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

Percentage Accurate: 99.9% → 99.9%

Time: 7.1s

Alternatives: 12

Speedup: 1.0×

• 26.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

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) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

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) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x + y\right) - z}{t \cdot 2} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ (- (+ x y) z) (* t 2.0)))

C

double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

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) / (t * 2.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((x + y) - z) / (t * 2.0);
}

Python

def code(x, y, z, t):
	return ((x + y) - z) / (t * 2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(x + y) - z) / Float64(t * 2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((x + y) - z) / (t * 2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(x + y), $MachinePrecision] - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

Alternative 2: 46.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-160} \lor \neg \left(x \leq -3.4 \cdot 10^{-178}\right) \land x \leq -4.3 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.2)
   (* 0.5 (/ x t))
   (if (or (<= x -4.4e-160) (and (not (<= x -3.4e-178)) (<= x -4.3e-243)))
     (* z (/ -0.5 t))
     (* y (/ 0.5 t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -4.4e-160) || (!(x <= -3.4e-178) && (x <= -4.3e-243))) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y * (0.5 / 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 <= (-6.2d0)) then
        tmp = 0.5d0 * (x / t)
    else if ((x <= (-4.4d-160)) .or. (.not. (x <= (-3.4d-178))) .and. (x <= (-4.3d-243))) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = y * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -4.4e-160) || (!(x <= -3.4e-178) && (x <= -4.3e-243))) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.2:
		tmp = 0.5 * (x / t)
	elif (x <= -4.4e-160) or (not (x <= -3.4e-178) and (x <= -4.3e-243)):
		tmp = z * (-0.5 / t)
	else:
		tmp = y * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.2)
		tmp = Float64(0.5 * Float64(x / t));
	elseif ((x <= -4.4e-160) || (!(x <= -3.4e-178) && (x <= -4.3e-243)))
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(y * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.2)
		tmp = 0.5 * (x / t);
	elseif ((x <= -4.4e-160) || (~((x <= -3.4e-178)) && (x <= -4.3e-243)))
		tmp = z * (-0.5 / t);
	else
		tmp = y * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.2], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -4.4e-160], And[N[Not[LessEqual[x, -3.4e-178]], $MachinePrecision], LessEqual[x, -4.3e-243]]], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.20000000000000018

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 64.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]

   if -6.20000000000000018 < x < -4.4e-160 or -3.39999999999999973e-178 < x < -4.3e-243

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 58.1%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. *-commutative 58.1%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

      2. associate-*l/ 58.1%

         \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

      3. associate-*r/ 58.0%

         \[\leadsto \color{blue}{z \cdot \frac{-0.5}{t}} \]

   5. Simplified 58.0%

      \[\leadsto \color{blue}{z \cdot \frac{-0.5}{t}} \]

   if -4.4e-160 < x < -3.39999999999999973e-178 or -4.3e-243 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 96.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t} + 0.5 \cdot \frac{y - z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 96.3%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} + 0.5 \cdot \frac{y - z}{t} \]

      2. associate-*l/ 96.2%

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot x} + 0.5 \cdot \frac{y - z}{t} \]

      3. associate-*r/ 96.2%

         \[\leadsto \frac{0.5}{t} \cdot x + \color{blue}{\frac{0.5 \cdot \left(y - z\right)}{t}} \]

      4. associate-*l/ 96.0%

         \[\leadsto \frac{0.5}{t} \cdot x + \color{blue}{\frac{0.5}{t} \cdot \left(y - z\right)} \]

      5. distribute-lft-in 99.7%

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(x + \left(y - z\right)\right)} \]

      6. associate-+r- 99.7%

         \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(\left(x + y\right) - z\right)} \]

      7. +-commutative 99.7%

         \[\leadsto \frac{0.5}{t} \cdot \left(\color{blue}{\left(y + x\right)} - z\right) \]

      8. associate--l+ 99.7%

         \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(y + \left(x - z\right)\right)} \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y + \left(x - z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y + \left(x - z\right)\right)}{t}} \]

      2. clear-num 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t}{0.5 \cdot \left(y + \left(x - z\right)\right)}}} \]

   7. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{t}{0.5 \cdot \left(y + \left(x - z\right)\right)}}} \]

   8. Taylor expanded in y around inf 40.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 40.9%

         \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]

      2. *-commutative 40.9%

         \[\leadsto \frac{\color{blue}{y \cdot 0.5}}{t} \]

      3. associate-*r/ 40.8%

         \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]

   10. Simplified 40.8%

       \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 50.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-160} \lor \neg \left(x \leq -3.4 \cdot 10^{-178}\right) \land x \leq -4.3 \cdot 10^{-243}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 46.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot -0.5}{t}\\ \mathbf{if}\;x \leq -6:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-243}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (* z -0.5) t)))
   (if (<= x -6.0)
     (* 0.5 (/ x t))
     (if (<= x -2.3e-161)
       t_1
       (if (<= x -5.2e-177)
         (* y (/ 0.5 t))
         (if (<= x -1.3e-243) t_1 (/ (* y 0.5) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (x <= -6.0) {
		tmp = 0.5 * (x / t);
	} else if (x <= -2.3e-161) {
		tmp = t_1;
	} else if (x <= -5.2e-177) {
		tmp = y * (0.5 / t);
	} else if (x <= -1.3e-243) {
		tmp = t_1;
	} else {
		tmp = (y * 0.5) / 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) :: t_1
    real(8) :: tmp
    t_1 = (z * (-0.5d0)) / t
    if (x <= (-6.0d0)) then
        tmp = 0.5d0 * (x / t)
    else if (x <= (-2.3d-161)) then
        tmp = t_1
    else if (x <= (-5.2d-177)) then
        tmp = y * (0.5d0 / t)
    else if (x <= (-1.3d-243)) then
        tmp = t_1
    else
        tmp = (y * 0.5d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * -0.5) / t;
	double tmp;
	if (x <= -6.0) {
		tmp = 0.5 * (x / t);
	} else if (x <= -2.3e-161) {
		tmp = t_1;
	} else if (x <= -5.2e-177) {
		tmp = y * (0.5 / t);
	} else if (x <= -1.3e-243) {
		tmp = t_1;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * -0.5) / t
	tmp = 0
	if x <= -6.0:
		tmp = 0.5 * (x / t)
	elif x <= -2.3e-161:
		tmp = t_1
	elif x <= -5.2e-177:
		tmp = y * (0.5 / t)
	elif x <= -1.3e-243:
		tmp = t_1
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * -0.5) / t)
	tmp = 0.0
	if (x <= -6.0)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (x <= -2.3e-161)
		tmp = t_1;
	elseif (x <= -5.2e-177)
		tmp = Float64(y * Float64(0.5 / t));
	elseif (x <= -1.3e-243)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * -0.5) / t;
	tmp = 0.0;
	if (x <= -6.0)
		tmp = 0.5 * (x / t);
	elseif (x <= -2.3e-161)
		tmp = t_1;
	elseif (x <= -5.2e-177)
		tmp = y * (0.5 / t);
	elseif (x <= -1.3e-243)
		tmp = t_1;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision]}, If[LessEqual[x, -6.0], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e-161], t$95$1, If[LessEqual[x, -5.2e-177], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e-243], t$95$1, N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 64.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]

   if -6 < x < -2.3e-161 or -5.2000000000000002e-177 < x < -1.2999999999999999e-243

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 58.1%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. *-commutative 58.1%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

      2. associate-*l/ 58.1%

         \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

   5. Simplified 58.1%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

   if -2.3e-161 < x < -5.2000000000000002e-177

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t} + 0.5 \cdot \frac{y - z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} + 0.5 \cdot \frac{y - z}{t} \]

      2. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot x} + 0.5 \cdot \frac{y - z}{t} \]

      3. associate-*r/ 100.0%

         \[\leadsto \frac{0.5}{t} \cdot x + \color{blue}{\frac{0.5 \cdot \left(y - z\right)}{t}} \]

      4. associate-*l/ 99.7%

         \[\leadsto \frac{0.5}{t} \cdot x + \color{blue}{\frac{0.5}{t} \cdot \left(y - z\right)} \]

      5. distribute-lft-in 99.7%

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(x + \left(y - z\right)\right)} \]

      6. associate-+r- 99.7%

         \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(\left(x + y\right) - z\right)} \]

      7. +-commutative 99.7%

         \[\leadsto \frac{0.5}{t} \cdot \left(\color{blue}{\left(y + x\right)} - z\right) \]

      8. associate--l+ 99.7%

         \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(y + \left(x - z\right)\right)} \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y + \left(x - z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y + \left(x - z\right)\right)}{t}} \]

      2. clear-num 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t}{0.5 \cdot \left(y + \left(x - z\right)\right)}}} \]

   7. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{t}{0.5 \cdot \left(y + \left(x - z\right)\right)}}} \]

   8. Taylor expanded in y around inf 86.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 86.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]

      2. *-commutative 86.0%

         \[\leadsto \frac{\color{blue}{y \cdot 0.5}}{t} \]

      3. associate-*r/ 86.0%

         \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]

   10. Simplified 86.0%

       \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]

   if -1.2999999999999999e-243 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 38.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 38.9%

         \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]

   5. Simplified 38.9%

      \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-161}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-243}:\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 46.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \frac{-0.5}{t}\\ \mathbf{if}\;x \leq -12:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-161}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-242}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* z (/ -0.5 t))))
   (if (<= x -12.0)
     (* 0.5 (/ x t))
     (if (<= x -5.2e-161)
       t_1
       (if (<= x -2.5e-178)
         (* y (/ 0.5 t))
         (if (<= x -1.5e-242) t_1 (/ (* y 0.5) t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = z * (-0.5 / t);
	double tmp;
	if (x <= -12.0) {
		tmp = 0.5 * (x / t);
	} else if (x <= -5.2e-161) {
		tmp = t_1;
	} else if (x <= -2.5e-178) {
		tmp = y * (0.5 / t);
	} else if (x <= -1.5e-242) {
		tmp = t_1;
	} else {
		tmp = (y * 0.5) / 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) :: t_1
    real(8) :: tmp
    t_1 = z * ((-0.5d0) / t)
    if (x <= (-12.0d0)) then
        tmp = 0.5d0 * (x / t)
    else if (x <= (-5.2d-161)) then
        tmp = t_1
    else if (x <= (-2.5d-178)) then
        tmp = y * (0.5d0 / t)
    else if (x <= (-1.5d-242)) then
        tmp = t_1
    else
        tmp = (y * 0.5d0) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = z * (-0.5 / t);
	double tmp;
	if (x <= -12.0) {
		tmp = 0.5 * (x / t);
	} else if (x <= -5.2e-161) {
		tmp = t_1;
	} else if (x <= -2.5e-178) {
		tmp = y * (0.5 / t);
	} else if (x <= -1.5e-242) {
		tmp = t_1;
	} else {
		tmp = (y * 0.5) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = z * (-0.5 / t)
	tmp = 0
	if x <= -12.0:
		tmp = 0.5 * (x / t)
	elif x <= -5.2e-161:
		tmp = t_1
	elif x <= -2.5e-178:
		tmp = y * (0.5 / t)
	elif x <= -1.5e-242:
		tmp = t_1
	else:
		tmp = (y * 0.5) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(z * Float64(-0.5 / t))
	tmp = 0.0
	if (x <= -12.0)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (x <= -5.2e-161)
		tmp = t_1;
	elseif (x <= -2.5e-178)
		tmp = Float64(y * Float64(0.5 / t));
	elseif (x <= -1.5e-242)
		tmp = t_1;
	else
		tmp = Float64(Float64(y * 0.5) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = z * (-0.5 / t);
	tmp = 0.0;
	if (x <= -12.0)
		tmp = 0.5 * (x / t);
	elseif (x <= -5.2e-161)
		tmp = t_1;
	elseif (x <= -2.5e-178)
		tmp = y * (0.5 / t);
	elseif (x <= -1.5e-242)
		tmp = t_1;
	else
		tmp = (y * 0.5) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -12.0], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.2e-161], t$95$1, If[LessEqual[x, -2.5e-178], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.5e-242], t$95$1, N[(N[(y * 0.5), $MachinePrecision] / t), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -12

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 64.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]

   if -12 < x < -5.19999999999999991e-161 or -2.49999999999999988e-178 < x < -1.5e-242

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 58.1%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. *-commutative 58.1%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

      2. associate-*l/ 58.1%

         \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

      3. associate-*r/ 58.0%

         \[\leadsto \color{blue}{z \cdot \frac{-0.5}{t}} \]

   5. Simplified 58.0%

      \[\leadsto \color{blue}{z \cdot \frac{-0.5}{t}} \]

   if -5.19999999999999991e-161 < x < -2.49999999999999988e-178

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t} + 0.5 \cdot \frac{y - z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 100.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} + 0.5 \cdot \frac{y - z}{t} \]

      2. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot x} + 0.5 \cdot \frac{y - z}{t} \]

      3. associate-*r/ 100.0%

         \[\leadsto \frac{0.5}{t} \cdot x + \color{blue}{\frac{0.5 \cdot \left(y - z\right)}{t}} \]

      4. associate-*l/ 99.7%

         \[\leadsto \frac{0.5}{t} \cdot x + \color{blue}{\frac{0.5}{t} \cdot \left(y - z\right)} \]

      5. distribute-lft-in 99.7%

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(x + \left(y - z\right)\right)} \]

      6. associate-+r- 99.7%

         \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(\left(x + y\right) - z\right)} \]

      7. +-commutative 99.7%

         \[\leadsto \frac{0.5}{t} \cdot \left(\color{blue}{\left(y + x\right)} - z\right) \]

      8. associate--l+ 99.7%

         \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(y + \left(x - z\right)\right)} \]

   5. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y + \left(x - z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y + \left(x - z\right)\right)}{t}} \]

      2. clear-num 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t}{0.5 \cdot \left(y + \left(x - z\right)\right)}}} \]

   7. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{t}{0.5 \cdot \left(y + \left(x - z\right)\right)}}} \]

   8. Taylor expanded in y around inf 86.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 86.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]

      2. *-commutative 86.0%

         \[\leadsto \frac{\color{blue}{y \cdot 0.5}}{t} \]

      3. associate-*r/ 86.0%

         \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]

   10. Simplified 86.0%

       \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]

   if -1.5e-242 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 38.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 38.9%

         \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]

   5. Simplified 38.9%

      \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-161}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-178}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-242}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot 0.5}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x - z}{t}\\ \mathbf{if}\;x \leq -3.7 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{+78}:\\ \;\;\;\;0.5 \cdot \left(\frac{y}{t} + \frac{x}{t}\right)\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ (- x z) t))))
   (if (<= x -3.7e+124)
     t_1
     (if (<= x -2.4e+78)
       (* 0.5 (+ (/ y t) (/ x t)))
       (if (<= x -4.2e-87) t_1 (/ (* 0.5 (- y z)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * ((x - z) / t);
	double tmp;
	if (x <= -3.7e+124) {
		tmp = t_1;
	} else if (x <= -2.4e+78) {
		tmp = 0.5 * ((y / t) + (x / t));
	} else if (x <= -4.2e-87) {
		tmp = t_1;
	} else {
		tmp = (0.5 * (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) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * ((x - z) / t)
    if (x <= (-3.7d+124)) then
        tmp = t_1
    else if (x <= (-2.4d+78)) then
        tmp = 0.5d0 * ((y / t) + (x / t))
    else if (x <= (-4.2d-87)) then
        tmp = t_1
    else
        tmp = (0.5d0 * (y - z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * ((x - z) / t);
	double tmp;
	if (x <= -3.7e+124) {
		tmp = t_1;
	} else if (x <= -2.4e+78) {
		tmp = 0.5 * ((y / t) + (x / t));
	} else if (x <= -4.2e-87) {
		tmp = t_1;
	} else {
		tmp = (0.5 * (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.5 * ((x - z) / t)
	tmp = 0
	if x <= -3.7e+124:
		tmp = t_1
	elif x <= -2.4e+78:
		tmp = 0.5 * ((y / t) + (x / t))
	elif x <= -4.2e-87:
		tmp = t_1
	else:
		tmp = (0.5 * (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.5 * Float64(Float64(x - z) / t))
	tmp = 0.0
	if (x <= -3.7e+124)
		tmp = t_1;
	elseif (x <= -2.4e+78)
		tmp = Float64(0.5 * Float64(Float64(y / t) + Float64(x / t)));
	elseif (x <= -4.2e-87)
		tmp = t_1;
	else
		tmp = Float64(Float64(0.5 * Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.5 * ((x - z) / t);
	tmp = 0.0;
	if (x <= -3.7e+124)
		tmp = t_1;
	elseif (x <= -2.4e+78)
		tmp = 0.5 * ((y / t) + (x / t));
	elseif (x <= -4.2e-87)
		tmp = t_1;
	else
		tmp = (0.5 * (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.7e+124], t$95$1, If[LessEqual[x, -2.4e+78], N[(0.5 * N[(N[(y / t), $MachinePrecision] + N[(x / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-87], t$95$1, N[(N[(0.5 * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.70000000000000008e124 or -2.3999999999999999e78 < x < -4.20000000000000014e-87

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x - z}{t}} \]

   if -3.70000000000000008e124 < x < -2.3999999999999999e78

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{y + x}}{t} \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y + x}{t}} \]

   6. Taylor expanded in y around 0 100.0%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{x}{t} + \frac{y}{t}\right)} \]
   7. Step-by-step derivation

      1. +-commutative 100.0%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{t} + \frac{x}{t}\right)} \]

   8. Simplified 100.0%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\frac{y}{t} + \frac{x}{t}\right)} \]

   if -4.20000000000000014e-87 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y - z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 77.6%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y - z\right)}{t}} \]

   5. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y - z\right)}{t}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 76.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x - z}{t}\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+77}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ (- x z) t))))
   (if (<= x -5.4e+124)
     t_1
     (if (<= x -1.05e+77)
       (* 0.5 (/ (+ x y) t))
       (if (<= x -3.4e-87) t_1 (/ (* 0.5 (- y z)) t))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * ((x - z) / t);
	double tmp;
	if (x <= -5.4e+124) {
		tmp = t_1;
	} else if (x <= -1.05e+77) {
		tmp = 0.5 * ((x + y) / t);
	} else if (x <= -3.4e-87) {
		tmp = t_1;
	} else {
		tmp = (0.5 * (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) :: t_1
    real(8) :: tmp
    t_1 = 0.5d0 * ((x - z) / t)
    if (x <= (-5.4d+124)) then
        tmp = t_1
    else if (x <= (-1.05d+77)) then
        tmp = 0.5d0 * ((x + y) / t)
    else if (x <= (-3.4d-87)) then
        tmp = t_1
    else
        tmp = (0.5d0 * (y - z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * ((x - z) / t);
	double tmp;
	if (x <= -5.4e+124) {
		tmp = t_1;
	} else if (x <= -1.05e+77) {
		tmp = 0.5 * ((x + y) / t);
	} else if (x <= -3.4e-87) {
		tmp = t_1;
	} else {
		tmp = (0.5 * (y - z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.5 * ((x - z) / t)
	tmp = 0
	if x <= -5.4e+124:
		tmp = t_1
	elif x <= -1.05e+77:
		tmp = 0.5 * ((x + y) / t)
	elif x <= -3.4e-87:
		tmp = t_1
	else:
		tmp = (0.5 * (y - z)) / t
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.5 * Float64(Float64(x - z) / t))
	tmp = 0.0
	if (x <= -5.4e+124)
		tmp = t_1;
	elseif (x <= -1.05e+77)
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	elseif (x <= -3.4e-87)
		tmp = t_1;
	else
		tmp = Float64(Float64(0.5 * Float64(y - z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.5 * ((x - z) / t);
	tmp = 0.0;
	if (x <= -5.4e+124)
		tmp = t_1;
	elseif (x <= -1.05e+77)
		tmp = 0.5 * ((x + y) / t);
	elseif (x <= -3.4e-87)
		tmp = t_1;
	else
		tmp = (0.5 * (y - z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e+124], t$95$1, If[LessEqual[x, -1.05e+77], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.4e-87], t$95$1, N[(N[(0.5 * N[(y - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.39999999999999956e124 or -1.0499999999999999e77 < x < -3.3999999999999999e-87

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x - z}{t}} \]

   if -5.39999999999999956e124 < x < -1.0499999999999999e77

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{y + x}}{t} \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y + x}{t}} \]

   if -3.3999999999999999e-87 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y - z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 77.6%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y - z\right)}{t}} \]

   5. Simplified 77.6%

      \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y - z\right)}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+124}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{+77}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-87}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5 \cdot \left(y - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.5 \cdot \frac{x - z}{t}\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{+77}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.5 (/ (- x z) t))))
   (if (<= x -6.2e+124)
     t_1
     (if (<= x -1.95e+77)
       (* 0.5 (/ (+ x y) t))
       (if (<= x -4.2e-87) t_1 (* (/ 0.5 t) (- y z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * ((x - z) / t);
	double tmp;
	if (x <= -6.2e+124) {
		tmp = t_1;
	} else if (x <= -1.95e+77) {
		tmp = 0.5 * ((x + y) / t);
	} else if (x <= -4.2e-87) {
		tmp = t_1;
	} else {
		tmp = (0.5 / t) * (y - z);
	}
	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 = 0.5d0 * ((x - z) / t)
    if (x <= (-6.2d+124)) then
        tmp = t_1
    else if (x <= (-1.95d+77)) then
        tmp = 0.5d0 * ((x + y) / t)
    else if (x <= (-4.2d-87)) then
        tmp = t_1
    else
        tmp = (0.5d0 / t) * (y - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.5 * ((x - z) / t);
	double tmp;
	if (x <= -6.2e+124) {
		tmp = t_1;
	} else if (x <= -1.95e+77) {
		tmp = 0.5 * ((x + y) / t);
	} else if (x <= -4.2e-87) {
		tmp = t_1;
	} else {
		tmp = (0.5 / t) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.5 * ((x - z) / t)
	tmp = 0
	if x <= -6.2e+124:
		tmp = t_1
	elif x <= -1.95e+77:
		tmp = 0.5 * ((x + y) / t)
	elif x <= -4.2e-87:
		tmp = t_1
	else:
		tmp = (0.5 / t) * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.5 * Float64(Float64(x - z) / t))
	tmp = 0.0
	if (x <= -6.2e+124)
		tmp = t_1;
	elseif (x <= -1.95e+77)
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	elseif (x <= -4.2e-87)
		tmp = t_1;
	else
		tmp = Float64(Float64(0.5 / t) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.5 * ((x - z) / t);
	tmp = 0.0;
	if (x <= -6.2e+124)
		tmp = t_1;
	elseif (x <= -1.95e+77)
		tmp = 0.5 * ((x + y) / t);
	elseif (x <= -4.2e-87)
		tmp = t_1;
	else
		tmp = (0.5 / t) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+124], t$95$1, If[LessEqual[x, -1.95e+77], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.2e-87], t$95$1, N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.2000000000000004e124 or -1.9499999999999999e77 < x < -4.20000000000000014e-87

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 83.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x - z}{t}} \]

   if -6.2000000000000004e124 < x < -1.9499999999999999e77

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{y + x}}{t} \]

   5. Simplified 99.9%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y + x}{t}} \]

   if -4.20000000000000014e-87 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y - z}{t}} \]
   4. Step-by-step derivation

      1. *-commutative 77.6%

         \[\leadsto \color{blue}{\frac{y - z}{t} \cdot 0.5} \]

      2. associate-*l/ 77.6%

         \[\leadsto \color{blue}{\frac{\left(y - z\right) \cdot 0.5}{t}} \]

      3. associate-*r/ 77.3%

         \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{0.5}{t}} \]

   5. Simplified 77.3%

      \[\leadsto \color{blue}{\left(y - z\right) \cdot \frac{0.5}{t}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+124}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{+77}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-87}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+130} \lor \neg \left(z \leq 2.3 \cdot 10^{+19}\right):\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.75e+130) (not (<= z 2.3e+19)))
   (* 0.5 (/ (- x z) t))
   (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.75e+130) || !(z <= 2.3e+19)) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((x + 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 <= (-1.75d+130)) .or. (.not. (z <= 2.3d+19))) then
        tmp = 0.5d0 * ((x - z) / t)
    else
        tmp = 0.5d0 * ((x + 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 <= -1.75e+130) || !(z <= 2.3e+19)) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.75e+130) or not (z <= 2.3e+19):
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * ((x + y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.75e+130) || !(z <= 2.3e+19))
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.75e+130) || ~((z <= 2.3e+19)))
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * ((x + y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.75e+130], N[Not[LessEqual[z, 2.3e+19]], $MachinePrecision]], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.75e130 or 2.3e19 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0 84.2%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x - z}{t}} \]

   if -1.75e130 < z < 2.3e19

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 89.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. +-commutative 89.0%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{y + x}}{t} \]

   5. Simplified 89.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y + x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+130} \lor \neg \left(z \leq 2.3 \cdot 10^{+19}\right):\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+147} \lor \neg \left(z \leq 9 \cdot 10^{+153}\right):\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.3e+147) (not (<= z 9e+153)))
   (/ (* z -0.5) t)
   (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.3e+147) || !(z <= 9e+153)) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = 0.5 * ((x + 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 <= (-1.3d+147)) .or. (.not. (z <= 9d+153))) then
        tmp = (z * (-0.5d0)) / t
    else
        tmp = 0.5d0 * ((x + 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 <= -1.3e+147) || !(z <= 9e+153)) {
		tmp = (z * -0.5) / t;
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.3e+147) or not (z <= 9e+153):
		tmp = (z * -0.5) / t
	else:
		tmp = 0.5 * ((x + y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.3e+147) || !(z <= 9e+153))
		tmp = Float64(Float64(z * -0.5) / t);
	else
		tmp = Float64(0.5 * Float64(Float64(x + y) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.3e+147) || ~((z <= 9e+153)))
		tmp = (z * -0.5) / t;
	else
		tmp = 0.5 * ((x + y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.3e+147], N[Not[LessEqual[z, 9e+153]], $MachinePrecision]], N[(N[(z * -0.5), $MachinePrecision] / t), $MachinePrecision], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2999999999999999e147 or 9.0000000000000002e153 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 78.8%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{z}{t}} \]
   4. Step-by-step derivation

      1. *-commutative 78.8%

         \[\leadsto \color{blue}{\frac{z}{t} \cdot -0.5} \]

      2. associate-*l/ 78.8%

         \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

   5. Simplified 78.8%

      \[\leadsto \color{blue}{\frac{z \cdot -0.5}{t}} \]

   if -1.2999999999999999e147 < z < 9.0000000000000002e153

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 85.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x + y}{t}} \]
   4. Step-by-step derivation

      1. +-commutative 85.5%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{y + x}}{t} \]

   5. Simplified 85.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y + x}{t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+147} \lor \neg \left(z \leq 9 \cdot 10^{+153}\right):\\ \;\;\;\;\frac{z \cdot -0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 44.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.02 \cdot 10^{-109}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.02e-109) (* 0.5 (/ x t)) (* y (/ 0.5 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.02e-109) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = y * (0.5 / 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 <= 1.02d-109) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = y * (0.5d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.02e-109) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = y * (0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.02e-109:
		tmp = 0.5 * (x / t)
	else:
		tmp = y * (0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.02e-109)
		tmp = Float64(0.5 * Float64(x / t));
	else
		tmp = Float64(y * Float64(0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.02e-109)
		tmp = 0.5 * (x / t);
	else
		tmp = y * (0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.02e-109], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(y * N[(0.5 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.02e-109

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 44.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]

   if 1.02e-109 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 97.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t} + 0.5 \cdot \frac{y - z}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 97.8%

         \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} + 0.5 \cdot \frac{y - z}{t} \]

      2. associate-*l/ 97.8%

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot x} + 0.5 \cdot \frac{y - z}{t} \]

      3. associate-*r/ 97.8%

         \[\leadsto \frac{0.5}{t} \cdot x + \color{blue}{\frac{0.5 \cdot \left(y - z\right)}{t}} \]

      4. associate-*l/ 97.5%

         \[\leadsto \frac{0.5}{t} \cdot x + \color{blue}{\frac{0.5}{t} \cdot \left(y - z\right)} \]

      5. distribute-lft-in 99.6%

         \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(x + \left(y - z\right)\right)} \]

      6. associate-+r- 99.6%

         \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(\left(x + y\right) - z\right)} \]

      7. +-commutative 99.6%

         \[\leadsto \frac{0.5}{t} \cdot \left(\color{blue}{\left(y + x\right)} - z\right) \]

      8. associate--l+ 99.6%

         \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(y + \left(x - z\right)\right)} \]

   5. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y + \left(x - z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{0.5 \cdot \left(y + \left(x - z\right)\right)}{t}} \]

      2. clear-num 99.7%

         \[\leadsto \color{blue}{\frac{1}{\frac{t}{0.5 \cdot \left(y + \left(x - z\right)\right)}}} \]

   7. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{1}{\frac{t}{0.5 \cdot \left(y + \left(x - z\right)\right)}}} \]

   8. Taylor expanded in y around inf 52.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{y}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 52.7%

         \[\leadsto \color{blue}{\frac{0.5 \cdot y}{t}} \]

      2. *-commutative 52.7%

         \[\leadsto \frac{\color{blue}{y \cdot 0.5}}{t} \]

      3. associate-*r/ 52.6%

         \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]

   10. Simplified 52.6%

       \[\leadsto \color{blue}{y \cdot \frac{0.5}{t}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 11: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{0.5}{t} \cdot \left(y + \left(x - z\right)\right) \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* (/ 0.5 t) (+ y (- x z))))

C

double code(double x, double y, double z, double t) {
	return (0.5 / t) * (y + (x - z));
}

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 = (0.5d0 / t) * (y + (x - z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (0.5 / t) * (y + (x - z));
}

Python

def code(x, y, z, t):
	return (0.5 / t) * (y + (x - z))

Julia

function code(x, y, z, t)
	return Float64(Float64(0.5 / t) * Float64(y + Float64(x - z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (0.5 / t) * (y + (x - z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(0.5 / t), $MachinePrecision] * N[(y + N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0 96.5%

   \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t} + 0.5 \cdot \frac{y - z}{t}} \]
4. Step-by-step derivation

   1. associate-*r/ 96.5%

      \[\leadsto \color{blue}{\frac{0.5 \cdot x}{t}} + 0.5 \cdot \frac{y - z}{t} \]

   2. associate-*l/ 96.3%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot x} + 0.5 \cdot \frac{y - z}{t} \]

   3. associate-*r/ 96.3%

      \[\leadsto \frac{0.5}{t} \cdot x + \color{blue}{\frac{0.5 \cdot \left(y - z\right)}{t}} \]

   4. associate-*l/ 96.1%

      \[\leadsto \frac{0.5}{t} \cdot x + \color{blue}{\frac{0.5}{t} \cdot \left(y - z\right)} \]

   5. distribute-lft-in 99.6%

      \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(x + \left(y - z\right)\right)} \]

   6. associate-+r- 99.6%

      \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(\left(x + y\right) - z\right)} \]

   7. +-commutative 99.6%

      \[\leadsto \frac{0.5}{t} \cdot \left(\color{blue}{\left(y + x\right)} - z\right) \]

   8. associate--l+ 99.6%

      \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(y + \left(x - z\right)\right)} \]

5. Simplified 99.6%

   \[\leadsto \color{blue}{\frac{0.5}{t} \cdot \left(y + \left(x - z\right)\right)} \]
6. Add Preprocessing

Alternative 12: 38.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \frac{x}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 0.5 (/ x t)))

C

double code(double x, double y, double z, double t) {
	return 0.5 * (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 = 0.5d0 * (x / t)
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.5 * (x / t);
}

Python

def code(x, y, z, t):
	return 0.5 * (x / t)

Julia

function code(x, y, z, t)
	return Float64(0.5 * Float64(x / t))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.5 * (x / t);
end

Wolfram

code[x_, y_, z_, t_] := N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 39.8%

   \[\leadsto \color{blue}{0.5 \cdot \frac{x}{t}} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, B"
  :precision binary64
  (/ (- (+ x y) z) (* t 2.0)))