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

Percentage Accurate: 92.9% → 97.6%

Time: 8.9s

Alternatives: 11

Speedup: 1.0×

• 25.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.0%

   \[x + \frac{y \cdot \left(z - x\right)}{t} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 89.1%

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

   1. +-commutative 89.1%

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

   2. *-commutative 89.1%

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

   3. associate-*r/ 88.3%

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

   4. mul-1-neg 88.3%

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

   5. associate-/l* 93.4%

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

   6. distribute-lft-neg-in 93.4%

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

   7. distribute-rgt-in 98.5%

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

   8. sub-neg 98.5%

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

5. Simplified 98.5%

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

Alternative 2: 51.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-50)
   (* x (/ y (- t)))
   (if (<= y 2.4e-20) x (if (<= y 2.3e+87) (* y (/ z t)) (/ x (/ (- t) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-50) {
		tmp = x * (y / -t);
	} else if (y <= 2.4e-20) {
		tmp = x;
	} else if (y <= 2.3e+87) {
		tmp = y * (z / t);
	} else {
		tmp = x / (-t / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.4d-50)) then
        tmp = x * (y / -t)
    else if (y <= 2.4d-20) then
        tmp = x
    else if (y <= 2.3d+87) then
        tmp = y * (z / t)
    else
        tmp = x / (-t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-50) {
		tmp = x * (y / -t);
	} else if (y <= 2.4e-20) {
		tmp = x;
	} else if (y <= 2.3e+87) {
		tmp = y * (z / t);
	} else {
		tmp = x / (-t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-50:
		tmp = x * (y / -t)
	elif y <= 2.4e-20:
		tmp = x
	elif y <= 2.3e+87:
		tmp = y * (z / t)
	else:
		tmp = x / (-t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e-50)
		tmp = Float64(x * Float64(y / Float64(-t)));
	elseif (y <= 2.4e-20)
		tmp = x;
	elseif (y <= 2.3e+87)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = Float64(x / Float64(Float64(-t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e-50)
		tmp = x * (y / -t);
	elseif (y <= 2.4e-20)
		tmp = x;
	elseif (y <= 2.3e+87)
		tmp = y * (z / t);
	else
		tmp = x / (-t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e-50], N[(x * N[(y / (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-20], x, If[LessEqual[y, 2.3e+87], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], N[(x / N[((-t) / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.3999999999999999e-50

   1. Initial program 84.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 73.7%

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

   4. Taylor expanded in z around 0 56.0%

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

      1. mul-1-neg 56.0%

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

      2. associate-/l* 57.1%

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

      3. distribute-rgt-neg-in 57.1%

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

      4. mul-1-neg 57.1%

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

      5. associate-*r/ 57.1%

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

      6. mul-1-neg 57.1%

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

   6. Simplified 57.1%

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

   if -1.3999999999999999e-50 < y < 2.39999999999999993e-20

   1. Initial program 97.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.3%

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

   if 2.39999999999999993e-20 < y < 2.3000000000000002e87

   1. Initial program 93.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 64.3%

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

   4. Taylor expanded in z around inf 48.2%

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

      1. associate-/l* 80.5%

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

   6. Simplified 50.1%

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

   if 2.3000000000000002e87 < y

   1. Initial program 79.4%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 70.6%

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

   4. Taylor expanded in z around 0 49.8%

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

      1. mul-1-neg 49.8%

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

      2. associate-/l* 64.9%

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

      3. distribute-rgt-neg-in 64.9%

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

      4. mul-1-neg 64.9%

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

      5. associate-*r/ 64.9%

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

      6. mul-1-neg 64.9%

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

   6. Simplified 64.9%

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

      1. distribute-frac-neg 64.9%

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

      2. distribute-rgt-neg-out 64.9%

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

      3. add-sqr-sqrt 64.8%

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

      4. sqrt-unprod 52.7%

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

      5. sqr-neg 52.7%

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

      6. sqrt-unprod 0.0%

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

      7. add-sqr-sqrt 1.2%

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

      8. clear-num 1.2%

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

      9. un-div-inv 1.2%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 52.7%

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

      12. sqr-neg 52.7%

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

      13. sqrt-unprod 64.7%

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

      14. add-sqr-sqrt 65.0%

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

   8. Applied egg-rr 65.0%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \frac{y}{-t}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{\frac{-t}{y}}\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{-50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.65 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (/ (- t) y))))
   (if (<= y -1.6e-50)
     t_1
     (if (<= y 9.8e-23) x (if (<= y 3.65e+90) (* y (/ z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (-t / y);
	double tmp;
	if (y <= -1.6e-50) {
		tmp = t_1;
	} else if (y <= 9.8e-23) {
		tmp = x;
	} else if (y <= 3.65e+90) {
		tmp = y * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (-t / y)
    if (y <= (-1.6d-50)) then
        tmp = t_1
    else if (y <= 9.8d-23) then
        tmp = x
    else if (y <= 3.65d+90) then
        tmp = y * (z / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (-t / y);
	double tmp;
	if (y <= -1.6e-50) {
		tmp = t_1;
	} else if (y <= 9.8e-23) {
		tmp = x;
	} else if (y <= 3.65e+90) {
		tmp = y * (z / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (-t / y)
	tmp = 0
	if y <= -1.6e-50:
		tmp = t_1
	elif y <= 9.8e-23:
		tmp = x
	elif y <= 3.65e+90:
		tmp = y * (z / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(Float64(-t) / y))
	tmp = 0.0
	if (y <= -1.6e-50)
		tmp = t_1;
	elseif (y <= 9.8e-23)
		tmp = x;
	elseif (y <= 3.65e+90)
		tmp = Float64(y * Float64(z / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (-t / y);
	tmp = 0.0;
	if (y <= -1.6e-50)
		tmp = t_1;
	elseif (y <= 9.8e-23)
		tmp = x;
	elseif (y <= 3.65e+90)
		tmp = y * (z / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[((-t) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e-50], t$95$1, If[LessEqual[y, 9.8e-23], x, If[LessEqual[y, 3.65e+90], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6e-50 or 3.64999999999999997e90 < y

   1. Initial program 82.9%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 72.7%

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

   4. Taylor expanded in z around 0 54.1%

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

      1. mul-1-neg 54.1%

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

      2. associate-/l* 59.5%

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

      3. distribute-rgt-neg-in 59.5%

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

      4. mul-1-neg 59.5%

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

      5. associate-*r/ 59.5%

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

      6. mul-1-neg 59.5%

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

   6. Simplified 59.5%

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

      1. distribute-frac-neg 59.5%

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

      2. distribute-rgt-neg-out 59.5%

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

      3. add-sqr-sqrt 19.8%

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

      4. sqrt-unprod 17.9%

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

      5. sqr-neg 17.9%

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

      6. sqrt-unprod 2.0%

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

      7. add-sqr-sqrt 2.4%

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

      8. clear-num 2.4%

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

      9. un-div-inv 2.4%

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

      10. add-sqr-sqrt 2.0%

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

      11. sqrt-unprod 18.0%

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

      12. sqr-neg 18.0%

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

      13. sqrt-unprod 19.7%

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

      14. add-sqr-sqrt 59.5%

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

   8. Applied egg-rr 59.5%

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

   if -1.6e-50 < y < 9.7999999999999996e-23

   1. Initial program 97.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 64.3%

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

   if 9.7999999999999996e-23 < y < 3.64999999999999997e90

   1. Initial program 93.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 64.3%

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

   4. Taylor expanded in z around inf 48.2%

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

      1. associate-/l* 80.5%

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

   6. Simplified 50.1%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-50}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-23}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.65 \cdot 10^{+90}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-t}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+94} \lor \neg \left(z \leq 2.8\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.25e+94) (not (<= z 2.8)))
   (+ x (* (/ y t) z))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.25e+94) || !(z <= 2.8)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.25d+94)) .or. (.not. (z <= 2.8d0))) then
        tmp = x + ((y / t) * z)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.25e+94) || !(z <= 2.8)) {
		tmp = x + ((y / t) * z);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.25e+94) or not (z <= 2.8):
		tmp = x + ((y / t) * z)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.25e+94) || !(z <= 2.8))
		tmp = Float64(x + Float64(Float64(y / t) * z));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.25e+94) || ~((z <= 2.8)))
		tmp = x + ((y / t) * z);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.25e+94], N[Not[LessEqual[z, 2.8]], $MachinePrecision]], N[(x + N[(N[(y / t), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.24999999999999988e94 or 2.7999999999999998 < z

   1. Initial program 86.9%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 84.9%

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

      1. +-commutative 84.9%

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

      2. *-commutative 84.9%

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

      3. associate-*r/ 90.9%

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

      4. mul-1-neg 90.9%

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

      5. associate-/l* 96.4%

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

      6. distribute-lft-neg-in 96.4%

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

      7. distribute-rgt-in 98.3%

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

      8. sub-neg 98.3%

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

   5. Simplified 98.3%

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

   6. Taylor expanded in z around inf 94.6%

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

   if -3.24999999999999988e94 < z < 2.7999999999999998

   1. Initial program 93.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 89.7%

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

      1. mul-1-neg 89.7%

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

      2. unsub-neg 89.7%

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

   5. Simplified 89.7%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.25 \cdot 10^{+94} \lor \neg \left(z \leq 2.8\right):\\ \;\;\;\;x + \frac{y}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+93} \lor \neg \left(z \leq 1.6 \cdot 10^{+125}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.9e+93) (not (<= z 1.6e+125)))
   (* y (/ (- z x) t))
   (* x (- 1.0 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e+93) || !(z <= 1.6e+125)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.9d+93)) .or. (.not. (z <= 1.6d+125))) then
        tmp = y * ((z - x) / t)
    else
        tmp = x * (1.0d0 - (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.9e+93) || !(z <= 1.6e+125)) {
		tmp = y * ((z - x) / t);
	} else {
		tmp = x * (1.0 - (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.9e+93) or not (z <= 1.6e+125):
		tmp = y * ((z - x) / t)
	else:
		tmp = x * (1.0 - (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.9e+93) || !(z <= 1.6e+125))
		tmp = Float64(y * Float64(Float64(z - x) / t));
	else
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.9e+93) || ~((z <= 1.6e+125)))
		tmp = y * ((z - x) / t);
	else
		tmp = x * (1.0 - (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.9e+93], N[Not[LessEqual[z, 1.6e+125]], $MachinePrecision]], N[(y * N[(N[(z - x), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.9000000000000002e93 or 1.59999999999999992e125 < z

   1. Initial program 85.6%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 63.6%

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

      1. associate-/l* 66.5%

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

      2. *-commutative 66.5%

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

   5. Applied egg-rr 66.5%

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

   if -3.9000000000000002e93 < z < 1.59999999999999992e125

   1. Initial program 93.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   5. Simplified 86.6%

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{y}{t}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.9 \cdot 10^{+93} \lor \neg \left(z \leq 1.6 \cdot 10^{+125}\right):\\ \;\;\;\;y \cdot \frac{z - x}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-14}:\\ \;\;\;\;x + y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{t - y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.5e+55)
   (* x (- 1.0 (/ y t)))
   (if (<= x 1.9e-14) (+ x (* y (/ z t))) (* x (/ (- t y) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e+55) {
		tmp = x * (1.0 - (y / t));
	} else if (x <= 1.9e-14) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * ((t - y) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.5d+55)) then
        tmp = x * (1.0d0 - (y / t))
    else if (x <= 1.9d-14) then
        tmp = x + (y * (z / t))
    else
        tmp = x * ((t - y) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e+55) {
		tmp = x * (1.0 - (y / t));
	} else if (x <= 1.9e-14) {
		tmp = x + (y * (z / t));
	} else {
		tmp = x * ((t - y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.5e+55:
		tmp = x * (1.0 - (y / t))
	elif x <= 1.9e-14:
		tmp = x + (y * (z / t))
	else:
		tmp = x * ((t - y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.5e+55)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	elseif (x <= 1.9e-14)
		tmp = Float64(x + Float64(y * Float64(z / t)));
	else
		tmp = Float64(x * Float64(Float64(t - y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.5e+55)
		tmp = x * (1.0 - (y / t));
	elseif (x <= 1.9e-14)
		tmp = x + (y * (z / t));
	else
		tmp = x * ((t - y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.5e+55], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-14], N[(x + N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(t - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.49999999999999998e55

   1. Initial program 89.0%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.0%

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

      1. mul-1-neg 97.0%

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

      2. unsub-neg 97.0%

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

   5. Simplified 97.0%

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

   if -4.49999999999999998e55 < x < 1.9000000000000001e-14

   1. Initial program 91.4%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 81.6%

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

      1. associate-/l* 83.6%

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

   5. Simplified 83.6%

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

   if 1.9000000000000001e-14 < x

   1. Initial program 92.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 89.4%

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

      1. mul-1-neg 89.4%

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

      2. unsub-neg 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in t around 0 89.4%

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

Alternative 7: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+96}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+125}:\\ \;\;\;\;x \cdot \left(1 - \frac{y}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.15e+96)
   (/ (* y z) t)
   (if (<= z 2.1e+125) (* x (- 1.0 (/ y t))) (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.15e+96) {
		tmp = (y * z) / t;
	} else if (z <= 2.1e+125) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.15d+96)) then
        tmp = (y * z) / t
    else if (z <= 2.1d+125) then
        tmp = x * (1.0d0 - (y / t))
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.15e+96) {
		tmp = (y * z) / t;
	} else if (z <= 2.1e+125) {
		tmp = x * (1.0 - (y / t));
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.15e+96:
		tmp = (y * z) / t
	elif z <= 2.1e+125:
		tmp = x * (1.0 - (y / t))
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.15e+96)
		tmp = Float64(Float64(y * z) / t);
	elseif (z <= 2.1e+125)
		tmp = Float64(x * Float64(1.0 - Float64(y / t)));
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.15e+96)
		tmp = (y * z) / t;
	elseif (z <= 2.1e+125)
		tmp = x * (1.0 - (y / t));
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.15e+96], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 2.1e+125], N[(x * N[(1.0 - N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.15000000000000008e96

   1. Initial program 89.4%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 66.4%

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

   4. Taylor expanded in z around inf 64.3%

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

   if -1.15000000000000008e96 < z < 2.1000000000000001e125

   1. Initial program 93.5%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 86.6%

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

      1. mul-1-neg 86.6%

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

      2. unsub-neg 86.6%

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

   5. Simplified 86.6%

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

   if 2.1000000000000001e125 < z

   1. Initial program 80.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 59.8%

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

   4. Taylor expanded in z around inf 59.3%

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

      1. associate-/l* 80.2%

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

   6. Simplified 62.4%

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

Alternative 8: 52.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+112} \lor \neg \left(y \leq 1.6 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e+112) (not (<= y 1.6e-20))) (* y (/ z t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e+112) || !(y <= 1.6e-20)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.3d+112)) .or. (.not. (y <= 1.6d-20))) then
        tmp = y * (z / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e+112) || !(y <= 1.6e-20)) {
		tmp = y * (z / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.3e+112) or not (y <= 1.6e-20):
		tmp = y * (z / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.3e+112) || !(y <= 1.6e-20))
		tmp = Float64(y * Float64(z / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.3e+112) || ~((y <= 1.6e-20)))
		tmp = y * (z / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.3e+112], N[Not[LessEqual[y, 1.6e-20]], $MachinePrecision]], N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.3e112 or 1.59999999999999985e-20 < y

   1. Initial program 84.3%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 71.9%

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

   4. Taylor expanded in z around inf 41.4%

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

      1. associate-/l* 61.9%

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

   6. Simplified 47.1%

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

   if -1.3e112 < y < 1.59999999999999985e-20

   1. Initial program 96.0%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 59.3%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+112} \lor \neg \left(y \leq 1.6 \cdot 10^{-20}\right):\\ \;\;\;\;y \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-181}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.2e+20) x (if (<= t 6.2e-181) (/ (* y z) t) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.2e+20) {
		tmp = x;
	} else if (t <= 6.2e-181) {
		tmp = (y * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-2.2d+20)) then
        tmp = x
    else if (t <= 6.2d-181) then
        tmp = (y * z) / t
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.2e+20) {
		tmp = x;
	} else if (t <= 6.2e-181) {
		tmp = (y * z) / t;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.2e+20:
		tmp = x
	elif t <= 6.2e-181:
		tmp = (y * z) / t
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.2e+20)
		tmp = x;
	elseif (t <= 6.2e-181)
		tmp = Float64(Float64(y * z) / t);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.2e+20)
		tmp = x;
	elseif (t <= 6.2e-181)
		tmp = (y * z) / t;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.2e+20], x, If[LessEqual[t, 6.2e-181], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if t < -2.2e20 or 6.20000000000000043e-181 < t

   1. Initial program 86.6%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 59.8%

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

   if -2.2e20 < t < 6.20000000000000043e-181

   1. Initial program 97.7%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 84.8%

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

   4. Taylor expanded in z around inf 49.1%

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

Alternative 10: 52.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+110}:\\ \;\;\;\;\frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e+110) (/ y (/ t z)) (if (<= y 2.25e-22) x (* y (/ z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+110) {
		tmp = y / (t / z);
	} else if (y <= 2.25e-22) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.25d+110)) then
        tmp = y / (t / z)
    else if (y <= 2.25d-22) then
        tmp = x
    else
        tmp = y * (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+110) {
		tmp = y / (t / z);
	} else if (y <= 2.25e-22) {
		tmp = x;
	} else {
		tmp = y * (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.25e+110:
		tmp = y / (t / z)
	elif y <= 2.25e-22:
		tmp = x
	else:
		tmp = y * (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e+110)
		tmp = Float64(y / Float64(t / z));
	elseif (y <= 2.25e-22)
		tmp = x;
	else
		tmp = Float64(y * Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.25e+110)
		tmp = y / (t / z);
	elseif (y <= 2.25e-22)
		tmp = x;
	else
		tmp = y * (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e+110], N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.25e-22], x, N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.24999999999999995e110

   1. Initial program 81.8%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 77.6%

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

   4. Taylor expanded in z around inf 42.8%

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

      1. associate-/l* 61.3%

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

   6. Simplified 54.8%

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

      1. clear-num 54.7%

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

      2. un-div-inv 54.8%

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

   8. Applied egg-rr 54.8%

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

   if -1.24999999999999995e110 < y < 2.24999999999999993e-22

   1. Initial program 96.0%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 59.3%

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

   if 2.24999999999999993e-22 < y

   1. Initial program 86.2%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
   2. Add Preprocessing

   3. Taylor expanded in y around -inf 67.6%

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

   4. Taylor expanded in z around inf 40.4%

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

      1. associate-/l* 62.4%

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

   6. Simplified 41.4%

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

Alternative 11: 38.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.0%

   \[x + \frac{y \cdot \left(z - x\right)}{t} \]
2. Add Preprocessing

3. Taylor expanded in y around 0 41.4%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 90.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024172 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (+ (* x (/ y t)) (* (- z) (/ y t)))))

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