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

Percentage Accurate: 99.9% → 99.7%

Time: 8.5s

Alternatives: 11

Speedup: N/A×

• 27.0% 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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. associate--l+ 99.6%

      \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

4. Taylor expanded in x around 0 95.3%

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

   1. +-commutative 95.3%

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

   2. associate-*r/ 95.7%

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

   3. associate-*l/ 95.6%

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

   4. associate-*r/ 95.6%

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

   5. associate-*l/ 95.5%

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

   6. distribute-lft-out 99.8%

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

6. Simplified 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 47.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-205} \lor \neg \left(x \leq 4.4 \cdot 10^{-307}\right) \land x \leq 6 \cdot 10^{-230}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.2e+23)
   (* 0.5 (/ x t))
   (if (or (<= x -2.5e-205) (and (not (<= x 4.4e-307)) (<= x 6e-230)))
     (* z (/ -0.5 t))
     (/ 0.5 (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.2e+23) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -2.5e-205) || (!(x <= 4.4e-307) && (x <= 6e-230))) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 / (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 (x <= (-7.2d+23)) then
        tmp = 0.5d0 * (x / t)
    else if ((x <= (-2.5d-205)) .or. (.not. (x <= 4.4d-307)) .and. (x <= 6d-230)) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = 0.5d0 / (t / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.2e+23) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -2.5e-205) || (!(x <= 4.4e-307) && (x <= 6e-230))) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 / (t / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.2e+23:
		tmp = 0.5 * (x / t)
	elif (x <= -2.5e-205) or (not (x <= 4.4e-307) and (x <= 6e-230)):
		tmp = z * (-0.5 / t)
	else:
		tmp = 0.5 / (t / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.2e+23)
		tmp = Float64(0.5 * Float64(x / t));
	elseif ((x <= -2.5e-205) || (!(x <= 4.4e-307) && (x <= 6e-230)))
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(0.5 / Float64(t / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.2e+23)
		tmp = 0.5 * (x / t);
	elseif ((x <= -2.5e-205) || (~((x <= 4.4e-307)) && (x <= 6e-230)))
		tmp = z * (-0.5 / t);
	else
		tmp = 0.5 / (t / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.2e+23], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -2.5e-205], And[N[Not[LessEqual[x, 4.4e-307]], $MachinePrecision], LessEqual[x, 6e-230]]], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 / N[(t / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.1999999999999997e23

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around inf 64.6%

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

   if -7.1999999999999997e23 < x < -2.5e-205 or 4.4e-307 < x < 6e-230

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in z around inf 52.2%

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

      1. associate-*r/ 53.4%

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

      2. associate-/l* 53.2%

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

   6. Simplified 53.2%

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

      1. associate-/r/ 53.4%

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

   8. Applied egg-rr 53.4%

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

   if -2.5e-205 < x < 4.4e-307 or 6e-230 < x

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around 0 97.1%

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

      1. +-commutative 97.1%

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

      2. associate-*r/ 97.1%

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

      3. associate-*l/ 97.0%

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

      4. associate-*r/ 97.0%

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

      5. associate-*l/ 96.9%

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

      6. distribute-lft-out 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 73.9%

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

      1. associate-/r/ 73.7%

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

   9. Applied egg-rr 73.7%

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

   10. Taylor expanded in y around inf 41.3%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+23}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-205} \lor \neg \left(x \leq 4.4 \cdot 10^{-307}\right) \land x \leq 6 \cdot 10^{-230}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\frac{t}{y}}\\ \end{array} \]

Alternative 3: 47.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+23}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-206} \lor \neg \left(x \leq -1.45 \cdot 10^{-301}\right) \land x \leq 8.2 \cdot 10^{-227}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.2e+23)
   (* 0.5 (/ x t))
   (if (or (<= x -1.56e-206) (and (not (<= x -1.45e-301)) (<= x 8.2e-227)))
     (* z (/ -0.5 t))
     (/ y (* t 2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2e+23) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -1.56e-206) || (!(x <= -1.45e-301) && (x <= 8.2e-227))) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y / (t * 2.0);
	}
	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 <= (-6.2d+23)) then
        tmp = 0.5d0 * (x / t)
    else if ((x <= (-1.56d-206)) .or. (.not. (x <= (-1.45d-301))) .and. (x <= 8.2d-227)) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = y / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2e+23) {
		tmp = 0.5 * (x / t);
	} else if ((x <= -1.56e-206) || (!(x <= -1.45e-301) && (x <= 8.2e-227))) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = y / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.2e+23:
		tmp = 0.5 * (x / t)
	elif (x <= -1.56e-206) or (not (x <= -1.45e-301) and (x <= 8.2e-227)):
		tmp = z * (-0.5 / t)
	else:
		tmp = y / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.2e+23)
		tmp = Float64(0.5 * Float64(x / t));
	elseif ((x <= -1.56e-206) || (!(x <= -1.45e-301) && (x <= 8.2e-227)))
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(y / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.2e+23)
		tmp = 0.5 * (x / t);
	elseif ((x <= -1.56e-206) || (~((x <= -1.45e-301)) && (x <= 8.2e-227)))
		tmp = z * (-0.5 / t);
	else
		tmp = y / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.2e+23], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.56e-206], And[N[Not[LessEqual[x, -1.45e-301]], $MachinePrecision], LessEqual[x, 8.2e-227]]], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.19999999999999941e23

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around inf 64.6%

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

   if -6.19999999999999941e23 < x < -1.56000000000000008e-206 or -1.44999999999999992e-301 < x < 8.20000000000000018e-227

   1. Initial program 98.5%

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

      1. associate--l+ 98.5%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 98.5%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in z around inf 52.9%

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

      1. associate-*r/ 54.1%

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

      2. associate-/l* 53.9%

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

   6. Simplified 53.9%

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

      1. associate-/r/ 54.0%

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

   8. Applied egg-rr 54.0%

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

   if -1.56000000000000008e-206 < x < -1.44999999999999992e-301 or 8.20000000000000018e-227 < x

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in y around inf 41.5%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+23}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -1.56 \cdot 10^{-206} \lor \neg \left(x \leq -1.45 \cdot 10^{-301}\right) \land x \leq 8.2 \cdot 10^{-227}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \end{array} \]

Alternative 4: 47.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+23}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{\frac{z}{-2}}{t}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-302} \lor \neg \left(x \leq 1.02 \cdot 10^{-225}\right):\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.2e+23)
   (* 0.5 (/ x t))
   (if (<= x -9.5e-204)
     (/ (/ z -2.0) t)
     (if (or (<= x 3.5e-302) (not (<= x 1.02e-225)))
       (/ y (* t 2.0))
       (* z (/ -0.5 t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2e+23) {
		tmp = 0.5 * (x / t);
	} else if (x <= -9.5e-204) {
		tmp = (z / -2.0) / t;
	} else if ((x <= 3.5e-302) || !(x <= 1.02e-225)) {
		tmp = y / (t * 2.0);
	} else {
		tmp = z * (-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 <= (-6.2d+23)) then
        tmp = 0.5d0 * (x / t)
    else if (x <= (-9.5d-204)) then
        tmp = (z / (-2.0d0)) / t
    else if ((x <= 3.5d-302) .or. (.not. (x <= 1.02d-225))) then
        tmp = y / (t * 2.0d0)
    else
        tmp = z * ((-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 <= -6.2e+23) {
		tmp = 0.5 * (x / t);
	} else if (x <= -9.5e-204) {
		tmp = (z / -2.0) / t;
	} else if ((x <= 3.5e-302) || !(x <= 1.02e-225)) {
		tmp = y / (t * 2.0);
	} else {
		tmp = z * (-0.5 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.2e+23:
		tmp = 0.5 * (x / t)
	elif x <= -9.5e-204:
		tmp = (z / -2.0) / t
	elif (x <= 3.5e-302) or not (x <= 1.02e-225):
		tmp = y / (t * 2.0)
	else:
		tmp = z * (-0.5 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.2e+23)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (x <= -9.5e-204)
		tmp = Float64(Float64(z / -2.0) / t);
	elseif ((x <= 3.5e-302) || !(x <= 1.02e-225))
		tmp = Float64(y / Float64(t * 2.0));
	else
		tmp = Float64(z * Float64(-0.5 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.2e+23)
		tmp = 0.5 * (x / t);
	elseif (x <= -9.5e-204)
		tmp = (z / -2.0) / t;
	elseif ((x <= 3.5e-302) || ~((x <= 1.02e-225)))
		tmp = y / (t * 2.0);
	else
		tmp = z * (-0.5 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.2e+23], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -9.5e-204], N[(N[(z / -2.0), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[x, 3.5e-302], N[Not[LessEqual[x, 1.02e-225]], $MachinePrecision]], N[(y / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -6.19999999999999941e23

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around inf 64.6%

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

   if -6.19999999999999941e23 < x < -9.50000000000000063e-204

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in z around inf 53.7%

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

      1. associate-*r/ 53.7%

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

      2. associate-/l* 53.5%

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

   6. Simplified 53.5%

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

      1. associate-/r/ 53.6%

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

   8. Applied egg-rr 53.6%

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

      1. associate-/r/ 53.5%

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

      2. div-inv 53.5%

         \[\leadsto \color{blue}{-0.5 \cdot \frac{1}{\frac{t}{z}}} \]

      3. metadata-eval 53.5%

         \[\leadsto \color{blue}{\frac{1}{-2}} \cdot \frac{1}{\frac{t}{z}} \]

      4. metadata-eval 53.5%

         \[\leadsto \frac{1}{\color{blue}{-2}} \cdot \frac{1}{\frac{t}{z}} \]

      5. clear-num 53.7%

         \[\leadsto \frac{1}{-2} \cdot \color{blue}{\frac{z}{t}} \]

      6. times-frac 53.7%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\left(-2\right) \cdot t}} \]

      7. *-lft-identity 53.7%

         \[\leadsto \frac{\color{blue}{z}}{\left(-2\right) \cdot t} \]

      8. associate-/r* 53.7%

         \[\leadsto \color{blue}{\frac{\frac{z}{-2}}{t}} \]

      9. metadata-eval 53.7%

         \[\leadsto \frac{\frac{z}{\color{blue}{-2}}}{t} \]

   10. Applied egg-rr 53.7%

       \[\leadsto \color{blue}{\frac{\frac{z}{-2}}{t}} \]

   if -9.50000000000000063e-204 < x < 3.5000000000000001e-302 or 1.01999999999999995e-225 < x

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in y around inf 40.7%

      \[\leadsto \frac{\color{blue}{y}}{t \cdot 2} \]

   if 3.5000000000000001e-302 < x < 1.01999999999999995e-225

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in z around inf 47.8%

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

      1. associate-*r/ 52.8%

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

      2. associate-/l* 52.4%

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

   6. Simplified 52.4%

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

      1. associate-/r/ 52.8%

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

   8. Applied egg-rr 52.8%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+23}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{-204}:\\ \;\;\;\;\frac{\frac{z}{-2}}{t}\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-302} \lor \neg \left(x \leq 1.02 \cdot 10^{-225}\right):\\ \;\;\;\;\frac{y}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \end{array} \]

Alternative 5: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+32} \lor \neg \left(z \leq 9.5 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y + x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e+32) (not (<= z 9.5e-23)))
   (* (/ 0.5 t) (- y z))
   (* (/ 0.5 t) (+ y x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+32) || !(z <= 9.5e-23)) {
		tmp = (0.5 / t) * (y - z);
	} else {
		tmp = (0.5 / t) * (y + 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 ((z <= (-3.1d+32)) .or. (.not. (z <= 9.5d-23))) then
        tmp = (0.5d0 / t) * (y - z)
    else
        tmp = (0.5d0 / t) * (y + x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e+32) || !(z <= 9.5e-23)) {
		tmp = (0.5 / t) * (y - z);
	} else {
		tmp = (0.5 / t) * (y + x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e+32) or not (z <= 9.5e-23):
		tmp = (0.5 / t) * (y - z)
	else:
		tmp = (0.5 / t) * (y + x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e+32) || !(z <= 9.5e-23))
		tmp = Float64(Float64(0.5 / t) * Float64(y - z));
	else
		tmp = Float64(Float64(0.5 / t) * Float64(y + x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.1e+32) || ~((z <= 9.5e-23)))
		tmp = (0.5 / t) * (y - z);
	else
		tmp = (0.5 / t) * (y + x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e+32], N[Not[LessEqual[z, 9.5e-23]], $MachinePrecision]], N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / t), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.09999999999999993e32 or 9.50000000000000058e-23 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around 0 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-*r/ 92.4%

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

      3. associate-*l/ 92.3%

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

      4. associate-*r/ 92.3%

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

      5. associate-*l/ 92.2%

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

      6. distribute-lft-out 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 87.8%

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

   if -3.09999999999999993e32 < z < 9.50000000000000058e-23

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around 0 98.5%

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

      1. +-commutative 98.5%

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

      2. associate-*r/ 98.5%

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

      3. associate-*l/ 98.4%

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

      4. associate-*r/ 98.4%

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

      5. associate-*l/ 98.3%

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

      6. distribute-lft-out 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around 0 94.7%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+32} \lor \neg \left(z \leq 9.5 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y + x\right)\\ \end{array} \]

Alternative 6: 81.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+88}:\\ \;\;\;\;\frac{\frac{z}{-2}}{t}\\ \mathbf{elif}\;z \leq 10^{+108}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.3e+88)
   (/ (/ z -2.0) t)
   (if (<= z 1e+108) (* (/ 0.5 t) (+ y x)) (* (/ z t) -0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.3e+88) {
		tmp = (z / -2.0) / t;
	} else if (z <= 1e+108) {
		tmp = (0.5 / t) * (y + x);
	} else {
		tmp = (z / t) * -0.5;
	}
	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 <= (-5.3d+88)) then
        tmp = (z / (-2.0d0)) / t
    else if (z <= 1d+108) then
        tmp = (0.5d0 / t) * (y + x)
    else
        tmp = (z / t) * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.3e+88) {
		tmp = (z / -2.0) / t;
	} else if (z <= 1e+108) {
		tmp = (0.5 / t) * (y + x);
	} else {
		tmp = (z / t) * -0.5;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.3e+88:
		tmp = (z / -2.0) / t
	elif z <= 1e+108:
		tmp = (0.5 / t) * (y + x)
	else:
		tmp = (z / t) * -0.5
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.3e+88)
		tmp = Float64(Float64(z / -2.0) / t);
	elseif (z <= 1e+108)
		tmp = Float64(Float64(0.5 / t) * Float64(y + x));
	else
		tmp = Float64(Float64(z / t) * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.3e+88)
		tmp = (z / -2.0) / t;
	elseif (z <= 1e+108)
		tmp = (0.5 / t) * (y + x);
	else
		tmp = (z / t) * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.3e+88], N[(N[(z / -2.0), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[z, 1e+108], N[(N[(0.5 / t), $MachinePrecision] * N[(y + x), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.29999999999999987e88

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in z around inf 85.7%

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

      1. associate-*r/ 87.7%

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

      2. associate-/l* 87.3%

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

   6. Simplified 87.3%

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

      1. associate-/r/ 87.5%

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

   8. Applied egg-rr 87.5%

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

      1. associate-/r/ 87.3%

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

      2. div-inv 85.4%

         \[\leadsto \color{blue}{-0.5 \cdot \frac{1}{\frac{t}{z}}} \]

      3. metadata-eval 85.4%

         \[\leadsto \color{blue}{\frac{1}{-2}} \cdot \frac{1}{\frac{t}{z}} \]

      4. metadata-eval 85.4%

         \[\leadsto \frac{1}{\color{blue}{-2}} \cdot \frac{1}{\frac{t}{z}} \]

      5. clear-num 85.7%

         \[\leadsto \frac{1}{-2} \cdot \color{blue}{\frac{z}{t}} \]

      6. times-frac 87.7%

         \[\leadsto \color{blue}{\frac{1 \cdot z}{\left(-2\right) \cdot t}} \]

      7. *-lft-identity 87.7%

         \[\leadsto \frac{\color{blue}{z}}{\left(-2\right) \cdot t} \]

      8. associate-/r* 87.7%

         \[\leadsto \color{blue}{\frac{\frac{z}{-2}}{t}} \]

      9. metadata-eval 87.7%

         \[\leadsto \frac{\frac{z}{\color{blue}{-2}}}{t} \]

   10. Applied egg-rr 87.7%

       \[\leadsto \color{blue}{\frac{\frac{z}{-2}}{t}} \]

   if -5.29999999999999987e88 < z < 1e108

   1. Initial program 99.4%

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

      1. associate--l+ 99.4%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around 0 95.9%

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

      1. +-commutative 95.9%

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

      2. associate-*r/ 95.9%

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

      3. associate-*l/ 95.8%

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

      4. associate-*r/ 95.9%

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

      5. associate-*l/ 95.8%

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

      6. distribute-lft-out 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in z around 0 88.5%

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

   if 1e108 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in z around inf 83.6%

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

      1. *-commutative 83.6%

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

   6. Simplified 83.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{+88}:\\ \;\;\;\;\frac{\frac{z}{-2}}{t}\\ \mathbf{elif}\;z \leq 10^{+108}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y + x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \end{array} \]

Alternative 7: 68.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ y x) -5e-130) (/ (- x z) (* t 2.0)) (* (/ 0.5 t) (- y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y + x) <= -5e-130) {
		tmp = (x - z) / (t * 2.0);
	} 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) :: tmp
    if ((y + x) <= (-5d-130)) then
        tmp = (x - z) / (t * 2.0d0)
    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 tmp;
	if ((y + x) <= -5e-130) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (0.5 / t) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y + x) <= -5e-130:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (0.5 / t) * (y - z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y + x) <= -5e-130)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(0.5 / t) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y + x) <= -5e-130)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (0.5 / t) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y + x), $MachinePrecision], -5e-130], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / t), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.9999999999999996e-130

   1. Initial program 99.1%

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

      1. associate--l+ 99.1%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in y around 0 60.7%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if -4.9999999999999996e-130 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around 0 95.1%

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

      1. +-commutative 95.1%

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

      2. associate-*r/ 95.7%

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

      3. associate-*l/ 95.6%

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

      4. associate-*r/ 95.6%

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

      5. associate-*l/ 95.6%

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

      6. distribute-lft-out 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around 0 74.2%

      \[\leadsto \frac{0.5}{t} \cdot \color{blue}{\left(y - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(y - z\right)\\ \end{array} \]

Alternative 8: 68.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (+ y x) -5e-130) (/ (- x z) (* t 2.0)) (/ (- y z) (* t 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y + x) <= -5e-130) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	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 + x) <= (-5d-130)) then
        tmp = (x - z) / (t * 2.0d0)
    else
        tmp = (y - z) / (t * 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y + x) <= -5e-130) {
		tmp = (x - z) / (t * 2.0);
	} else {
		tmp = (y - z) / (t * 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y + x) <= -5e-130:
		tmp = (x - z) / (t * 2.0)
	else:
		tmp = (y - z) / (t * 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(y + x) <= -5e-130)
		tmp = Float64(Float64(x - z) / Float64(t * 2.0));
	else
		tmp = Float64(Float64(y - z) / Float64(t * 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y + x) <= -5e-130)
		tmp = (x - z) / (t * 2.0);
	else
		tmp = (y - z) / (t * 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(y + x), $MachinePrecision], -5e-130], N[(N[(x - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(y - z), $MachinePrecision] / N[(t * 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x y) < -4.9999999999999996e-130

   1. Initial program 99.1%

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

      1. associate--l+ 99.1%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.1%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in y around 0 60.7%

      \[\leadsto \frac{\color{blue}{x - z}}{t \cdot 2} \]

   if -4.9999999999999996e-130 < (+.f64 x y)

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around 0 74.3%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y + x \leq -5 \cdot 10^{-130}:\\ \;\;\;\;\frac{x - z}{t \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - z}{t \cdot 2}\\ \end{array} \]

Alternative 9: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+30} \lor \neg \left(z \leq 3.7 \cdot 10^{-21}\right):\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7e+30) (not (<= z 3.7e-21))) (* z (/ -0.5 t)) (* 0.5 (/ x t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7e+30) || !(z <= 3.7e-21)) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 * (x / 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 <= (-7d+30)) .or. (.not. (z <= 3.7d-21))) then
        tmp = z * ((-0.5d0) / t)
    else
        tmp = 0.5d0 * (x / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7e+30) || !(z <= 3.7e-21)) {
		tmp = z * (-0.5 / t);
	} else {
		tmp = 0.5 * (x / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7e+30) or not (z <= 3.7e-21):
		tmp = z * (-0.5 / t)
	else:
		tmp = 0.5 * (x / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7e+30) || !(z <= 3.7e-21))
		tmp = Float64(z * Float64(-0.5 / t));
	else
		tmp = Float64(0.5 * Float64(x / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7e+30) || ~((z <= 3.7e-21)))
		tmp = z * (-0.5 / t);
	else
		tmp = 0.5 * (x / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7e+30], N[Not[LessEqual[z, 3.7e-21]], $MachinePrecision]], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.00000000000000042e30 or 3.7000000000000002e-21 < z

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in z around inf 70.6%

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

      1. associate-*r/ 71.3%

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

      2. associate-/l* 71.0%

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

   6. Simplified 71.0%

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

      1. associate-/r/ 71.1%

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

   8. Applied egg-rr 71.1%

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

   if -7.00000000000000042e30 < z < 3.7000000000000002e-21

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around inf 49.9%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+30} \lor \neg \left(z \leq 3.7 \cdot 10^{-21}\right):\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \end{array} \]

Alternative 10: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-27}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.6e+30)
   (* z (/ -0.5 t))
   (if (<= z 1.5e-27) (* 0.5 (/ x t)) (* (/ z t) -0.5))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.6e+30) {
		tmp = z * (-0.5 / t);
	} else if (z <= 1.5e-27) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = (z / t) * -0.5;
	}
	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 <= (-8.6d+30)) then
        tmp = z * ((-0.5d0) / t)
    else if (z <= 1.5d-27) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = (z / t) * (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.6e+30) {
		tmp = z * (-0.5 / t);
	} else if (z <= 1.5e-27) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = (z / t) * -0.5;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.6e+30:
		tmp = z * (-0.5 / t)
	elif z <= 1.5e-27:
		tmp = 0.5 * (x / t)
	else:
		tmp = (z / t) * -0.5
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.6e+30)
		tmp = Float64(z * Float64(-0.5 / t));
	elseif (z <= 1.5e-27)
		tmp = Float64(0.5 * Float64(x / t));
	else
		tmp = Float64(Float64(z / t) * -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.6e+30)
		tmp = z * (-0.5 / t);
	elseif (z <= 1.5e-27)
		tmp = 0.5 * (x / t);
	else
		tmp = (z / t) * -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.6e+30], N[(z * N[(-0.5 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.5e-27], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(N[(z / t), $MachinePrecision] * -0.5), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.6e30

   1. Initial program 100.0%

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

      1. associate--l+ 100.0%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in z around inf 78.5%

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

      1. associate-*r/ 80.1%

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

      2. associate-/l* 79.7%

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

   6. Simplified 79.7%

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

      1. associate-/r/ 79.9%

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

   8. Applied egg-rr 79.9%

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

   if -8.6e30 < z < 1.5000000000000001e-27

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in x around inf 49.9%

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

   if 1.5000000000000001e-27 < z

   1. Initial program 99.9%

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

      1. associate--l+ 99.9%

         \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

   4. Taylor expanded in z around inf 65.1%

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

      1. *-commutative 65.1%

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

   6. Simplified 65.1%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.6 \cdot 10^{+30}:\\ \;\;\;\;z \cdot \frac{-0.5}{t}\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-27}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{t} \cdot -0.5\\ \end{array} \]

Alternative 11: 37.1% 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 99.6%

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

   1. associate--l+ 99.6%

      \[\leadsto \frac{\color{blue}{x + \left(y - z\right)}}{t \cdot 2} \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\frac{x + \left(y - z\right)}{t \cdot 2}} \]

4. Taylor expanded in x around inf 36.0%

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

5. Final simplification 36.0%

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

Reproduce

herbie shell --seed 2023297 
(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)))