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

Percentage Accurate: 93.3% → 97.1%

Time: 10.9s

Alternatives: 13

Speedup: 0.6×

• 24.5% 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: 93.3% 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: 97.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-136}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y 1.2e-136) (+ x (* (- z t) (/ y a))) (+ x (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 1.2e-136) {
		tmp = x + ((z - t) * (y / a));
	} else {
		tmp = x + (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 (y <= 1.2d-136) then
        tmp = x + ((z - t) * (y / a))
    else
        tmp = x + (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 (y <= 1.2e-136) {
		tmp = x + ((z - t) * (y / a));
	} else {
		tmp = x + (y * ((z - t) / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 1.2e-136:
		tmp = x + ((z - t) * (y / a))
	else:
		tmp = x + (y * ((z - t) / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 1.2e-136)
		tmp = Float64(x + Float64(Float64(z - t) * Float64(y / a)));
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 1.2e-136)
		tmp = x + ((z - t) * (y / a));
	else
		tmp = x + (y * ((z - t) / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 1.2e-136], N[(x + N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.1999999999999999e-136

   1. Initial program 95.8%

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

      1. associate-/l* 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in y around 0 95.8%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   if 1.1999999999999999e-136 < y

   1. Initial program 93.9%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.2 \cdot 10^{-136}:\\ \;\;\;\;x + \left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 67.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-191} \lor \neg \left(y \leq 2.8 \cdot 10^{-164} \lor \neg \left(y \leq 6 \cdot 10^{-149}\right) \land y \leq 3.5 \cdot 10^{-79}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -8.4e-191)
         (not (or (<= y 2.8e-164) (and (not (<= y 6e-149)) (<= y 3.5e-79)))))
   (* y (/ (- z t) a))
   x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -8.4e-191) || !((y <= 2.8e-164) || (!(y <= 6e-149) && (y <= 3.5e-79)))) {
		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 <= (-8.4d-191)) .or. (.not. (y <= 2.8d-164) .or. (.not. (y <= 6d-149)) .and. (y <= 3.5d-79))) 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 <= -8.4e-191) || !((y <= 2.8e-164) || (!(y <= 6e-149) && (y <= 3.5e-79)))) {
		tmp = y * ((z - t) / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -8.4e-191) or not ((y <= 2.8e-164) or (not (y <= 6e-149) and (y <= 3.5e-79))):
		tmp = y * ((z - t) / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -8.4e-191) || !((y <= 2.8e-164) || (!(y <= 6e-149) && (y <= 3.5e-79))))
		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 <= -8.4e-191) || ~(((y <= 2.8e-164) || (~((y <= 6e-149)) && (y <= 3.5e-79)))))
		tmp = y * ((z - t) / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -8.4e-191], N[Not[Or[LessEqual[y, 2.8e-164], And[N[Not[LessEqual[y, 6e-149]], $MachinePrecision], LessEqual[y, 3.5e-79]]]], $MachinePrecision]], N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.39999999999999941e-191 or 2.8000000000000001e-164 < y < 6.0000000000000003e-149 or 3.5000000000000003e-79 < y

   1. Initial program 93.0%

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

      1. associate-/l* 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 80.1%

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

      1. associate-/l* 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in x around 0 70.1%

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

      1. associate-/l* 74.4%

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

   10. Simplified 74.4%

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

   if -8.39999999999999941e-191 < y < 2.8000000000000001e-164 or 6.0000000000000003e-149 < y < 3.5000000000000003e-79

   1. Initial program 99.9%

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

      1. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in x around inf 79.7%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-191} \lor \neg \left(y \leq 2.8 \cdot 10^{-164} \lor \neg \left(y \leq 6 \cdot 10^{-149}\right) \land y \leq 3.5 \cdot 10^{-79}\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-190}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-164} \lor \neg \left(y \leq 2.3 \cdot 10^{-149}\right) \land y \leq 7 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -1.15e-190)
   (* (- z t) (/ y a))
   (if (or (<= y 2.7e-164) (and (not (<= y 2.3e-149)) (<= y 7e-80)))
     x
     (* y (/ (- z t) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.15e-190) {
		tmp = (z - t) * (y / a);
	} else if ((y <= 2.7e-164) || (!(y <= 2.3e-149) && (y <= 7e-80))) {
		tmp = x;
	} 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 (y <= (-1.15d-190)) then
        tmp = (z - t) * (y / a)
    else if ((y <= 2.7d-164) .or. (.not. (y <= 2.3d-149)) .and. (y <= 7d-80)) then
        tmp = x
    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 (y <= -1.15e-190) {
		tmp = (z - t) * (y / a);
	} else if ((y <= 2.7e-164) || (!(y <= 2.3e-149) && (y <= 7e-80))) {
		tmp = x;
	} else {
		tmp = y * ((z - t) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.15e-190:
		tmp = (z - t) * (y / a)
	elif (y <= 2.7e-164) or (not (y <= 2.3e-149) and (y <= 7e-80)):
		tmp = x
	else:
		tmp = y * ((z - t) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.15e-190)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	elseif ((y <= 2.7e-164) || (!(y <= 2.3e-149) && (y <= 7e-80)))
		tmp = x;
	else
		tmp = Float64(y * Float64(Float64(z - t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.15e-190)
		tmp = (z - t) * (y / a);
	elseif ((y <= 2.7e-164) || (~((y <= 2.3e-149)) && (y <= 7e-80)))
		tmp = x;
	else
		tmp = y * ((z - t) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.15e-190], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, 2.7e-164], And[N[Not[LessEqual[y, 2.3e-149]], $MachinePrecision], LessEqual[y, 7e-80]]], x, N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.14999999999999996e-190

   1. Initial program 92.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 84.2%

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

      1. associate-/l* 85.3%

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

   7. Simplified 85.3%

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

   8. Taylor expanded in x around 0 64.0%

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

      1. associate-/l* 68.1%

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

   10. Simplified 68.1%

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

   11. Taylor expanded in y around 0 64.0%

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

       1. associate-*l/ 98.8%

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

       2. *-commutative 98.8%

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

   13. Simplified 70.1%

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

   if -1.14999999999999996e-190 < y < 2.7000000000000001e-164 or 2.3e-149 < y < 7.00000000000000029e-80

   1. Initial program 99.9%

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

      1. associate-/l* 85.1%

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

   3. Simplified 85.1%

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

   5. Taylor expanded in x around inf 79.7%

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

   if 2.7000000000000001e-164 < y < 2.3e-149 or 7.00000000000000029e-80 < y

   1. Initial program 93.3%

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

      1. associate-/l* 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in x around inf 75.6%

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

      1. associate-/l* 76.9%

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

   7. Simplified 76.9%

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

   8. Taylor expanded in x around 0 76.7%

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

      1. associate-/l* 81.1%

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

   10. Simplified 81.1%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-190}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-164} \lor \neg \left(y \leq 2.3 \cdot 10^{-149}\right) \land y \leq 7 \cdot 10^{-80}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.058:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 28000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+129} \lor \neg \left(y \leq 1.52 \cdot 10^{+150}\right):\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -0.058)
   (/ y (/ a z))
   (if (<= y 28000000.0)
     x
     (if (or (<= y 1e+129) (not (<= y 1.52e+150)))
       (* y (/ (- t) a))
       (* y (/ z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.058) {
		tmp = y / (a / z);
	} else if (y <= 28000000.0) {
		tmp = x;
	} else if ((y <= 1e+129) || !(y <= 1.52e+150)) {
		tmp = y * (-t / a);
	} else {
		tmp = 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 <= (-0.058d0)) then
        tmp = y / (a / z)
    else if (y <= 28000000.0d0) then
        tmp = x
    else if ((y <= 1d+129) .or. (.not. (y <= 1.52d+150))) then
        tmp = y * (-t / a)
    else
        tmp = 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 <= -0.058) {
		tmp = y / (a / z);
	} else if (y <= 28000000.0) {
		tmp = x;
	} else if ((y <= 1e+129) || !(y <= 1.52e+150)) {
		tmp = y * (-t / a);
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -0.058:
		tmp = y / (a / z)
	elif y <= 28000000.0:
		tmp = x
	elif (y <= 1e+129) or not (y <= 1.52e+150):
		tmp = y * (-t / a)
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -0.058)
		tmp = Float64(y / Float64(a / z));
	elseif (y <= 28000000.0)
		tmp = x;
	elseif ((y <= 1e+129) || !(y <= 1.52e+150))
		tmp = Float64(y * Float64(Float64(-t) / a));
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -0.058)
		tmp = y / (a / z);
	elseif (y <= 28000000.0)
		tmp = x;
	elseif ((y <= 1e+129) || ~((y <= 1.52e+150)))
		tmp = y * (-t / a);
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -0.058], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 28000000.0], x, If[Or[LessEqual[y, 1e+129], N[Not[LessEqual[y, 1.52e+150]], $MachinePrecision]], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.0580000000000000029

   1. Initial program 87.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 83.9%

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

      1. associate-/l* 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around inf 55.0%

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

      1. associate-*r/ 62.8%

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

   10. Simplified 62.8%

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

       1. clear-num 62.8%

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

       2. un-div-inv 62.8%

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

   12. Applied egg-rr 62.8%

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

   if -0.0580000000000000029 < y < 2.8e7

   1. Initial program 99.8%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around inf 61.4%

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

   if 2.8e7 < y < 1e129 or 1.52e150 < y

   1. Initial program 95.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 76.8%

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

      1. associate-/l* 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in t around inf 63.2%

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

      1. associate-*r/ 63.2%

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

      2. neg-mul-1 63.2%

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

      3. distribute-rgt-neg-in 63.2%

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

      4. associate-*l/ 63.2%

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

   10. Simplified 63.2%

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

   if 1e129 < y < 1.52e150

   1. Initial program 43.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 23.3%

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

      1. associate-/l* 25.1%

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

   7. Simplified 25.1%

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

   8. Taylor expanded in z around inf 43.2%

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

      1. associate-*r/ 99.7%

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

   10. Simplified 99.7%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.058:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 28000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 10^{+129} \lor \neg \left(y \leq 1.52 \cdot 10^{+150}\right):\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.052:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 100000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+129}:\\ \;\;\;\;\frac{y}{\frac{a}{-t}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -0.052)
   (/ y (/ a z))
   (if (<= y 100000.0)
     x
     (if (<= y 1.2e+129)
       (/ y (/ a (- t)))
       (if (<= y 1.2e+151) (* y (/ z a)) (* y (/ (- t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.052) {
		tmp = y / (a / z);
	} else if (y <= 100000.0) {
		tmp = x;
	} else if (y <= 1.2e+129) {
		tmp = y / (a / -t);
	} else if (y <= 1.2e+151) {
		tmp = y * (z / a);
	} else {
		tmp = y * (-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 (y <= (-0.052d0)) then
        tmp = y / (a / z)
    else if (y <= 100000.0d0) then
        tmp = x
    else if (y <= 1.2d+129) then
        tmp = y / (a / -t)
    else if (y <= 1.2d+151) then
        tmp = y * (z / a)
    else
        tmp = y * (-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 (y <= -0.052) {
		tmp = y / (a / z);
	} else if (y <= 100000.0) {
		tmp = x;
	} else if (y <= 1.2e+129) {
		tmp = y / (a / -t);
	} else if (y <= 1.2e+151) {
		tmp = y * (z / a);
	} else {
		tmp = y * (-t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -0.052:
		tmp = y / (a / z)
	elif y <= 100000.0:
		tmp = x
	elif y <= 1.2e+129:
		tmp = y / (a / -t)
	elif y <= 1.2e+151:
		tmp = y * (z / a)
	else:
		tmp = y * (-t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -0.052)
		tmp = Float64(y / Float64(a / z));
	elseif (y <= 100000.0)
		tmp = x;
	elseif (y <= 1.2e+129)
		tmp = Float64(y / Float64(a / Float64(-t)));
	elseif (y <= 1.2e+151)
		tmp = Float64(y * Float64(z / a));
	else
		tmp = Float64(y * Float64(Float64(-t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -0.052)
		tmp = y / (a / z);
	elseif (y <= 100000.0)
		tmp = x;
	elseif (y <= 1.2e+129)
		tmp = y / (a / -t);
	elseif (y <= 1.2e+151)
		tmp = y * (z / a);
	else
		tmp = y * (-t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -0.052], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 100000.0], x, If[LessEqual[y, 1.2e+129], N[(y / N[(a / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e+151], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -0.0519999999999999976

   1. Initial program 87.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 83.9%

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

      1. associate-/l* 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around inf 55.0%

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

      1. associate-*r/ 62.8%

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

   10. Simplified 62.8%

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

       1. clear-num 62.8%

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

       2. un-div-inv 62.8%

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

   12. Applied egg-rr 62.8%

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

   if -0.0519999999999999976 < y < 1e5

   1. Initial program 99.8%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around inf 61.4%

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

   if 1e5 < y < 1.1999999999999999e129

   1. Initial program 96.4%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 68.4%

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

      1. associate-/l* 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in t around inf 62.6%

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

      1. mul-1-neg 62.6%

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

      2. *-commutative 62.6%

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

      3. associate-*l/ 62.4%

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

      4. associate-/r/ 62.5%

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

      5. distribute-neg-frac2 62.5%

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

   10. Simplified 62.5%

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

   if 1.1999999999999999e129 < y < 1.20000000000000005e151

   1. Initial program 43.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 23.3%

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

      1. associate-/l* 25.1%

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

   7. Simplified 25.1%

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

   8. Taylor expanded in z around inf 43.2%

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

      1. associate-*r/ 99.7%

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

   10. Simplified 99.7%

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

   if 1.20000000000000005e151 < y

   1. Initial program 93.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 84.4%

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

      1. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in t around inf 63.7%

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

      1. associate-*r/ 63.7%

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

      2. neg-mul-1 63.7%

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

      3. distribute-rgt-neg-in 63.7%

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

      4. associate-*l/ 64.0%

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

   10. Simplified 64.0%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.052:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 100000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+129}:\\ \;\;\;\;\frac{y}{\frac{a}{-t}}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{+151}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.225:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 31000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+129}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -0.225)
   (/ y (/ a z))
   (if (<= y 31000000000000.0)
     x
     (if (<= y 4.8e+129)
       (/ (* y (- t)) a)
       (if (<= y 4.5e+149) (* y (/ z a)) (* y (/ (- t) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.225) {
		tmp = y / (a / z);
	} else if (y <= 31000000000000.0) {
		tmp = x;
	} else if (y <= 4.8e+129) {
		tmp = (y * -t) / a;
	} else if (y <= 4.5e+149) {
		tmp = y * (z / a);
	} else {
		tmp = y * (-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 (y <= (-0.225d0)) then
        tmp = y / (a / z)
    else if (y <= 31000000000000.0d0) then
        tmp = x
    else if (y <= 4.8d+129) then
        tmp = (y * -t) / a
    else if (y <= 4.5d+149) then
        tmp = y * (z / a)
    else
        tmp = y * (-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 (y <= -0.225) {
		tmp = y / (a / z);
	} else if (y <= 31000000000000.0) {
		tmp = x;
	} else if (y <= 4.8e+129) {
		tmp = (y * -t) / a;
	} else if (y <= 4.5e+149) {
		tmp = y * (z / a);
	} else {
		tmp = y * (-t / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -0.225:
		tmp = y / (a / z)
	elif y <= 31000000000000.0:
		tmp = x
	elif y <= 4.8e+129:
		tmp = (y * -t) / a
	elif y <= 4.5e+149:
		tmp = y * (z / a)
	else:
		tmp = y * (-t / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -0.225)
		tmp = Float64(y / Float64(a / z));
	elseif (y <= 31000000000000.0)
		tmp = x;
	elseif (y <= 4.8e+129)
		tmp = Float64(Float64(y * Float64(-t)) / a);
	elseif (y <= 4.5e+149)
		tmp = Float64(y * Float64(z / a));
	else
		tmp = Float64(y * Float64(Float64(-t) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -0.225)
		tmp = y / (a / z);
	elseif (y <= 31000000000000.0)
		tmp = x;
	elseif (y <= 4.8e+129)
		tmp = (y * -t) / a;
	elseif (y <= 4.5e+149)
		tmp = y * (z / a);
	else
		tmp = y * (-t / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -0.225], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 31000000000000.0], x, If[LessEqual[y, 4.8e+129], N[(N[(y * (-t)), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[y, 4.5e+149], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], N[(y * N[((-t) / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -0.225000000000000006

   1. Initial program 87.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 83.9%

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

      1. associate-/l* 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around inf 55.0%

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

      1. associate-*r/ 62.8%

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

   10. Simplified 62.8%

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

       1. clear-num 62.8%

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

       2. un-div-inv 62.8%

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

   12. Applied egg-rr 62.8%

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

   if -0.225000000000000006 < y < 3.1e13

   1. Initial program 99.8%

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

      1. associate-/l* 89.1%

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

   3. Simplified 89.1%

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

   5. Taylor expanded in x around inf 61.4%

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

   if 3.1e13 < y < 4.7999999999999997e129

   1. Initial program 96.4%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 68.4%

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

      1. associate-/l* 72.1%

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

   7. Simplified 72.1%

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

   8. Taylor expanded in x around 0 76.6%

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

      1. associate-/l* 76.4%

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

   10. Simplified 76.4%

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

   11. Taylor expanded in z around 0 62.6%

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

       1. associate-*r/ 62.6%

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

       2. mul-1-neg 62.6%

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

       3. distribute-lft-neg-out 62.6%

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

       4. *-commutative 62.6%

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

   13. Simplified 62.6%

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

   if 4.7999999999999997e129 < y < 4.49999999999999982e149

   1. Initial program 43.2%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 23.3%

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

      1. associate-/l* 25.1%

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

   7. Simplified 25.1%

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

   8. Taylor expanded in z around inf 43.2%

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

      1. associate-*r/ 99.7%

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

   10. Simplified 99.7%

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

   if 4.49999999999999982e149 < y

   1. Initial program 93.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 84.4%

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

      1. associate-/l* 90.6%

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

   7. Simplified 90.6%

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

   8. Taylor expanded in t around inf 63.7%

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

      1. associate-*r/ 63.7%

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

      2. neg-mul-1 63.7%

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

      3. distribute-rgt-neg-in 63.7%

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

      4. associate-*l/ 64.0%

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

   10. Simplified 64.0%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.225:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 31000000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+129}:\\ \;\;\;\;\frac{y \cdot \left(-t\right)}{a}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+149}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 36:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+206}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= z -1.6e-39)
     t_1
     (if (<= z 36.0)
       (- x (* t (/ y a)))
       (if (<= z 4.1e+206) (* (- z t) (/ y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (z <= -1.6e-39) {
		tmp = t_1;
	} else if (z <= 36.0) {
		tmp = x - (t * (y / a));
	} else if (z <= 4.1e+206) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (z <= (-1.6d-39)) then
        tmp = t_1
    else if (z <= 36.0d0) then
        tmp = x - (t * (y / a))
    else if (z <= 4.1d+206) then
        tmp = (z - t) * (y / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (z <= -1.6e-39) {
		tmp = t_1;
	} else if (z <= 36.0) {
		tmp = x - (t * (y / a));
	} else if (z <= 4.1e+206) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if z <= -1.6e-39:
		tmp = t_1
	elif z <= 36.0:
		tmp = x - (t * (y / a))
	elif z <= 4.1e+206:
		tmp = (z - t) * (y / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (z <= -1.6e-39)
		tmp = t_1;
	elseif (z <= 36.0)
		tmp = Float64(x - Float64(t * Float64(y / a)));
	elseif (z <= 4.1e+206)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (z <= -1.6e-39)
		tmp = t_1;
	elseif (z <= 36.0)
		tmp = x - (t * (y / a));
	elseif (z <= 4.1e+206)
		tmp = (z - t) * (y / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e-39], t$95$1, If[LessEqual[z, 36.0], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e+206], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.5999999999999999e-39 or 4.1000000000000003e206 < z

   1. Initial program 90.5%

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

      1. associate-/l* 91.4%

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

   3. Simplified 91.4%

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

   5. Taylor expanded in t around 0 82.9%

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

      1. +-commutative 82.9%

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

      2. associate-/l* 81.5%

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

   7. Simplified 81.5%

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

      1. clear-num 55.5%

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

      2. un-div-inv 55.5%

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

   9. Applied egg-rr 82.5%

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

       1. associate-/r/ 88.5%

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

   11. Applied egg-rr 88.5%

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

   if -1.5999999999999999e-39 < z < 36

   1. Initial program 99.1%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in y around 0 99.1%

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

      1. associate-*l/ 96.1%

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

      2. *-commutative 96.1%

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

   7. Simplified 96.1%

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

   8. Taylor expanded in z around 0 92.8%

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

      1. associate-*l/ 91.3%

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

      2. *-commutative 91.3%

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

      3. neg-mul-1 91.3%

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

      4. sub-neg 91.3%

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

      5. *-commutative 91.3%

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

      6. associate-*l/ 92.8%

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

      7. associate-*r/ 92.8%

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

   10. Simplified 92.8%

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

   if 36 < z < 4.1000000000000003e206

   1. Initial program 93.9%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in x around inf 79.0%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in x around 0 82.1%

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

      1. associate-/l* 76.1%

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

   10. Simplified 76.1%

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

   11. Taylor expanded in y around 0 82.1%

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

       1. associate-*l/ 99.9%

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

       2. *-commutative 99.9%

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

   13. Simplified 88.1%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-39}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 36:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{+206}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 82.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.55 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 0.0018:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+206}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= z -1.55e-44)
     t_1
     (if (<= z 0.0018)
       (- x (/ (* y t) a))
       (if (<= z 3.8e+206) (* (- z t) (/ y a)) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (z <= -1.55e-44) {
		tmp = t_1;
	} else if (z <= 0.0018) {
		tmp = x - ((y * t) / a);
	} else if (z <= 3.8e+206) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (z <= (-1.55d-44)) then
        tmp = t_1
    else if (z <= 0.0018d0) then
        tmp = x - ((y * t) / a)
    else if (z <= 3.8d+206) then
        tmp = (z - t) * (y / a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (z <= -1.55e-44) {
		tmp = t_1;
	} else if (z <= 0.0018) {
		tmp = x - ((y * t) / a);
	} else if (z <= 3.8e+206) {
		tmp = (z - t) * (y / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if z <= -1.55e-44:
		tmp = t_1
	elif z <= 0.0018:
		tmp = x - ((y * t) / a)
	elif z <= 3.8e+206:
		tmp = (z - t) * (y / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (z <= -1.55e-44)
		tmp = t_1;
	elseif (z <= 0.0018)
		tmp = Float64(x - Float64(Float64(y * t) / a));
	elseif (z <= 3.8e+206)
		tmp = Float64(Float64(z - t) * Float64(y / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (z <= -1.55e-44)
		tmp = t_1;
	elseif (z <= 0.0018)
		tmp = x - ((y * t) / a);
	elseif (z <= 3.8e+206)
		tmp = (z - t) * (y / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.55e-44], t$95$1, If[LessEqual[z, 0.0018], N[(x - N[(N[(y * t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.8e+206], N[(N[(z - t), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.54999999999999992e-44 or 3.7999999999999999e206 < z

   1. Initial program 90.6%

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

      1. associate-/l* 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in t around 0 83.0%

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

      1. +-commutative 83.0%

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

      2. associate-/l* 81.7%

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

   7. Simplified 81.7%

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

      1. clear-num 55.9%

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

      2. un-div-inv 56.0%

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

   9. Applied egg-rr 82.6%

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

       1. associate-/r/ 88.7%

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

   11. Applied egg-rr 88.7%

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

   if -1.54999999999999992e-44 < z < 0.0018

   1. Initial program 99.1%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in z around 0 93.6%

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

      1. +-commutative 93.6%

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

      2. associate-*r/ 93.6%

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

      3. mul-1-neg 93.6%

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

      4. distribute-lft-neg-out 93.6%

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

      5. *-commutative 93.6%

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

   7. Simplified 93.6%

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

   if 0.0018 < z < 3.7999999999999999e206

   1. Initial program 93.9%

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

      1. associate-/l* 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in x around inf 79.0%

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

      1. associate-/l* 67.0%

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

   7. Simplified 67.0%

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

   8. Taylor expanded in x around 0 82.1%

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

      1. associate-/l* 76.1%

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

   10. Simplified 76.1%

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

   11. Taylor expanded in y around 0 82.1%

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

       1. associate-*l/ 99.9%

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

       2. *-commutative 99.9%

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

   13. Simplified 88.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-44}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;z \leq 0.0018:\\ \;\;\;\;x - \frac{y \cdot t}{a}\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{+206}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-190} \lor \neg \left(y \leq 5 \cdot 10^{-208}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -2.15e-190) (not (<= y 5e-208)))
   (+ x (* 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 <= -2.15e-190) || !(y <= 5e-208)) {
		tmp = x + (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 <= (-2.15d-190)) .or. (.not. (y <= 5d-208))) then
        tmp = x + (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 <= -2.15e-190) || !(y <= 5e-208)) {
		tmp = x + (y * ((z - t) / a));
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -2.15e-190) or not (y <= 5e-208):
		tmp = x + (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 <= -2.15e-190) || !(y <= 5e-208))
		tmp = Float64(x + 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 <= -2.15e-190) || ~((y <= 5e-208)))
		tmp = x + (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, -2.15e-190], N[Not[LessEqual[y, 5e-208]], $MachinePrecision]], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15e-190 or 4.99999999999999963e-208 < y

   1. Initial program 93.9%

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

      1. associate-/l* 97.6%

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

   3. Simplified 97.6%

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

   if -2.15e-190 < y < 4.99999999999999963e-208

   1. Initial program 99.9%

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

      1. associate-/l* 78.3%

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

   3. Simplified 78.3%

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

   5. Taylor expanded in z around inf 96.0%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{-190} \lor \neg \left(y \leq 5 \cdot 10^{-208}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+50} \lor \neg \left(y \leq 23000000000000\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -5.8e+50) (not (<= y 23000000000000.0)))
   (* 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 <= -5.8e+50) || !(y <= 23000000000000.0)) {
		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 <= (-5.8d+50)) .or. (.not. (y <= 23000000000000.0d0))) 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 <= -5.8e+50) || !(y <= 23000000000000.0)) {
		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 <= -5.8e+50) or not (y <= 23000000000000.0):
		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 <= -5.8e+50) || !(y <= 23000000000000.0))
		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 <= -5.8e+50) || ~((y <= 23000000000000.0)))
		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, -5.8e+50], N[Not[LessEqual[y, 23000000000000.0]], $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 < -5.8e50 or 2.3e13 < y

   1. Initial program 88.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 75.3%

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

      1. associate-/l* 81.0%

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

   7. Simplified 81.0%

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

   8. Taylor expanded in x around 0 75.2%

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

      1. associate-/l* 86.0%

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

   10. Simplified 86.0%

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

   if -5.8e50 < y < 2.3e13

   1. Initial program 99.8%

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

      1. associate-/l* 89.9%

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

   3. Simplified 89.9%

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

   5. Taylor expanded in z around inf 84.2%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+50} \lor \neg \left(y \leq 23000000000000\right):\\ \;\;\;\;y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.15 \lor \neg \left(y \leq 1.85 \cdot 10^{+111}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -0.15) (not (<= y 1.85e+111))) (* y (/ z a)) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -0.15) || !(y <= 1.85e+111)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-0.15d0)) .or. (.not. (y <= 1.85d+111))) then
        tmp = y * (z / a)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -0.15) || !(y <= 1.85e+111)) {
		tmp = y * (z / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -0.15) or not (y <= 1.85e+111):
		tmp = y * (z / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -0.15) || !(y <= 1.85e+111))
		tmp = Float64(y * Float64(z / a));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -0.15) || ~((y <= 1.85e+111)))
		tmp = y * (z / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -0.15], N[Not[LessEqual[y, 1.85e+111]], $MachinePrecision]], N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -0.149999999999999994 or 1.8500000000000001e111 < y

   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

   5. Taylor expanded in x around inf 79.7%

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

      1. associate-/l* 84.9%

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

   7. Simplified 84.9%

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

   8. Taylor expanded in z around inf 49.4%

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

      1. associate-*r/ 56.9%

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

   10. Simplified 56.9%

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

   if -0.149999999999999994 < y < 1.8500000000000001e111

   1. Initial program 99.3%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 57.0%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.15 \lor \neg \left(y \leq 1.85 \cdot 10^{+111}\right):\\ \;\;\;\;y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0135:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= y -0.0135) (/ y (/ a z)) (if (<= y 2.1e+111) x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -0.0135) {
		tmp = y / (a / z);
	} else if (y <= 2.1e+111) {
		tmp = x;
	} else {
		tmp = 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 <= (-0.0135d0)) then
        tmp = y / (a / z)
    else if (y <= 2.1d+111) then
        tmp = x
    else
        tmp = 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 <= -0.0135) {
		tmp = y / (a / z);
	} else if (y <= 2.1e+111) {
		tmp = x;
	} else {
		tmp = y * (z / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -0.0135:
		tmp = y / (a / z)
	elif y <= 2.1e+111:
		tmp = x
	else:
		tmp = y * (z / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -0.0135)
		tmp = Float64(y / Float64(a / z));
	elseif (y <= 2.1e+111)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -0.0135)
		tmp = y / (a / z);
	elseif (y <= 2.1e+111)
		tmp = x;
	else
		tmp = y * (z / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -0.0135], N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.1e+111], x, N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0134999999999999998

   1. Initial program 87.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 83.9%

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

      1. associate-/l* 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around inf 55.0%

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

      1. associate-*r/ 62.8%

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

   10. Simplified 62.8%

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

       1. clear-num 62.8%

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

       2. un-div-inv 62.8%

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

   12. Applied egg-rr 62.8%

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

   if -0.0134999999999999998 < y < 2.09999999999999995e111

   1. Initial program 99.3%

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

      1. associate-/l* 90.6%

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

   3. Simplified 90.6%

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

   5. Taylor expanded in x around inf 57.0%

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

   if 2.09999999999999995e111 < y

   1. Initial program 88.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 x around inf 74.0%

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

      1. associate-/l* 78.8%

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

   7. Simplified 78.8%

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

   8. Taylor expanded in z around inf 41.8%

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

      1. associate-*r/ 48.8%

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

   10. Simplified 48.8%

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

4. Final simplification 56.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0135:\\ \;\;\;\;\frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+111}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 39.7% 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 95.1%

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

   1. associate-/l* 93.9%

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

3. Simplified 93.9%

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

5. Taylor expanded in x around inf 41.6%

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

6. Final simplification 41.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 99.4% 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 2024066 
(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)))