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

Percentage Accurate: 92.8% → 98.9%

Time: 7.9s

Alternatives: 8

Speedup: 1.0×

• 24.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y \cdot \left(z - x\right)}{t}\\ \mathbf{if}\;t_1 \leq -\infty \lor \neg \left(t_1 \leq 5 \cdot 10^{+263}\right):\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (* y (- z x)) t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+263)))
     (+ x (* (- z x) (/ y t)))
     t_1)))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+263)) {
		tmp = x + ((z - x) * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y * (z - x)) / t);
	double tmp;
	if ((t_1 <= -Double.POSITIVE_INFINITY) || !(t_1 <= 5e+263)) {
		tmp = x + ((z - x) * (y / t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y * (z - x)) / t)
	tmp = 0
	if (t_1 <= -math.inf) or not (t_1 <= 5e+263):
		tmp = x + ((z - x) * (y / t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y * Float64(z - x)) / t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+263))
		tmp = Float64(x + Float64(Float64(z - x) * Float64(y / t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y * (z - x)) / t);
	tmp = 0.0;
	if ((t_1 <= -Inf) || ~((t_1 <= 5e+263)))
		tmp = x + ((z - x) * (y / t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+263]], $MachinePrecision]], N[(x + N[(N[(z - x), $MachinePrecision] * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < -inf.0 or 5.00000000000000022e263 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t))

   1. Initial program 74.5%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   if -inf.0 < (+.f64 x (/.f64 (*.f64 y (-.f64 z x)) t)) < 5.00000000000000022e263

   1. Initial program 99.4%

      \[x + \frac{y \cdot \left(z - x\right)}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} \leq -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \leq 5 \cdot 10^{+263}\right):\\ \;\;\;\;x + \left(z - x\right) \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array} \]

Alternative 2: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-116} \lor \neg \left(z \leq 1.04 \cdot 10^{-10}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{-t}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.6e-116) (not (<= z 1.04e-10)))
   (+ x (* z (/ y t)))
   (+ x (/ y (/ (- t) x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e-116) || !(z <= 1.04e-10)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + (y / (-t / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-7.6d-116)) .or. (.not. (z <= 1.04d-10))) then
        tmp = x + (z * (y / t))
    else
        tmp = x + (y / (-t / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.6e-116) || !(z <= 1.04e-10)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x + (y / (-t / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.6e-116) or not (z <= 1.04e-10):
		tmp = x + (z * (y / t))
	else:
		tmp = x + (y / (-t / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.6e-116) || !(z <= 1.04e-10))
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x + Float64(y / Float64(Float64(-t) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -7.6e-116) || ~((z <= 1.04e-10)))
		tmp = x + (z * (y / t));
	else
		tmp = x + (y / (-t / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.6e-116], N[Not[LessEqual[z, 1.04e-10]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[((-t) / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.6000000000000003e-116 or 1.04e-10 < z

   1. Initial program 89.5%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around inf 85.1%

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

      1. associate-*l/ 89.6%

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

      2. *-commutative 89.6%

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

   6. Simplified 89.6%

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

   if -7.6000000000000003e-116 < z < 1.04e-10

   1. Initial program 94.8%

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

      1. associate-/l* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in z around 0 88.7%

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

      1. associate-*r/ 88.7%

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

      2. neg-mul-1 88.7%

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

   6. Simplified 88.7%

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

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-116} \lor \neg \left(z \leq 1.04 \cdot 10^{-10}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{-t}{x}}\\ \end{array} \]

Alternative 3: 85.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-110} \lor \neg \left(z \leq 4.6 \cdot 10^{-9}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.25e-110) (not (<= z 4.6e-9)))
   (+ x (* z (/ y t)))
   (- x (* x (/ y t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e-110) || !(z <= 4.6e-9)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x - (x * (y / t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.25d-110)) .or. (.not. (z <= 4.6d-9))) then
        tmp = x + (z * (y / t))
    else
        tmp = x - (x * (y / t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e-110) || !(z <= 4.6e-9)) {
		tmp = x + (z * (y / t));
	} else {
		tmp = x - (x * (y / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.25e-110) or not (z <= 4.6e-9):
		tmp = x + (z * (y / t))
	else:
		tmp = x - (x * (y / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.25e-110) || !(z <= 4.6e-9))
		tmp = Float64(x + Float64(z * Float64(y / t)));
	else
		tmp = Float64(x - Float64(x * Float64(y / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.25e-110) || ~((z <= 4.6e-9)))
		tmp = x + (z * (y / t));
	else
		tmp = x - (x * (y / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.25e-110], N[Not[LessEqual[z, 4.6e-9]], $MachinePrecision]], N[(x + N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25e-110 or 4.5999999999999998e-9 < z

   1. Initial program 89.5%

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

      1. associate-*l/ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in z around inf 85.1%

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

      1. associate-*l/ 89.6%

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

      2. *-commutative 89.6%

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

   6. Simplified 89.6%

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

   if -1.25e-110 < z < 4.5999999999999998e-9

   1. Initial program 94.8%

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

      1. associate-*l/ 95.7%

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

   3. Simplified 95.7%

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

   4. Taylor expanded in z around 0 84.5%

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

      1. mul-1-neg 84.5%

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

      2. associate-*l/ 87.9%

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

      3. distribute-rgt-neg-out 87.9%

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

   6. Simplified 87.9%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-110} \lor \neg \left(z \leq 4.6 \cdot 10^{-9}\right):\\ \;\;\;\;x + z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{y}{t}\\ \end{array} \]

Alternative 4: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-113} \lor \neg \left(z \leq 10^{+34}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.8e-113) (not (<= z 1e+34))) (* z (/ y t)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-113) || !(z <= 1e+34)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-8.8d-113)) .or. (.not. (z <= 1d+34))) then
        tmp = z * (y / t)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.8e-113) || !(z <= 1e+34)) {
		tmp = z * (y / t);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.8e-113) or not (z <= 1e+34):
		tmp = z * (y / t)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.8e-113) || !(z <= 1e+34))
		tmp = Float64(z * Float64(y / t));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.8e-113) || ~((z <= 1e+34)))
		tmp = z * (y / t);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.8e-113], N[Not[LessEqual[z, 1e+34]], $MachinePrecision]], N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -8.80000000000000016e-113 or 9.99999999999999946e33 < z

   1. Initial program 90.0%

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

      1. associate-*l/ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in z around inf 85.1%

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

      1. associate-*l/ 90.1%

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

      2. *-commutative 90.1%

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

   6. Simplified 90.1%

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

      1. associate-*r/ 85.1%

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

      2. *-commutative 85.1%

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

      3. frac-2neg 85.1%

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

      4. div-inv 84.9%

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

      5. add-sqr-sqrt 51.6%

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

      6. sqrt-unprod 53.2%

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

      7. sqr-neg 53.2%

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

      8. sqrt-unprod 8.8%

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

      9. add-sqr-sqrt 27.4%

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

      10. cancel-sign-sub-inv 27.4%

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

      11. div-inv 27.4%

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

      12. *-commutative 27.4%

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

      13. associate-/l* 27.4%

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

   8. Applied egg-rr 27.4%

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

      1. associate-/r/ 27.3%

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

      2. *-commutative 27.3%

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

   10. Simplified 27.3%

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

   11. Taylor expanded in x around 0 2.4%

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

       1. mul-1-neg 2.4%

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

       2. associate-/l* 2.4%

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

       3. distribute-frac-neg 2.4%

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

   13. Simplified 2.4%

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

       1. add-sqr-sqrt 0.8%

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

       2. sqrt-unprod 27.0%

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

       3. sqr-neg 27.0%

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

       4. sqrt-unprod 30.9%

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

       5. add-sqr-sqrt 59.5%

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

       6. associate-/r/ 65.2%

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

   15. Applied egg-rr 65.2%

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

   if -8.80000000000000016e-113 < z < 9.99999999999999946e33

   1. Initial program 93.7%

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

      1. associate-*l/ 96.1%

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

   3. Simplified 96.1%

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

   4. Taylor expanded in z around inf 67.9%

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

      1. associate-*l/ 67.6%

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

      2. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   7. Taylor expanded in x around inf 58.2%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{-113} \lor \neg \left(z \leq 10^{+34}\right):\\ \;\;\;\;z \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 97.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

4. Final simplification 96.6%

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

Alternative 6: 73.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z}{t} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

   1. associate-/r/ 94.2%

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

   2. div-inv 94.1%

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

   3. associate-/r* 96.5%

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

5. Applied egg-rr 96.5%

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

6. Taylor expanded in z around inf 76.7%

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

   1. associate-*r/ 76.0%

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

8. Simplified 76.0%

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

9. Final simplification 76.0%

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

Alternative 7: 76.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x + z \cdot \frac{y}{t} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

4. Taylor expanded in z around inf 76.7%

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

   1. associate-*l/ 79.2%

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

   2. *-commutative 79.2%

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

6. Simplified 79.2%

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

7. Final simplification 79.2%

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

Alternative 8: 37.9% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

   1. associate-*l/ 96.6%

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

3. Simplified 96.6%

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

4. Taylor expanded in z around inf 76.7%

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

   1. associate-*l/ 79.2%

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

   2. *-commutative 79.2%

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

6. Simplified 79.2%

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

7. Taylor expanded in x around inf 42.6%

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

8. Final simplification 42.6%

   \[\leadsto x \]

Developer target: 91.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023185 
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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