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

Percentage Accurate: 93.3% → 97.4%

Time: 8.8s

Alternatives: 9

Speedup: 1.1×

• 25.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y}{a}, z - t, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma (/ y a) (- z t) x))

C

double code(double x, double y, double z, double t, double a) {
	return fma((y / a), (z - t), x);
}

Julia

function code(x, y, z, t, a)
	return fma(Float64(y / a), Float64(z - t), x)
end

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. lift-+.f64 N/A

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

   2. +-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. *-commutative N/A

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

   6. associate-/l* N/A

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

   7. *-commutative N/A

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

   8. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

   9. lower-/.f64 96.9

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z - t, x\right) \]

4. Applied rewrites 96.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]
5. Add Preprocessing

Alternative 2: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+111} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -5e+111) (not (<= t_1 4e+80)))
     (* (/ y a) (- z t))
     (+ x (/ (* z y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -5e+111) || !(t_1 <= 4e+80)) {
		tmp = (y / a) * (z - t);
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y * (z - t)) / a
    if ((t_1 <= (-5d+111)) .or. (.not. (t_1 <= 4d+80))) then
        tmp = (y / a) * (z - t)
    else
        tmp = x + ((z * y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -5e+111) || !(t_1 <= 4e+80)) {
		tmp = (y / a) * (z - t);
	} else {
		tmp = x + ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if (t_1 <= -5e+111) or not (t_1 <= 4e+80):
		tmp = (y / a) * (z - t)
	else:
		tmp = x + ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -5e+111) || !(t_1 <= 4e+80))
		tmp = Float64(Float64(y / a) * Float64(z - t));
	else
		tmp = Float64(x + Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if ((t_1 <= -5e+111) || ~((t_1 <= 4e+80)))
		tmp = (y / a) * (z - t);
	else
		tmp = x + ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+111], N[Not[LessEqual[t$95$1, 4e+80]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -4.9999999999999997e111 or 4e80 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 88.2%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

      9. lower-/.f64 96.5

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z - t, x\right) \]

   4. Applied rewrites 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 85.6

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

   7. Applied rewrites 85.6%

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

   9. Applied rewrites 93.9%

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

   if -4.9999999999999997e111 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4e80

   1. Initial program 98.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 88.5

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

   5. Applied rewrites 88.5%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -5 \cdot 10^{+111} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 4 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+16} \lor \neg \left(t\_1 \leq 4 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -1e+16) (not (<= t_1 4e+80)))
     (* (/ y a) (- z t))
     (fma (/ z a) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -1e+16) || !(t_1 <= 4e+80)) {
		tmp = (y / a) * (z - t);
	} else {
		tmp = fma((z / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -1e+16) || !(t_1 <= 4e+80))
		tmp = Float64(Float64(y / a) * Float64(z - t));
	else
		tmp = fma(Float64(z / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e+16], N[Not[LessEqual[t$95$1, 4e+80]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -1e16 or 4e80 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 89.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

      9. lower-/.f64 96.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z - t, x\right) \]

   4. Applied rewrites 96.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 82.9

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

   7. Applied rewrites 82.9%

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

   9. Applied rewrites 90.1%

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

   if -1e16 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4e80

   1. Initial program 98.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

      9. lower-/.f64 96.8

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z - t, x\right) \]

   4. Applied rewrites 96.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z, x\right)} \]

      4. lower-/.f64 89.9

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z, x\right) \]

   7. Applied rewrites 89.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z, x\right)} \]
   8. Step-by-step derivation

   9. Applied rewrites 91.3%

      \[\leadsto \mathsf{fma}\left(\frac{z}{a}, \color{blue}{y}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -1 \cdot 10^{+16} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 4 \cdot 10^{+80}\right):\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2200 \lor \neg \left(z \leq 2.5 \cdot 10^{-8}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -2200.0) (not (<= z 2.5e-8)))
   (fma (/ y a) z x)
   (- x (* t (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -2200.0) || !(z <= 2.5e-8)) {
		tmp = fma((y / a), z, x);
	} else {
		tmp = x - (t * (y / a));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -2200.0) || !(z <= 2.5e-8))
		tmp = fma(Float64(y / a), z, x);
	else
		tmp = Float64(x - Float64(t * Float64(y / a)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -2200.0], N[Not[LessEqual[z, 2.5e-8]], $MachinePrecision]], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], N[(x - N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2200 or 2.4999999999999999e-8 < z

   1. Initial program 92.6%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z, x\right)} \]

      4. lower-/.f64 85.1

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z, x\right) \]

   5. Applied rewrites 85.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z, x\right)} \]

   if -2200 < z < 2.4999999999999999e-8

   1. Initial program 95.7%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. associate-*l/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 88.7

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

   5. Applied rewrites 88.7%

      \[\leadsto \color{blue}{x - \frac{t}{a} \cdot y} \]
   6. Step-by-step derivation

   7. Applied rewrites 90.8%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2200 \lor \neg \left(z \leq 2.5 \cdot 10^{-8}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - t \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+222} \lor \neg \left(t \leq 3.5 \cdot 10^{+163}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.8e+222) (not (<= t 3.5e+163)))
   (* (- t) (/ y a))
   (fma (/ z a) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.8e+222) || !(t <= 3.5e+163)) {
		tmp = -t * (y / a);
	} else {
		tmp = fma((z / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.8e+222) || !(t <= 3.5e+163))
		tmp = Float64(Float64(-t) * Float64(y / a));
	else
		tmp = fma(Float64(z / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.8e+222], N[Not[LessEqual[t, 3.5e+163]], $MachinePrecision]], N[((-t) * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.80000000000000018e222 or 3.5000000000000003e163 < t

   1. Initial program 87.3%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. associate-*l/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 83.7

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

   5. Applied rewrites 83.7%

      \[\leadsto \color{blue}{x - \frac{t}{a} \cdot y} \]
   6. Step-by-step derivation

   7. Applied rewrites 87.2%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 67.0%

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

   if -3.80000000000000018e222 < t < 3.5000000000000003e163

   1. Initial program 95.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

      9. lower-/.f64 96.6

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z - t, x\right) \]

   4. Applied rewrites 96.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z, x\right)} \]

      4. lower-/.f64 79.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z, x\right) \]

   7. Applied rewrites 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z, x\right)} \]
   8. Step-by-step derivation

   9. Applied rewrites 79.5%

      \[\leadsto \mathsf{fma}\left(\frac{z}{a}, \color{blue}{y}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.8 \cdot 10^{+222} \lor \neg \left(t \leq 3.5 \cdot 10^{+163}\right):\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+222}:\\ \;\;\;\;\frac{\left(-t\right) \cdot y}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -4e+222)
   (/ (* (- t) y) a)
   (if (<= t 3.5e+163) (fma (/ z a) y x) (* (- t) (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -4e+222) {
		tmp = (-t * y) / a;
	} else if (t <= 3.5e+163) {
		tmp = fma((z / a), y, x);
	} else {
		tmp = -t * (y / a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -4e+222)
		tmp = Float64(Float64(Float64(-t) * y) / a);
	elseif (t <= 3.5e+163)
		tmp = fma(Float64(z / a), y, x);
	else
		tmp = Float64(Float64(-t) * Float64(y / a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -4e+222], N[(N[((-t) * y), $MachinePrecision] / a), $MachinePrecision], If[LessEqual[t, 3.5e+163], N[(N[(z / a), $MachinePrecision] * y + x), $MachinePrecision], N[((-t) * N[(y / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.0000000000000002e222

   1. Initial program 99.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

      9. lower-/.f64 94.4

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z - t, x\right) \]

   4. Applied rewrites 94.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

   5. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower--.f64 83.4

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

   7. Applied rewrites 83.4%

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

   8. Taylor expanded in z around 0

      \[\leadsto \frac{\left(-1 \cdot t\right) \cdot y}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 81.6%

       \[\leadsto \frac{\left(-t\right) \cdot y}{a} \]

   if -4.0000000000000002e222 < t < 3.5000000000000003e163

   1. Initial program 95.9%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. *-commutative N/A

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

      8. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

      9. lower-/.f64 96.6

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z - t, x\right) \]

   4. Applied rewrites 96.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)} \]

   5. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z, x\right)} \]

      4. lower-/.f64 79.0

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z, x\right) \]

   7. Applied rewrites 79.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z, x\right)} \]
   8. Step-by-step derivation

   9. Applied rewrites 79.5%

      \[\leadsto \mathsf{fma}\left(\frac{z}{a}, \color{blue}{y}, x\right) \]

   if 3.5000000000000003e163 < t

   1. Initial program 80.9%

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

   3. Taylor expanded in z around 0

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

      1. fp-cancel-sign-sub-inv N/A

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

      2. metadata-eval N/A

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

      3. *-lft-identity N/A

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

      4. lower--.f64 N/A

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

      5. associate-*l/ N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 81.8

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

   5. Applied rewrites 81.8%

      \[\leadsto \color{blue}{x - \frac{t}{a} \cdot y} \]
   6. Step-by-step derivation

   7. Applied rewrites 84.4%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 62.2%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+222}:\\ \;\;\;\;\frac{\left(-t\right) \cdot y}{a}\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+163}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-t\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\frac{y}{a}, z, x\right) \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (fma (/ y a) z x))

C

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

Julia

function code(x, y, z, t, a)
	return fma(Float64(y / a), z, x)
end

Wolfram

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

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in t around 0

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

   1. +-commutative N/A

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

   2. associate-*l/ N/A

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

   3. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z, x\right)} \]

   4. lower-/.f64 70.7

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{y}{a}}, z, x\right) \]

5. Applied rewrites 70.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z, x\right)} \]

6. Final simplification 70.7%

   \[\leadsto \mathsf{fma}\left(\frac{y}{a}, z, x\right) \]
7. Add Preprocessing

Alternative 8: 33.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \frac{y}{a} \cdot z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in z around inf

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 32.5

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

5. Applied rewrites 32.5%

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

6. Final simplification 32.5%

   \[\leadsto \frac{y}{a} \cdot z \]
7. Add Preprocessing

Alternative 9: 31.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ y \cdot \frac{z}{a} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_] := N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.1%

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

3. Taylor expanded in z around inf

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 32.5

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

5. Applied rewrites 32.5%

   \[\leadsto \color{blue}{\frac{y}{a} \cdot z} \]
6. Step-by-step derivation

7. Applied rewrites 32.2%

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

8. Final simplification 32.2%

   \[\leadsto y \cdot \frac{z}{a} \]
9. Add Preprocessing

Developer Target 1: 99.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{z - t}\\ \mathbf{if}\;y < -1.0761266216389975 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{t\_1}{y}}\\ \mathbf{elif}\;y < 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{t\_1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ a (- z t))))
   (if (< y -1.0761266216389975e-10)
     (+ x (/ 1.0 (/ t_1 y)))
     (if (< y 2.894426862792089e-49)
       (+ x (/ (* y (- z t)) a))
       (+ x (/ y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (z - t)
    if (y < (-1.0761266216389975d-10)) then
        tmp = x + (1.0d0 / (t_1 / y))
    else if (y < 2.894426862792089d-49) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = x + (y / t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = a / (z - t);
	double tmp;
	if (y < -1.0761266216389975e-10) {
		tmp = x + (1.0 / (t_1 / y));
	} else if (y < 2.894426862792089e-49) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = x + (y / t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = a / (z - t)
	tmp = 0
	if y < -1.0761266216389975e-10:
		tmp = x + (1.0 / (t_1 / y))
	elif y < 2.894426862792089e-49:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = x + (y / t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(a / Float64(z - t))
	tmp = 0.0
	if (y < -1.0761266216389975e-10)
		tmp = Float64(x + Float64(1.0 / Float64(t_1 / y)));
	elseif (y < 2.894426862792089e-49)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = Float64(x + Float64(y / t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = a / (z - t);
	tmp = 0.0;
	if (y < -1.0761266216389975e-10)
		tmp = x + (1.0 / (t_1 / y));
	elseif (y < 2.894426862792089e-49)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = x + (y / t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -1.0761266216389975e-10], N[(x + N[(1.0 / N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Less[y, 2.894426862792089e-49], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Reproduce

herbie shell --seed 2024337 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -430450648655599/4000000000000000000000000) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2894426862792089/10000000000000000000000000000000000000000000000000000000000000000) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t)))))))

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