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

Percentage Accurate: 93.1% → 97.2%

Time: 10.5s

Alternatives: 12

Speedup: 1.0×

• 25.2% 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: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 1.0× speedup

Math

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

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-*r/ 91.2%

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

3. Simplified 91.2%

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

   1. *-commutative 91.2%

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

   2. associate-*l/ 92.9%

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

   3. associate-/l* 98.4%

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

5. Applied egg-rr 98.4%

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

6. Final simplification 98.4%

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

Alternative 2: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{t}{a}\\ t_2 := z \cdot \frac{y}{-a}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+291}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ t a)))) (t_2 (* z (/ y (- a)))))
   (if (<= z -1.2e+150)
     t_2
     (if (<= z 1.25e+71)
       t_1
       (if (<= z 9e+132)
         t_2
         (if (<= z 2.4e+180)
           t_1
           (if (<= z 4.4e+291) (* y (/ z (- a))) t_2)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y * (t / a));
	double t_2 = z * (y / -a);
	double tmp;
	if (z <= -1.2e+150) {
		tmp = t_2;
	} else if (z <= 1.25e+71) {
		tmp = t_1;
	} else if (z <= 9e+132) {
		tmp = t_2;
	} else if (z <= 2.4e+180) {
		tmp = t_1;
	} else if (z <= 4.4e+291) {
		tmp = y * (z / -a);
	} 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 + (y * (t / a))
    t_2 = z * (y / -a)
    if (z <= (-1.2d+150)) then
        tmp = t_2
    else if (z <= 1.25d+71) then
        tmp = t_1
    else if (z <= 9d+132) then
        tmp = t_2
    else if (z <= 2.4d+180) then
        tmp = t_1
    else if (z <= 4.4d+291) then
        tmp = y * (z / -a)
    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 + (y * (t / a));
	double t_2 = z * (y / -a);
	double tmp;
	if (z <= -1.2e+150) {
		tmp = t_2;
	} else if (z <= 1.25e+71) {
		tmp = t_1;
	} else if (z <= 9e+132) {
		tmp = t_2;
	} else if (z <= 2.4e+180) {
		tmp = t_1;
	} else if (z <= 4.4e+291) {
		tmp = y * (z / -a);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y * (t / a))
	t_2 = z * (y / -a)
	tmp = 0
	if z <= -1.2e+150:
		tmp = t_2
	elif z <= 1.25e+71:
		tmp = t_1
	elif z <= 9e+132:
		tmp = t_2
	elif z <= 2.4e+180:
		tmp = t_1
	elif z <= 4.4e+291:
		tmp = y * (z / -a)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y * Float64(t / a)))
	t_2 = Float64(z * Float64(y / Float64(-a)))
	tmp = 0.0
	if (z <= -1.2e+150)
		tmp = t_2;
	elseif (z <= 1.25e+71)
		tmp = t_1;
	elseif (z <= 9e+132)
		tmp = t_2;
	elseif (z <= 2.4e+180)
		tmp = t_1;
	elseif (z <= 4.4e+291)
		tmp = Float64(y * Float64(z / Float64(-a)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y * (t / a));
	t_2 = z * (y / -a);
	tmp = 0.0;
	if (z <= -1.2e+150)
		tmp = t_2;
	elseif (z <= 1.25e+71)
		tmp = t_1;
	elseif (z <= 9e+132)
		tmp = t_2;
	elseif (z <= 2.4e+180)
		tmp = t_1;
	elseif (z <= 4.4e+291)
		tmp = y * (z / -a);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e+150], t$95$2, If[LessEqual[z, 1.25e+71], t$95$1, If[LessEqual[z, 9e+132], t$95$2, If[LessEqual[z, 2.4e+180], t$95$1, If[LessEqual[z, 4.4e+291], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.20000000000000001e150 or 1.24999999999999993e71 < z < 8.99999999999999944e132 or 4.3999999999999999e291 < z

   1. Initial program 89.5%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. associate-*l/ 71.8%

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

      3. *-commutative 71.8%

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

      4. distribute-rgt-neg-in 71.8%

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

      5. distribute-frac-neg 71.8%

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

      6. *-lft-identity 71.8%

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

      7. metadata-eval 71.8%

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

      8. times-frac 71.8%

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

      9. neg-mul-1 71.8%

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

      10. remove-double-neg 71.8%

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

      11. neg-mul-1 71.8%

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

   6. Simplified 71.8%

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

   if -1.20000000000000001e150 < z < 1.24999999999999993e71 or 8.99999999999999944e132 < z < 2.3999999999999998e180

   1. Initial program 94.3%

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

      1. associate-*r/ 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around 0 83.2%

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

      1. sub-neg 83.2%

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

      2. mul-1-neg 83.2%

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

      3. remove-double-neg 83.2%

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

      4. +-commutative 83.2%

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

      5. *-commutative 83.2%

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

      6. associate-/l* 87.6%

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

      7. associate-/r/ 82.9%

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

   6. Simplified 82.9%

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

   if 2.3999999999999998e180 < z < 4.3999999999999999e291

   1. Initial program 86.6%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*l/ 86.6%

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

      3. associate-/l* 93.1%

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

   5. Applied egg-rr 93.1%

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

   6. Taylor expanded in z around inf 59.0%

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

      1. associate-*r/ 59.0%

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

      2. *-commutative 59.0%

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

      3. neg-mul-1 59.0%

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

      4. distribute-rgt-neg-out 59.0%

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

      5. associate-/l* 65.3%

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

      6. remove-double-neg 65.3%

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

      7. distribute-frac-neg 65.3%

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

      8. neg-mul-1 65.3%

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

      9. neg-mul-1 65.3%

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

      10. times-frac 65.3%

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

      11. metadata-eval 65.3%

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

      12. *-commutative 65.3%

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

      13. *-rgt-identity 65.3%

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

      14. distribute-frac-neg 65.3%

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

      15. associate-/r/ 72.2%

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

      16. *-commutative 72.2%

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

   8. Simplified 72.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+150}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+71}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+132}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{+180}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+291}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]

Alternative 3: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{y}{-a}\\ \mathbf{if}\;z \leq -5 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+71}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+179}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+278}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* z (/ y (- a)))))
   (if (<= z -5e+157)
     t_1
     (if (<= z 1.35e+71)
       (+ x (/ (* t y) a))
       (if (<= z 1.56e+131)
         t_1
         (if (<= z 7.4e+179)
           (+ x (* y (/ t a)))
           (if (<= z 1.35e+278) (* y (/ z (- a))) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (z <= -5e+157) {
		tmp = t_1;
	} else if (z <= 1.35e+71) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.56e+131) {
		tmp = t_1;
	} else if (z <= 7.4e+179) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.35e+278) {
		tmp = y * (z / -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (y / -a)
    if (z <= (-5d+157)) then
        tmp = t_1
    else if (z <= 1.35d+71) then
        tmp = x + ((t * y) / a)
    else if (z <= 1.56d+131) then
        tmp = t_1
    else if (z <= 7.4d+179) then
        tmp = x + (y * (t / a))
    else if (z <= 1.35d+278) then
        tmp = y * (z / -a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z * (y / -a);
	double tmp;
	if (z <= -5e+157) {
		tmp = t_1;
	} else if (z <= 1.35e+71) {
		tmp = x + ((t * y) / a);
	} else if (z <= 1.56e+131) {
		tmp = t_1;
	} else if (z <= 7.4e+179) {
		tmp = x + (y * (t / a));
	} else if (z <= 1.35e+278) {
		tmp = y * (z / -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z * (y / -a)
	tmp = 0
	if z <= -5e+157:
		tmp = t_1
	elif z <= 1.35e+71:
		tmp = x + ((t * y) / a)
	elif z <= 1.56e+131:
		tmp = t_1
	elif z <= 7.4e+179:
		tmp = x + (y * (t / a))
	elif z <= 1.35e+278:
		tmp = y * (z / -a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z * Float64(y / Float64(-a)))
	tmp = 0.0
	if (z <= -5e+157)
		tmp = t_1;
	elseif (z <= 1.35e+71)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (z <= 1.56e+131)
		tmp = t_1;
	elseif (z <= 7.4e+179)
		tmp = Float64(x + Float64(y * Float64(t / a)));
	elseif (z <= 1.35e+278)
		tmp = Float64(y * Float64(z / Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z * (y / -a);
	tmp = 0.0;
	if (z <= -5e+157)
		tmp = t_1;
	elseif (z <= 1.35e+71)
		tmp = x + ((t * y) / a);
	elseif (z <= 1.56e+131)
		tmp = t_1;
	elseif (z <= 7.4e+179)
		tmp = x + (y * (t / a));
	elseif (z <= 1.35e+278)
		tmp = y * (z / -a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5e+157], t$95$1, If[LessEqual[z, 1.35e+71], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.56e+131], t$95$1, If[LessEqual[z, 7.4e+179], N[(x + N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+278], N[(y * N[(z / (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.99999999999999976e157 or 1.34999999999999998e71 < z < 1.5600000000000001e131 or 1.35000000000000005e278 < z

   1. Initial program 89.5%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. associate-*l/ 71.8%

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

      3. *-commutative 71.8%

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

      4. distribute-rgt-neg-in 71.8%

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

      5. distribute-frac-neg 71.8%

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

      6. *-lft-identity 71.8%

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

      7. metadata-eval 71.8%

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

      8. times-frac 71.8%

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

      9. neg-mul-1 71.8%

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

      10. remove-double-neg 71.8%

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

      11. neg-mul-1 71.8%

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

   6. Simplified 71.8%

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

   if -4.99999999999999976e157 < z < 1.34999999999999998e71

   1. Initial program 94.1%

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

      1. associate-*r/ 93.8%

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

   3. Simplified 93.8%

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

   4. Taylor expanded in z around 0 83.4%

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

      1. sub-neg 83.4%

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

      2. mul-1-neg 83.4%

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

      3. remove-double-neg 83.4%

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

      4. +-commutative 83.4%

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

      5. *-commutative 83.4%

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

      6. associate-/l* 88.1%

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

      7. associate-/r/ 83.2%

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

   6. Simplified 83.2%

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

      1. associate-*l/ 83.4%

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

   8. Applied egg-rr 83.4%

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

   if 1.5600000000000001e131 < z < 7.3999999999999999e179

   1. Initial program 100.0%

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

      1. associate-*r/ 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in z around 0 78.3%

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

      1. sub-neg 78.3%

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

      2. mul-1-neg 78.3%

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

      3. remove-double-neg 78.3%

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

      4. +-commutative 78.3%

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

      5. *-commutative 78.3%

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

      6. associate-/l* 78.3%

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

      7. associate-/r/ 78.3%

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

   6. Simplified 78.3%

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

   if 7.3999999999999999e179 < z < 1.35000000000000005e278

   1. Initial program 86.6%

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

      1. associate-*r/ 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. Step-by-step derivation

      1. *-commutative 99.8%

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

      2. associate-*l/ 86.6%

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

      3. associate-/l* 93.1%

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

   5. Applied egg-rr 93.1%

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

   6. Taylor expanded in z around inf 59.0%

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

      1. associate-*r/ 59.0%

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

      2. *-commutative 59.0%

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

      3. neg-mul-1 59.0%

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

      4. distribute-rgt-neg-out 59.0%

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

      5. associate-/l* 65.3%

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

      6. remove-double-neg 65.3%

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

      7. distribute-frac-neg 65.3%

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

      8. neg-mul-1 65.3%

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

      9. neg-mul-1 65.3%

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

      10. times-frac 65.3%

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

      11. metadata-eval 65.3%

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

      12. *-commutative 65.3%

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

      13. *-rgt-identity 65.3%

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

      14. distribute-frac-neg 65.3%

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

      15. associate-/r/ 72.2%

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

      16. *-commutative 72.2%

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

   8. Simplified 72.2%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+157}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+71}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;z \leq 1.56 \cdot 10^{+131}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{+179}:\\ \;\;\;\;x + y \cdot \frac{t}{a}\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+278}:\\ \;\;\;\;y \cdot \frac{z}{-a}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \end{array} \]

Alternative 4: 92.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-138} \lor \neg \left(y \leq 1.05 \cdot 10^{-85}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.2e-138) (not (<= y 1.05e-85)))
   (- x (* 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 <= -2.2e-138) || !(y <= 1.05e-85)) {
		tmp = x - (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 <= (-2.2d-138)) .or. (.not. (y <= 1.05d-85))) then
        tmp = x - (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 <= -2.2e-138) || !(y <= 1.05e-85)) {
		tmp = x - (y * ((z - t) / a));
	} else {
		tmp = x - ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.2e-138) or not (y <= 1.05e-85):
		tmp = x - (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 <= -2.2e-138) || !(y <= 1.05e-85))
		tmp = Float64(x - Float64(y * Float64(Float64(z - t) / a)));
	else
		tmp = Float64(x - Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -2.2e-138) || ~((y <= 1.05e-85)))
		tmp = x - (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, -2.2e-138], N[Not[LessEqual[y, 1.05e-85]], $MachinePrecision]], N[(x - N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1999999999999999e-138 or 1.05e-85 < y

   1. Initial program 89.3%

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

      1. associate-*r/ 97.4%

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

   3. Simplified 97.4%

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

   if -2.1999999999999999e-138 < y < 1.05e-85

   1. Initial program 99.9%

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

      1. associate-*r/ 79.0%

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

   3. Simplified 79.0%

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

   4. Taylor expanded in z around inf 91.0%

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

4. Final simplification 95.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-138} \lor \neg \left(y \leq 1.05 \cdot 10^{-85}\right):\\ \;\;\;\;x - y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot y}{a}\\ \end{array} \]

Alternative 5: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+17} \lor \neg \left(z \leq 2.4 \cdot 10^{+41}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -4e+17) (not (<= z 2.4e+41)))
   (- 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 <= -4e+17) || !(z <= 2.4e+41)) {
		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 <= (-4d+17)) .or. (.not. (z <= 2.4d+41))) 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 <= -4e+17) || !(z <= 2.4e+41)) {
		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 <= -4e+17) or not (z <= 2.4e+41):
		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 <= -4e+17) || !(z <= 2.4e+41))
		tmp = Float64(x - Float64(z * Float64(y / a)));
	else
		tmp = Float64(x + Float64(Float64(t * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -4e+17) || ~((z <= 2.4e+41)))
		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, -4e+17], N[Not[LessEqual[z, 2.4e+41]], $MachinePrecision]], N[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4e17 or 2.4000000000000002e41 < z

   1. Initial program 90.0%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 82.2%

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

      1. associate-/l* 80.6%

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

      2. associate-/r/ 89.6%

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

   6. Applied egg-rr 89.6%

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

   if -4e17 < z < 2.4000000000000002e41

   1. Initial program 95.2%

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

      1. associate-*r/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around 0 89.1%

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

      1. sub-neg 89.1%

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

      2. mul-1-neg 89.1%

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

      3. remove-double-neg 89.1%

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

      4. +-commutative 89.1%

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

      5. *-commutative 89.1%

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

      6. associate-/l* 93.8%

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

      7. associate-/r/ 87.4%

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

   6. Simplified 87.4%

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

      1. associate-*l/ 89.1%

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

   8. Applied egg-rr 89.1%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+17} \lor \neg \left(z \leq 2.4 \cdot 10^{+41}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \end{array} \]

Alternative 6: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+17} \lor \neg \left(z \leq 4.6 \cdot 10^{+41}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2.75e+17) (not (<= z 4.6e+41)))
   (- 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 <= -2.75e+17) || !(z <= 4.6e+41)) {
		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 <= (-2.75d+17)) .or. (.not. (z <= 4.6d+41))) 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 <= -2.75e+17) || !(z <= 4.6e+41)) {
		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 <= -2.75e+17) or not (z <= 4.6e+41):
		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 <= -2.75e+17) || !(z <= 4.6e+41))
		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 <= -2.75e+17) || ~((z <= 4.6e+41)))
		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, -2.75e+17], N[Not[LessEqual[z, 4.6e+41]], $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 < -2.75e17 or 4.5999999999999997e41 < z

   1. Initial program 90.0%

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

      1. associate-*r/ 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. Taylor expanded in z around inf 82.2%

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

      1. associate-/l* 80.6%

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

      2. associate-/r/ 89.6%

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

   6. Applied egg-rr 89.6%

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

   if -2.75e17 < z < 4.5999999999999997e41

   1. Initial program 95.2%

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

      1. associate-*r/ 93.5%

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

   3. Simplified 93.5%

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

   4. Taylor expanded in z around 0 89.1%

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

      1. associate-*l/ 93.7%

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

      2. neg-mul-1 93.7%

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

      3. distribute-rgt-neg-out 93.7%

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

   6. Simplified 93.7%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+17} \lor \neg \left(z \leq 4.6 \cdot 10^{+41}\right):\\ \;\;\;\;x - z \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 7: 49.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-62} \lor \neg \left(y \leq 8.5 \cdot 10^{-50}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.85e-62) (not (<= y 8.5e-50))) (* y (/ t a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.85e-62) || !(y <= 8.5e-50)) {
		tmp = y * (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 <= (-1.85d-62)) .or. (.not. (y <= 8.5d-50))) then
        tmp = y * (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 <= -1.85e-62) || !(y <= 8.5e-50)) {
		tmp = y * (t / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.85e-62) or not (y <= 8.5e-50):
		tmp = y * (t / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.85e-62) || !(y <= 8.5e-50))
		tmp = Float64(y * Float64(t / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.85e-62) || ~((y <= 8.5e-50)))
		tmp = y * (t / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.85e-62], N[Not[LessEqual[y, 8.5e-50]], $MachinePrecision]], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.8499999999999999e-62 or 8.50000000000000012e-50 < y

   1. Initial program 86.9%

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

      1. associate-*r/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in t around inf 41.0%

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

      1. *-commutative 41.0%

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

      2. associate-/l* 47.8%

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

      3. associate-/r/ 45.1%

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

   6. Simplified 45.1%

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

   if -1.8499999999999999e-62 < y < 8.50000000000000012e-50

   1. Initial program 100.0%

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

      1. associate-*r/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in x around inf 69.1%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{-62} \lor \neg \left(y \leq 8.5 \cdot 10^{-50}\right):\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 50.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-61} \lor \neg \left(y \leq 1.52 \cdot 10^{-49}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.5e-61) (not (<= y 1.52e-49))) (* t (/ y a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.5e-61) || !(y <= 1.52e-49)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-1.5d-61)) .or. (.not. (y <= 1.52d-49))) then
        tmp = t * (y / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -1.5e-61) || !(y <= 1.52e-49)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -1.5e-61) or not (y <= 1.52e-49):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -1.5e-61) || !(y <= 1.52e-49))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -1.5e-61) || ~((y <= 1.52e-49)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -1.5e-61], N[Not[LessEqual[y, 1.52e-49]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000006e-61 or 1.52e-49 < y

   1. Initial program 86.9%

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

      1. associate-*r/ 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in t around inf 41.0%

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

      1. associate-/l* 45.1%

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

      2. associate-/r/ 48.4%

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

   6. Applied egg-rr 48.4%

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

   if -1.50000000000000006e-61 < y < 1.52e-49

   1. Initial program 100.0%

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

      1. associate-*r/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in x around inf 69.1%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-61} \lor \neg \left(y \leq 1.52 \cdot 10^{-49}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 50.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -9.5e-63) (/ t (/ a y)) (if (<= y 1.52e-49) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -9.5e-63) {
		tmp = t / (a / y);
	} else if (y <= 1.52e-49) {
		tmp = x;
	} 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 (y <= (-9.5d-63)) then
        tmp = t / (a / y)
    else if (y <= 1.52d-49) then
        tmp = x
    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 (y <= -9.5e-63) {
		tmp = t / (a / y);
	} else if (y <= 1.52e-49) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -9.5e-63:
		tmp = t / (a / y)
	elif y <= 1.52e-49:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -9.5e-63)
		tmp = Float64(t / Float64(a / y));
	elseif (y <= 1.52e-49)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -9.5e-63)
		tmp = t / (a / y);
	elseif (y <= 1.52e-49)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -9.5e-63], N[(t / N[(a / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e-49], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.50000000000000016e-63

   1. Initial program 86.7%

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

      1. associate-*r/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in t around inf 37.8%

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

      1. *-commutative 37.8%

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

      2. associate-/l* 44.4%

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

      3. associate-/r/ 41.8%

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

   6. Simplified 41.8%

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

      1. associate-/r/ 44.4%

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

   8. Applied egg-rr 44.4%

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

   if -9.50000000000000016e-63 < y < 1.52e-49

   1. Initial program 100.0%

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

      1. associate-*r/ 83.8%

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

   3. Simplified 83.8%

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

   4. Taylor expanded in x around inf 69.1%

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

   if 1.52e-49 < y

   1. Initial program 87.1%

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

      1. associate-*r/ 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. Taylor expanded in t around inf 44.5%

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

      1. associate-/l* 48.7%

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

      2. associate-/r/ 52.9%

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

   6. Applied egg-rr 52.9%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-63}:\\ \;\;\;\;\frac{t}{\frac{a}{y}}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 10: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.55e-60) (* z (/ y (- a))) (if (<= y 1.52e-49) x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.55e-60) {
		tmp = z * (y / -a);
	} else if (y <= 1.52e-49) {
		tmp = x;
	} 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 (y <= (-1.55d-60)) then
        tmp = z * (y / -a)
    else if (y <= 1.52d-49) then
        tmp = x
    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 (y <= -1.55e-60) {
		tmp = z * (y / -a);
	} else if (y <= 1.52e-49) {
		tmp = x;
	} else {
		tmp = t * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.55e-60:
		tmp = z * (y / -a)
	elif y <= 1.52e-49:
		tmp = x
	else:
		tmp = t * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.55e-60)
		tmp = Float64(z * Float64(y / Float64(-a)));
	elseif (y <= 1.52e-49)
		tmp = x;
	else
		tmp = Float64(t * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.55e-60)
		tmp = z * (y / -a);
	elseif (y <= 1.52e-49)
		tmp = x;
	else
		tmp = t * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.55e-60], N[(z * N[(y / (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.52e-49], x, N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.54999999999999994e-60

   1. Initial program 86.5%

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

      1. associate-*r/ 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in z around inf 41.1%

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

      1. mul-1-neg 41.1%

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

      2. associate-*l/ 46.5%

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

      3. *-commutative 46.5%

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

      4. distribute-rgt-neg-in 46.5%

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

      5. distribute-frac-neg 46.5%

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

      6. *-lft-identity 46.5%

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

      7. metadata-eval 46.5%

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

      8. times-frac 46.5%

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

      9. neg-mul-1 46.5%

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

      10. remove-double-neg 46.5%

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

      11. neg-mul-1 46.5%

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

   6. Simplified 46.5%

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

   if -1.54999999999999994e-60 < y < 1.52e-49

   1. Initial program 99.9%

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

      1. associate-*r/ 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in x around inf 68.6%

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

   if 1.52e-49 < y

   1. Initial program 87.1%

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

      1. associate-*r/ 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. Taylor expanded in t around inf 44.5%

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

      1. associate-/l* 48.7%

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

      2. associate-/r/ 52.9%

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

   6. Applied egg-rr 52.9%

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

4. Final simplification 58.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-60}:\\ \;\;\;\;z \cdot \frac{y}{-a}\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-49}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{y}{a}\\ \end{array} \]

Alternative 11: 97.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.9%

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

   1. associate-*l/ 98.4%

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

3. Simplified 98.4%

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

4. Final simplification 98.4%

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

Alternative 12: 39.3% 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-*r/ 91.2%

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

3. Simplified 91.2%

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

4. Taylor expanded in x around inf 42.9%

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

5. Final simplification 42.9%

   \[\leadsto x \]

Developer target: 99.3% 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 2023194 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :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)))