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

Percentage Accurate: 99.9% → 99.9%

Time: 5.6s

Alternatives: 8

Speedup: 1.0×

• Unsound rule application detected in e-graph. Results may not be sound.

• 26.5% 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. Final simplification 100.0%

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

Alternative 2: 82.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+133} \lor \neg \left(z \leq 1.2 \cdot 10^{+117}\right):\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2e+133) (not (<= z 1.2e+117)))
   (/ z (/ t -0.5))
   (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2e+133) || !(z <= 1.2e+117)) {
		tmp = z / (t / -0.5);
	} 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 <= (-2d+133)) .or. (.not. (z <= 1.2d+117))) then
        tmp = z / (t / (-0.5d0))
    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 <= -2e+133) || !(z <= 1.2e+117)) {
		tmp = z / (t / -0.5);
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2e+133) or not (z <= 1.2e+117):
		tmp = z / (t / -0.5)
	else:
		tmp = 0.5 * ((x + y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2e+133) || !(z <= 1.2e+117))
		tmp = Float64(z / Float64(t / -0.5));
	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 <= -2e+133) || ~((z <= 1.2e+117)))
		tmp = z / (t / -0.5);
	else
		tmp = 0.5 * ((x + y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2e+133], N[Not[LessEqual[z, 1.2e+117]], $MachinePrecision]], N[(z / N[(t / -0.5), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2e133 or 1.1999999999999999e117 < z

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.8%

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

      8. *-commutative 99.8%

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

      9. associate-/r* 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 82.2%

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

      1. *-commutative 82.2%

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

      2. associate-/r/ 82.2%

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

   6. Simplified 82.2%

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

   if -2e133 < z < 1.1999999999999999e117

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 85.4%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+133} \lor \neg \left(z \leq 1.2 \cdot 10^{+117}\right):\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]

Alternative 3: 46.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-285}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+14}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.5e-285)
   (* 0.5 (/ x t))
   (if (<= y 5.6e+14) (/ z (/ t -0.5)) (* 0.5 (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-285) {
		tmp = 0.5 * (x / t);
	} else if (y <= 5.6e+14) {
		tmp = z / (t / -0.5);
	} else {
		tmp = 0.5 * (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 (y <= (-3.5d-285)) then
        tmp = 0.5d0 * (x / t)
    else if (y <= 5.6d+14) then
        tmp = z / (t / (-0.5d0))
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.5e-285) {
		tmp = 0.5 * (x / t);
	} else if (y <= 5.6e+14) {
		tmp = z / (t / -0.5);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.5e-285:
		tmp = 0.5 * (x / t)
	elif y <= 5.6e+14:
		tmp = z / (t / -0.5)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.5e-285)
		tmp = Float64(0.5 * Float64(x / t));
	elseif (y <= 5.6e+14)
		tmp = Float64(z / Float64(t / -0.5));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.5e-285)
		tmp = 0.5 * (x / t);
	elseif (y <= 5.6e+14)
		tmp = z / (t / -0.5);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.5e-285], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+14], N[(z / N[(t / -0.5), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000004e-285

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 37.0%

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

   if -3.5000000000000004e-285 < y < 5.6e14

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 42.9%

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

      1. *-commutative 42.9%

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

      2. associate-/r/ 44.0%

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

   6. Simplified 44.0%

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

   if 5.6e14 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 78.2%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-285}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+14}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 4.1e+14) (* 0.5 (/ (- x z) t)) (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 4.1e+14) {
		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 (y <= 4.1d+14) 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 (y <= 4.1e+14) {
		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 y <= 4.1e+14:
		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 (y <= 4.1e+14)
		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 (y <= 4.1e+14)
		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[LessEqual[y, 4.1e+14], 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 y < 4.1e14

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.6%

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

   if 4.1e14 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 93.5%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]

Alternative 5: 77.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.5e+14) (* (/ 0.5 t) (- x z)) (* 0.5 (/ (+ x y) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.5e+14) {
		tmp = (0.5 / t) * (x - z);
	} 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 (y <= 1.5d+14) then
        tmp = (0.5d0 / t) * (x - z)
    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 (y <= 1.5e+14) {
		tmp = (0.5 / t) * (x - z);
	} else {
		tmp = 0.5 * ((x + y) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.5e+14:
		tmp = (0.5 / t) * (x - z)
	else:
		tmp = 0.5 * ((x + y) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.5e+14)
		tmp = Float64(Float64(0.5 / t) * Float64(x - z));
	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 (y <= 1.5e+14)
		tmp = (0.5 / t) * (x - z);
	else
		tmp = 0.5 * ((x + y) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.5e+14], N[(N[(0.5 / t), $MachinePrecision] * N[(x - z), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x + y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.5e14

   1. Initial program 100.0%

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

      1. div-sub 97.4%

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

      2. div-inv 97.2%

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

      3. *-commutative 97.2%

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

      4. associate-/r* 97.2%

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

      5. metadata-eval 97.2%

         \[\leadsto \left(x + y\right) \cdot \frac{\color{blue}{0.5}}{t} - \frac{z}{t \cdot 2} \]

      6. div-inv 97.2%

         \[\leadsto \left(x + y\right) \cdot \frac{0.5}{t} - \color{blue}{z \cdot \frac{1}{t \cdot 2}} \]

      7. *-commutative 97.2%

         \[\leadsto \left(x + y\right) \cdot \frac{0.5}{t} - z \cdot \frac{1}{\color{blue}{2 \cdot t}} \]

      8. associate-/r* 97.2%

         \[\leadsto \left(x + y\right) \cdot \frac{0.5}{t} - z \cdot \color{blue}{\frac{\frac{1}{2}}{t}} \]

      9. metadata-eval 97.2%

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

   3. Applied egg-rr 97.2%

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

   4. Taylor expanded in y around 0 75.5%

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

      1. distribute-lft-out-- 75.5%

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

      2. div-sub 77.6%

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

      3. associate-*r/ 77.9%

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

      4. associate-*l/ 77.7%

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

   6. Simplified 77.7%

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

   if 1.5e14 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 93.5%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{0.5}{t} \cdot \left(x - z\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + y}{t}\\ \end{array} \]

Alternative 6: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * (z - (x + y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

   4. associate-+l- 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   5. sub0-neg 100.0%

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

   6. neg-mul-1 100.0%

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

   7. associate-*l/ 99.7%

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

   8. *-commutative 99.7%

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

   9. associate-/r* 99.7%

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

   10. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 7: 45.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{-12}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 3.5e-12) (* 0.5 (/ x t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.5e-12) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (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 (y <= 3.5d-12) then
        tmp = 0.5d0 * (x / t)
    else
        tmp = 0.5d0 * (y / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 3.5e-12) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 3.5e-12:
		tmp = 0.5 * (x / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 3.5e-12)
		tmp = Float64(0.5 * Float64(x / t));
	else
		tmp = Float64(0.5 * Float64(y / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 3.5e-12)
		tmp = 0.5 * (x / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 3.5e-12], N[(0.5 * N[(x / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.5e-12

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 41.3%

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

   if 3.5e-12 < y

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. neg-sub0 100.0%

         \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

      5. sub0-neg 100.0%

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

      6. neg-mul-1 100.0%

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

      7. associate-*l/ 99.7%

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

      8. *-commutative 99.7%

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

      9. associate-/r* 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 71.0%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.5 \cdot 10^{-12}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 8: 36.7% 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. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - z\right)} + \left(x + y\right)}{t \cdot 2} \]

   4. associate-+l- 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(z - \left(x + y\right)\right)}}{t \cdot 2} \]

   5. sub0-neg 100.0%

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

   6. neg-mul-1 100.0%

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

   7. associate-*l/ 99.7%

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

   8. *-commutative 99.7%

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

   9. associate-/r* 99.7%

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

   10. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around inf 37.3%

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

5. Final simplification 37.3%

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

Reproduce

herbie shell --seed 2023174 
(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)))