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

Percentage Accurate: 100.0% → 100.0%

Time: 6.0s

Alternatives: 12

Speedup: 1.0×

• 26.3% 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: 100.0% 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: 100.0% 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: 75.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.22 \cdot 10^{+46} \lor \neg \left(y \leq 4.4 \cdot 10^{+86}\right) \land y \leq 7.8 \cdot 10^{+97}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y 1.22e+46) (and (not (<= y 4.4e+86)) (<= y 7.8e+97)))
   (* 0.5 (/ (- x z) t))
   (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= 1.22e+46) || (!(y <= 4.4e+86) && (y <= 7.8e+97))) {
		tmp = 0.5 * ((x - z) / 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 <= 1.22d+46) .or. (.not. (y <= 4.4d+86)) .and. (y <= 7.8d+97)) then
        tmp = 0.5d0 * ((x - z) / 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 <= 1.22e+46) || (!(y <= 4.4e+86) && (y <= 7.8e+97))) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= 1.22e+46) or (not (y <= 4.4e+86) and (y <= 7.8e+97)):
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= 1.22e+46) || (!(y <= 4.4e+86) && (y <= 7.8e+97)))
		tmp = Float64(0.5 * Float64(Float64(x - z) / 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 <= 1.22e+46) || (~((y <= 4.4e+86)) && (y <= 7.8e+97)))
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, 1.22e+46], And[N[Not[LessEqual[y, 4.4e+86]], $MachinePrecision], LessEqual[y, 7.8e+97]]], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.22e46 or 4.40000000000000006e86 < y < 7.7999999999999999e97

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.1%

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

   if 1.22e46 < y < 4.40000000000000006e86 or 7.7999999999999999e97 < 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 71.6%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.22 \cdot 10^{+46} \lor \neg \left(y \leq 4.4 \cdot 10^{+86}\right) \land y \leq 7.8 \cdot 10^{+97}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 3: 46.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-49} \lor \neg \left(x \leq 1.55 \cdot 10^{-288}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.5e+95)
   (* x (/ 0.5 t))
   (if (or (<= x -3.8e-49) (not (<= x 1.55e-288)))
     (* 0.5 (/ y t))
     (/ -0.5 (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e+95) {
		tmp = x * (0.5 / t);
	} else if ((x <= -3.8e-49) || !(x <= 1.55e-288)) {
		tmp = 0.5 * (y / t);
	} else {
		tmp = -0.5 / (t / 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 (x <= (-9.5d+95)) then
        tmp = x * (0.5d0 / t)
    else if ((x <= (-3.8d-49)) .or. (.not. (x <= 1.55d-288))) then
        tmp = 0.5d0 * (y / t)
    else
        tmp = (-0.5d0) / (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e+95) {
		tmp = x * (0.5 / t);
	} else if ((x <= -3.8e-49) || !(x <= 1.55e-288)) {
		tmp = 0.5 * (y / t);
	} else {
		tmp = -0.5 / (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.5e+95:
		tmp = x * (0.5 / t)
	elif (x <= -3.8e-49) or not (x <= 1.55e-288):
		tmp = 0.5 * (y / t)
	else:
		tmp = -0.5 / (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.5e+95)
		tmp = Float64(x * Float64(0.5 / t));
	elseif ((x <= -3.8e-49) || !(x <= 1.55e-288))
		tmp = Float64(0.5 * Float64(y / t));
	else
		tmp = Float64(-0.5 / Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.5e+95)
		tmp = x * (0.5 / t);
	elseif ((x <= -3.8e-49) || ~((x <= 1.55e-288)))
		tmp = 0.5 * (y / t);
	else
		tmp = -0.5 / (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.5e+95], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -3.8e-49], N[Not[LessEqual[x, 1.55e-288]], $MachinePrecision]], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(-0.5 / N[(t / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5000000000000004e95

   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 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-*l/ 70.6%

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

      3. associate-*r/ 70.4%

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

   6. Simplified 70.4%

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

   if -9.5000000000000004e95 < x < -3.7999999999999997e-49 or 1.54999999999999992e-288 < x

   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 41.7%

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

   if -3.7999999999999997e-49 < x < 1.54999999999999992e-288

   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. Step-by-step derivation

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in z around inf 46.4%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-49} \lor \neg \left(x \leq 1.55 \cdot 10^{-288}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{\frac{t}{z}}\\ \end{array} \]

Alternative 4: 46.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-49} \lor \neg \left(x \leq 4.5 \cdot 10^{-288}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.65e+96)
   (* x (/ 0.5 t))
   (if (or (<= x -6.6e-49) (not (<= x 4.5e-288)))
     (* 0.5 (/ y t))
     (/ z (/ t -0.5)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e+96) {
		tmp = x * (0.5 / t);
	} else if ((x <= -6.6e-49) || !(x <= 4.5e-288)) {
		tmp = 0.5 * (y / 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 (x <= (-1.65d+96)) then
        tmp = x * (0.5d0 / t)
    else if ((x <= (-6.6d-49)) .or. (.not. (x <= 4.5d-288))) then
        tmp = 0.5d0 * (y / 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 (x <= -1.65e+96) {
		tmp = x * (0.5 / t);
	} else if ((x <= -6.6e-49) || !(x <= 4.5e-288)) {
		tmp = 0.5 * (y / t);
	} else {
		tmp = z / (t / -0.5);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.65e+96:
		tmp = x * (0.5 / t)
	elif (x <= -6.6e-49) or not (x <= 4.5e-288):
		tmp = 0.5 * (y / t)
	else:
		tmp = z / (t / -0.5)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.65e+96)
		tmp = Float64(x * Float64(0.5 / t));
	elseif ((x <= -6.6e-49) || !(x <= 4.5e-288))
		tmp = Float64(0.5 * Float64(y / t));
	else
		tmp = Float64(z / Float64(t / -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.65e+96)
		tmp = x * (0.5 / t);
	elseif ((x <= -6.6e-49) || ~((x <= 4.5e-288)))
		tmp = 0.5 * (y / t);
	else
		tmp = z / (t / -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.65e+96], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -6.6e-49], N[Not[LessEqual[x, 4.5e-288]], $MachinePrecision]], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision], N[(z / N[(t / -0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.64999999999999992e96

   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 70.6%

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

      1. *-commutative 70.6%

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

      2. associate-*l/ 70.6%

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

      3. associate-*r/ 70.4%

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

   6. Simplified 70.4%

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

   if -1.64999999999999992e96 < x < -6.6e-49 or 4.5000000000000002e-288 < x

   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 41.7%

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

   if -6.6e-49 < x < 4.5000000000000002e-288

   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 46.6%

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

      1. *-commutative 46.6%

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

      2. associate-/r/ 46.6%

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

   6. Simplified 46.6%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-49} \lor \neg \left(x \leq 4.5 \cdot 10^{-288}\right):\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{\frac{t}{-0.5}}\\ \end{array} \]

Alternative 5: 77.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{-0.5}{\frac{-t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.8e-24) (/ -0.5 (/ (- t) (+ x y))) (* 0.5 (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e-24) {
		tmp = -0.5 / (-t / (x + y));
	} 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) :: tmp
    if (x <= (-5.8d-24)) then
        tmp = (-0.5d0) / (-t / (x + y))
    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 tmp;
	if (x <= -5.8e-24) {
		tmp = -0.5 / (-t / (x + y));
	} else {
		tmp = 0.5 * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.8e-24:
		tmp = -0.5 / (-t / (x + y))
	else:
		tmp = 0.5 * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.8e-24)
		tmp = Float64(-0.5 / Float64(Float64(-t) / Float64(x + y)));
	else
		tmp = Float64(0.5 * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.8e-24)
		tmp = -0.5 / (-t / (x + y));
	else
		tmp = 0.5 * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.8e-24], N[(-0.5 / N[((-t) / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7999999999999997e-24

   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. Step-by-step derivation

      1. associate-*l/ 100.0%

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

      2. associate-/l* 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in z around 0 87.8%

      \[\leadsto \frac{-0.5}{\color{blue}{-1 \cdot \frac{t}{y + x}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 87.8%

         \[\leadsto \frac{-0.5}{\color{blue}{\frac{-1 \cdot t}{y + x}}} \]

      2. neg-mul-1 87.8%

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

   8. Simplified 87.8%

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

   if -5.7999999999999997e-24 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-24}:\\ \;\;\;\;\frac{-0.5}{\frac{-t}{x + y}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 6: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.52 \cdot 10^{-78}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.52e-78) (* 0.5 (/ (- x z) t)) (* 0.5 (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.52e-78) {
		tmp = 0.5 * ((x - z) / t);
	} 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) :: tmp
    if (y <= 1.52d-78) then
        tmp = 0.5d0 * ((x - z) / t)
    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 tmp;
	if (y <= 1.52e-78) {
		tmp = 0.5 * ((x - z) / t);
	} else {
		tmp = 0.5 * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.52e-78:
		tmp = 0.5 * ((x - z) / t)
	else:
		tmp = 0.5 * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.52e-78)
		tmp = Float64(0.5 * Float64(Float64(x - z) / t));
	else
		tmp = Float64(0.5 * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 1.52e-78)
		tmp = 0.5 * ((x - z) / t);
	else
		tmp = 0.5 * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.52e-78], N[(0.5 * N[(N[(x - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.52e-78

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.8%

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

   if 1.52e-78 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 75.0%

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

4. Final simplification 73.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.52 \cdot 10^{-78}:\\ \;\;\;\;0.5 \cdot \frac{x - z}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 7: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-24}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.5e-24) (* (+ x y) (/ 0.5 t)) (* 0.5 (/ (- y z) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e-24) {
		tmp = (x + y) * (0.5 / t);
	} 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) :: tmp
    if (x <= (-9.5d-24)) then
        tmp = (x + y) * (0.5d0 / t)
    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 tmp;
	if (x <= -9.5e-24) {
		tmp = (x + y) * (0.5 / t);
	} else {
		tmp = 0.5 * ((y - z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.5e-24:
		tmp = (x + y) * (0.5 / t)
	else:
		tmp = 0.5 * ((y - z) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.5e-24)
		tmp = Float64(Float64(x + y) * Float64(0.5 / t));
	else
		tmp = Float64(0.5 * Float64(Float64(y - z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.5e-24)
		tmp = (x + y) * (0.5 / t);
	else
		tmp = 0.5 * ((y - z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.5e-24], N[(N[(x + y), $MachinePrecision] * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(y - z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.50000000000000029e-24

   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 87.9%

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

      1. +-commutative 87.9%

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

      2. associate-*r/ 87.9%

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

      3. associate-*l/ 87.7%

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

      4. *-commutative 87.7%

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

      5. +-commutative 87.7%

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

   6. Simplified 87.7%

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

   if -9.50000000000000029e-24 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 72.4%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-24}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y - z}{t}\\ \end{array} \]

Alternative 8: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(z - N[(x + y), $MachinePrecision]), $MachinePrecision] * N[(-0.5 / 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. Final simplification 99.7%

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

Alternative 9: 99.6% accurate, 1.0× speedup

Math

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

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(-0.5 / Float64(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[(-0.5 / N[(t / N[(z - N[(x + y), $MachinePrecision]), $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. Step-by-step derivation

   1. associate-*l/ 100.0%

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

   2. associate-/l* 99.7%

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

5. Applied egg-rr 99.7%

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

6. Final simplification 99.7%

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

Alternative 10: 45.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{-68}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.3e-68) (* 0.5 (/ x t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.3e-68) {
		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 <= 1.3d-68) 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 <= 1.3e-68) {
		tmp = 0.5 * (x / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.3e-68:
		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 <= 1.3e-68)
		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 <= 1.3e-68)
		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, 1.3e-68], 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 < 1.2999999999999999e-68

   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 1.2999999999999999e-68 < 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 59.1%

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

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{-68}:\\ \;\;\;\;0.5 \cdot \frac{x}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 11: 45.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 1.3e-68) (* x (/ 0.5 t)) (* 0.5 (/ y t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 1.3e-68) {
		tmp = x * (0.5 / 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 <= 1.3d-68) then
        tmp = x * (0.5d0 / 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 <= 1.3e-68) {
		tmp = x * (0.5 / t);
	} else {
		tmp = 0.5 * (y / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 1.3e-68:
		tmp = x * (0.5 / t)
	else:
		tmp = 0.5 * (y / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 1.3e-68)
		tmp = Float64(x * Float64(0.5 / 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 <= 1.3e-68)
		tmp = x * (0.5 / t);
	else
		tmp = 0.5 * (y / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 1.3e-68], N[(x * N[(0.5 / t), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(y / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.2999999999999999e-68

   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%

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

      1. *-commutative 41.3%

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

      2. associate-*l/ 41.3%

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

      3. associate-*r/ 41.2%

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

   6. Simplified 41.2%

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

   if 1.2999999999999999e-68 < 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 59.1%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.3 \cdot 10^{-68}:\\ \;\;\;\;x \cdot \frac{0.5}{t}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{y}{t}\\ \end{array} \]

Alternative 12: 37.6% 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 38.1%

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

5. Final simplification 38.1%

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

Reproduce

herbie shell --seed 2023224 
(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)))