a \leq 2 \cdot 10^{-132}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.3e-164) (not (<= a 2e-132)))
   (+ x (* y (/ (- z t) a)))
   (/ (* y (- z t)) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e-164) || !(a <= 2e-132)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = (y * (z - t)) / a;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-1.3d-164)) .or. (.not. (a <= 2d-132))) then
        tmp = x + (y * ((z - t) / a))
    else
        tmp = (y * (z - t)) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.3e-164) || !(a <= 2e-132)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = (y * (z - t)) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.3e-164) or not (a <= 2e-132):
		tmp = x + (y * ((z - t) / a))
	else:
		tmp = (y * (z - t)) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.3e-164) || !(a <= 2e-132))
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(Float64(y * Float64(z - t)) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.3e-164) || ~((a <= 2e-132)))
		tmp = x + (y * ((z - t) / a));
	else
		tmp = (y * (z - t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.3e-164], N[Not[LessEqual[a, 2e-132]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.3000000000000001e-164 or 2e-132 < a

   1. Initial program 90.5%

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

      1. associate-/l* 96.8%

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

   3. Simplified 96.8%

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

   if -1.3000000000000001e-164 < a < 2e-132

   1. Initial program 99.6%

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

      1. associate-/l* 80.7%

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

   3. Simplified 80.7%

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

   5. Taylor expanded in a around 0 99.6%

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

   6. Taylor expanded in a around 0 94.5%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-164} \lor \neg \left(a \leq 2 \cdot 10^{-132}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-35} \lor \neg \left(y \leq 2.9 \cdot 10^{-145}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.2e-35) (not (<= y 2.9e-145))) (* y (/ (- z t) a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.2e-35) || !(y <= 2.9e-145)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-6.2d-35)) .or. (.not. (y <= 2.9d-145))) then
        tmp = y * ((z - t) / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.2e-35) || !(y <= 2.9e-145)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.2e-35) or not (y <= 2.9e-145):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.2e-35) || !(y <= 2.9e-145))
		tmp = Float64(y * Float64(Float64(z - t) / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.2e-35) || ~((y <= 2.9e-145)))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.2e-35], N[Not[LessEqual[y, 2.9e-145]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000024e-35 or 2.89999999999999984e-145 < y

   1. Initial program 89.5%

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

      1. associate-/l* 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in a around 0 85.1%

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

   6. Taylor expanded in a around 0 71.2%

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

      1. associate-*r/ 78.3%

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

      2. *-commutative 78.3%

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

   8. Applied egg-rr 78.3%

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

   if -6.20000000000000024e-35 < y < 2.89999999999999984e-145

   1. Initial program 99.6%

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

      1. associate-/l* 82.4%

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

   3. Simplified 82.4%

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

   5. Taylor expanded in x around inf 63.2%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-35} \lor \neg \left(y \leq 2.9 \cdot 10^{-145}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -10500000 \lor \neg \left(y \leq 2 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -10500000.0) (not (<= y 2e+22)))
   (* y (/ (- z t) a))
   (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -10500000.0) || !(y <= 2e+22)) {
		tmp = y * ((z - t) / 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 ((y <= (-10500000.0d0)) .or. (.not. (y <= 2d+22))) then
        tmp = y * ((z - t) / 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 ((y <= -10500000.0) || !(y <= 2e+22)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -10500000.0) or not (y <= 2e+22):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -10500000.0) || !(y <= 2e+22))
		tmp = Float64(y * Float64(Float64(z - t) / 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 ((y <= -10500000.0) || ~((y <= 2e+22)))
		tmp = y * ((z - t) / a);
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -10500000.0], N[Not[LessEqual[y, 2e+22]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e7 or 2e22 < y

   1. Initial program 86.9%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around 0 83.4%

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

   6. Taylor expanded in a around 0 73.1%

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

      1. associate-*r/ 84.0%

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

      2. *-commutative 84.0%

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

   8. Applied egg-rr 84.0%

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

   if -1.05e7 < y < 2e22

   1. Initial program 99.7%

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

      1. associate-/l* 85.0%

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

   3. Simplified 85.0%

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

   5. Taylor expanded in y around 0 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*r/ 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in z around inf 79.1%

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

      1. associate-*l/ 78.4%

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

      2. *-commutative 78.4%

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

   10. Simplified 78.4%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -10500000 \lor \neg \left(y \leq 2 \cdot 10^{+22}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1700000 \lor \neg \left(y \leq 2.7 \cdot 10^{+21}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1700000.0) (not (<= y 2.7e+21)))
   (* y (/ (- z t) a))
   (+ x (/ (* y z) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1700000.0) || !(y <= 2.7e+21)) {
		tmp = y * ((z - t) / 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 ((y <= (-1700000.0d0)) .or. (.not. (y <= 2.7d+21))) then
        tmp = y * ((z - t) / 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 ((y <= -1700000.0) || !(y <= 2.7e+21)) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1700000.0) or not (y <= 2.7e+21):
		tmp = y * ((z - t) / a)
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1700000.0) || !(y <= 2.7e+21))
		tmp = Float64(y * Float64(Float64(z - t) / 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 ((y <= -1700000.0) || ~((y <= 2.7e+21)))
		tmp = y * ((z - t) / a);
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1700000.0], N[Not[LessEqual[y, 2.7e+21]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e6 or 2.7e21 < y

   1. Initial program 87.0%

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

      1. associate-/l* 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in a around 0 83.5%

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

   6. Taylor expanded in a around 0 73.3%

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

      1. associate-*r/ 84.1%

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

      2. *-commutative 84.1%

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

   8. Applied egg-rr 84.1%

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

   if -1.7e6 < y < 2.7e21

   1. Initial program 99.7%

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

      1. associate-/l* 84.9%

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

   3. Simplified 84.9%

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

   5. Taylor expanded in z around inf 79.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1700000 \lor \neg \left(y \leq 2.7 \cdot 10^{+21}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+24} \lor \neg \left(z \leq 3 \cdot 10^{+86}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.15e+24) (not (<= z 3e+86)))
   (+ x (* z (/ y a)))
   (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+24) || !(z <= 3e+86)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-1.15d+24)) .or. (.not. (z <= 3d+86))) then
        tmp = x + (z * (y / a))
    else
        tmp = x - (t * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.15e+24) || !(z <= 3e+86)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -1.15e+24) or not (z <= 3e+86):
		tmp = x + (z * (y / a))
	else:
		tmp = x - (t * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.15e+24) || !(z <= 3e+86))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -1.15e+24) || ~((z <= 3e+86)))
		tmp = x + (z * (y / a));
	else
		tmp = x - (t * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.15e+24], N[Not[LessEqual[z, 3e+86]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.15e24 or 2.99999999999999977e86 < z

   1. Initial program 91.5%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in y around 0 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*r/ 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in z around inf 84.9%

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

      1. associate-*l/ 90.5%

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

      2. *-commutative 90.5%

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

   10. Simplified 90.5%

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

   if -1.15e24 < z < 2.99999999999999977e86

   1. Initial program 94.0%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around 0 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*r/ 95.7%

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

   7. Simplified 95.7%

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

   8. Taylor expanded in z around 0 83.2%

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

      1. associate-*l/ 85.3%

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

      2. *-commutative 85.3%

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

      3. neg-mul-1 85.3%

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

      4. sub-neg 85.3%

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

      5. *-commutative 85.3%

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

      6. associate-*l/ 83.2%

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

      7. associate-*r/ 87.3%

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

   10. Simplified 87.3%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+24} \lor \neg \left(z \leq 3 \cdot 10^{+86}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+23} \lor \neg \left(z \leq 3.9 \cdot 10^{+87}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -9.5e+23) (not (<= z 3.9e+87)))
   (+ x (* z (/ y a)))
   (- x (/ t (/ a y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+23) || !(z <= 3.9e+87)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t / (a / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-9.5d+23)) .or. (.not. (z <= 3.9d+87))) then
        tmp = x + (z * (y / a))
    else
        tmp = x - (t / (a / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -9.5e+23) || !(z <= 3.9e+87)) {
		tmp = x + (z * (y / a));
	} else {
		tmp = x - (t / (a / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -9.5e+23) or not (z <= 3.9e+87):
		tmp = x + (z * (y / a))
	else:
		tmp = x - (t / (a / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -9.5e+23) || !(z <= 3.9e+87))
		tmp = Float64(x + Float64(z * Float64(y / a)));
	else
		tmp = Float64(x - Float64(t / Float64(a / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -9.5e+23) || ~((z <= 3.9e+87)))
		tmp = x + (z * (y / a));
	else
		tmp = x - (t / (a / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -9.5e+23], N[Not[LessEqual[z, 3.9e+87]], $MachinePrecision]], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.50000000000000038e23 or 3.9000000000000002e87 < z

   1. Initial program 91.5%

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

      1. associate-/l* 88.1%

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

   3. Simplified 88.1%

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

   5. Taylor expanded in y around 0 91.5%

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

      1. *-commutative 91.5%

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

      2. associate-*r/ 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in z around inf 84.9%

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

      1. associate-*l/ 90.5%

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

      2. *-commutative 90.5%

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

   10. Simplified 90.5%

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

   if -9.50000000000000038e23 < z < 3.9000000000000002e87

   1. Initial program 94.0%

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

      1. associate-/l* 96.0%

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

   3. Simplified 96.0%

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

   5. Taylor expanded in y around 0 94.0%

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

      1. *-commutative 94.0%

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

      2. associate-*r/ 95.7%

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

   7. Simplified 95.7%

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

   8. Taylor expanded in z around 0 83.2%

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

      1. associate-*l/ 85.3%

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

      2. *-commutative 85.3%

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

      3. neg-mul-1 85.3%

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

      4. sub-neg 85.3%

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

      5. *-commutative 85.3%

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

      6. associate-*l/ 83.2%

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

      7. associate-*r/ 87.3%

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

   10. Simplified 87.3%

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

       1. clear-num 86.8%

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

       2. un-div-inv 87.5%

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

   12. Applied egg-rr 87.5%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+23} \lor \neg \left(z \leq 3.9 \cdot 10^{+87}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t}{\frac{a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 52.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.9e-44) x (if (<= a 9.8e-5) (* z (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e-44) {
		tmp = x;
	} else if (a <= 9.8e-5) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.9d-44)) then
        tmp = x
    else if (a <= 9.8d-5) then
        tmp = z * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.9e-44) {
		tmp = x;
	} else if (a <= 9.8e-5) {
		tmp = z * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.9e-44:
		tmp = x
	elif a <= 9.8e-5:
		tmp = z * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.9e-44)
		tmp = x;
	elseif (a <= 9.8e-5)
		tmp = Float64(z * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.9e-44)
		tmp = x;
	elseif (a <= 9.8e-5)
		tmp = z * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.9e-44], x, If[LessEqual[a, 9.8e-5], N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if a < -3.9000000000000002e-44 or 9.8e-5 < a

   1. Initial program 85.8%

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

      1. associate-/l* 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in x around inf 55.1%

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

   if -3.9000000000000002e-44 < a < 9.8e-5

   1. Initial program 99.7%

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

      1. associate-/l* 86.3%

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

   3. Simplified 86.3%

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

   5. Taylor expanded in a around 0 99.7%

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

   6. Taylor expanded in z around inf 51.7%

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

      1. *-commutative 51.7%

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

      2. associate-/l* 52.6%

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

   8. Applied egg-rr 52.6%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.9 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.8 \cdot 10^{-5}:\\ \;\;\;\;z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 97.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-44}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1e-44) (+ 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 <= -1e-44) {
		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 <= (-1d-44)) 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 <= -1e-44) {
		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 <= -1e-44:
		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 <= -1e-44)
		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 <= -1e-44)
		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, -1e-44], 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 < -9.99999999999999953e-45

   1. Initial program 87.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

   if -9.99999999999999953e-45 < y

   1. Initial program 95.1%

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

      1. associate-/l* 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in y around 0 95.1%

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

      1. *-commutative 95.1%

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

      2. associate-*r/ 98.6%

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

   7. Simplified 98.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-44}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 39.5% 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* 92.5%

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

3. Simplified 92.5%

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

5. Taylor expanded in x around inf 35.6%

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

6. Final simplification 35.6%

   \[\leadsto x \]
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 2024057 
(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)))