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

Percentage Accurate: 93.3% → 96.2%

Time: 7.3s

Alternatives: 11

Speedup: 1.1×

• 25.8% 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: 96.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) a)))
   (if (<= t_1 (- INFINITY)) (fma (/ y a) (- z t) x) (+ x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma((y / a), (z - t), x);
	} else {
		tmp = x + t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / a)
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(y / a), Float64(z - t), x);
	else
		tmp = Float64(x + t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision], N[(x + t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -inf.0

   1. Initial program 73.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 99.9

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

   4. Applied rewrites 99.9%

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

   if -inf.0 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 98.1%

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

4. Final simplification 98.4%

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

Alternative 2: 49.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+148}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;t\_1 \leq 10^{-8}:\\ \;\;\;\;\frac{x \cdot a}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) a)))
   (if (<= t_1 -2e+148)
     (* (/ y a) z)
     (if (<= t_1 1e-8) (/ (* x a) a) (/ (* z y) a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double tmp;
	if (t_1 <= -2e+148) {
		tmp = (y / a) * z;
	} else if (t_1 <= 1e-8) {
		tmp = (x * a) / a;
	} else {
		tmp = (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 = ((z - t) * y) / a
    if (t_1 <= (-2d+148)) then
        tmp = (y / a) * z
    else if (t_1 <= 1d-8) then
        tmp = (x * a) / a
    else
        tmp = (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 = ((z - t) * y) / a;
	double tmp;
	if (t_1 <= -2e+148) {
		tmp = (y / a) * z;
	} else if (t_1 <= 1e-8) {
		tmp = (x * a) / a;
	} else {
		tmp = (z * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / a
	tmp = 0
	if t_1 <= -2e+148:
		tmp = (y / a) * z
	elif t_1 <= 1e-8:
		tmp = (x * a) / a
	else:
		tmp = (z * y) / a
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / a)
	tmp = 0.0
	if (t_1 <= -2e+148)
		tmp = Float64(Float64(y / a) * z);
	elseif (t_1 <= 1e-8)
		tmp = Float64(Float64(x * a) / a);
	else
		tmp = Float64(Float64(z * y) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / a;
	tmp = 0.0;
	if (t_1 <= -2e+148)
		tmp = (y / a) * z;
	elseif (t_1 <= 1e-8)
		tmp = (x * a) / a;
	else
		tmp = (z * y) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+148], N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 1e-8], N[(N[(x * a), $MachinePrecision] / a), $MachinePrecision], N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2.0000000000000001e148

   1. Initial program 82.4%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 47.3

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

   5. Applied rewrites 47.3%

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

   7. Applied rewrites 54.0%

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

   if -2.0000000000000001e148 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 80.8

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 19.7%

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

   9. Taylor expanded in x around inf

      \[\leadsto \frac{a \cdot x}{a} \]
   10. Step-by-step derivation

   11. Applied rewrites 51.5%

       \[\leadsto \frac{a \cdot x}{a} \]

   if 1e-8 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 94.4%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 53.0

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

   5. Applied rewrites 53.0%

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

   7. Applied rewrites 57.1%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a} \leq -2 \cdot 10^{+148}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a} \leq 10^{-8}:\\ \;\;\;\;\frac{x \cdot a}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(z - t\right) \cdot y}{a}\\ t_2 := \frac{y}{a} \cdot z\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+148}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{-8}:\\ \;\;\;\;\frac{x \cdot a}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* (- z t) y) a)) (t_2 (* (/ y a) z)))
   (if (<= t_1 -2e+148) t_2 (if (<= t_1 1e-8) (/ (* x a) a) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double t_2 = (y / a) * z;
	double tmp;
	if (t_1 <= -2e+148) {
		tmp = t_2;
	} else if (t_1 <= 1e-8) {
		tmp = (x * a) / a;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = ((z - t) * y) / a
    t_2 = (y / a) * z
    if (t_1 <= (-2d+148)) then
        tmp = t_2
    else if (t_1 <= 1d-8) then
        tmp = (x * a) / a
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((z - t) * y) / a;
	double t_2 = (y / a) * z;
	double tmp;
	if (t_1 <= -2e+148) {
		tmp = t_2;
	} else if (t_1 <= 1e-8) {
		tmp = (x * a) / a;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((z - t) * y) / a
	t_2 = (y / a) * z
	tmp = 0
	if t_1 <= -2e+148:
		tmp = t_2
	elif t_1 <= 1e-8:
		tmp = (x * a) / a
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(z - t) * y) / a)
	t_2 = Float64(Float64(y / a) * z)
	tmp = 0.0
	if (t_1 <= -2e+148)
		tmp = t_2;
	elseif (t_1 <= 1e-8)
		tmp = Float64(Float64(x * a) / a);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((z - t) * y) / a;
	t_2 = (y / a) * z;
	tmp = 0.0;
	if (t_1 <= -2e+148)
		tmp = t_2;
	elseif (t_1 <= 1e-8)
		tmp = (x * a) / a;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+148], t$95$2, If[LessEqual[t$95$1, 1e-8], N[(N[(x * a), $MachinePrecision] / a), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2.0000000000000001e148 or 1e-8 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 88.3%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 50.1

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

   5. Applied rewrites 50.1%

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

   7. Applied rewrites 54.8%

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

   if -2.0000000000000001e148 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1e-8

   1. Initial program 99.9%

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

   3. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. *-commutative N/A

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

      4. lower-fma.f64 N/A

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

      5. lower--.f64 N/A

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

      6. lower-*.f64 80.8

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 19.7%

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

   9. Taylor expanded in x around inf

      \[\leadsto \frac{a \cdot x}{a} \]
   10. Step-by-step derivation

   11. Applied rewrites 51.5%

       \[\leadsto \frac{a \cdot x}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(z - t\right) \cdot y}{a} \leq -2 \cdot 10^{+148}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \mathbf{elif}\;\frac{\left(z - t\right) \cdot y}{a} \leq 10^{-8}:\\ \;\;\;\;\frac{x \cdot a}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{if}\;z \leq -1.24 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-t, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) z x)))
   (if (<= z -1.24e+14) t_1 (if (<= z 4.2e-25) (fma (- t) (/ y a) x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), z, x);
	double tmp;
	if (z <= -1.24e+14) {
		tmp = t_1;
	} else if (z <= 4.2e-25) {
		tmp = fma(-t, (y / a), x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), z, x)
	tmp = 0.0
	if (z <= -1.24e+14)
		tmp = t_1;
	elseif (z <= 4.2e-25)
		tmp = fma(Float64(-t), Float64(y / a), x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[z, -1.24e+14], t$95$1, If[LessEqual[z, 4.2e-25], N[((-t) * N[(y / a), $MachinePrecision] + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24e14 or 4.20000000000000005e-25 < z

   1. Initial program 91.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 87.6

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

   5. Applied rewrites 87.6%

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

   if -1.24e14 < z < 4.20000000000000005e-25

   1. Initial program 95.5%

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

   3. Taylor expanded in z around 0

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 86.8

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

   5. Applied rewrites 86.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 90.4

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

   7. Applied rewrites 90.4%

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

Alternative 5: 85.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{if}\;z \leq -1.24 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) z x)))
   (if (<= z -1.24e+14) t_1 (if (<= z 1.4e-15) (- x (* (/ t a) y)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), z, x);
	double tmp;
	if (z <= -1.24e+14) {
		tmp = t_1;
	} else if (z <= 1.4e-15) {
		tmp = x - ((t / a) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), z, x)
	tmp = 0.0
	if (z <= -1.24e+14)
		tmp = t_1;
	elseif (z <= 1.4e-15)
		tmp = Float64(x - Float64(Float64(t / a) * y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision]}, If[LessEqual[z, -1.24e+14], t$95$1, If[LessEqual[z, 1.4e-15], N[(x - N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.24e14 or 1.40000000000000007e-15 < z

   1. Initial program 92.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 87.8

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

   5. Applied rewrites 87.8%

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

   if -1.24e14 < z < 1.40000000000000007e-15

   1. Initial program 94.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 87.8

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

   5. Applied rewrites 87.8%

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

Alternative 6: 77.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{a} \cdot t\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+238}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- y) a) t)))
   (if (<= t -7.8e+128) t_1 (if (<= t 2.1e+238) (fma (/ y a) z x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-y / a) * t;
	double tmp;
	if (t <= -7.8e+128) {
		tmp = t_1;
	} else if (t <= 2.1e+238) {
		tmp = fma((y / a), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(-y) / a) * t)
	tmp = 0.0
	if (t <= -7.8e+128)
		tmp = t_1;
	elseif (t <= 2.1e+238)
		tmp = fma(Float64(y / a), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[((-y) / a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -7.8e+128], t$95$1, If[LessEqual[t, 2.1e+238], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.7999999999999994e128 or 2.10000000000000007e238 < t

   1. Initial program 81.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.1

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

   5. Applied rewrites 85.1%

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

   7. Applied rewrites 74.2%

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

   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 69.4%

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

   if -7.7999999999999994e128 < t < 2.10000000000000007e238

   1. Initial program 97.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 80.2

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

   5. Applied rewrites 80.2%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+128}:\\ \;\;\;\;\frac{-y}{a} \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+238}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{a} \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-t}{a} \cdot y\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{+238}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- t) a) y)))
   (if (<= t -7.8e+128) t_1 (if (<= t 2.1e+238) (fma (/ y a) z x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-t / a) * y;
	double tmp;
	if (t <= -7.8e+128) {
		tmp = t_1;
	} else if (t <= 2.1e+238) {
		tmp = fma((y / a), z, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(-t) / a) * y)
	tmp = 0.0
	if (t <= -7.8e+128)
		tmp = t_1;
	elseif (t <= 2.1e+238)
		tmp = fma(Float64(y / a), z, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[((-t) / a), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t, -7.8e+128], t$95$1, If[LessEqual[t, 2.1e+238], N[(N[(y / a), $MachinePrecision] * z + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -7.7999999999999994e128 or 2.10000000000000007e238 < t

   1. Initial program 81.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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. mul-1-neg N/A

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

      2. unsub-neg N/A

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

      3. lower--.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 85.1

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

   5. Applied rewrites 85.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 69.2%

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

   if -7.7999999999999994e128 < t < 2.10000000000000007e238

   1. Initial program 97.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a} \]
   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 80.2

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

   5. Applied rewrites 80.2%

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

Alternative 8: 97.3% 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 93.6%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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 95.4

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

4. Applied rewrites 95.4%

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

Alternative 9: 71.1% 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 93.6%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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 70.0

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

5. Applied rewrites 70.0%

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

Alternative 10: 67.8% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.6%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
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 70.0

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

5. Applied rewrites 70.0%

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

7. Applied rewrites 68.1%

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

Alternative 11: 35.1% 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 93.6%

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

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

   2. *-commutative N/A

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

   3. lower-*.f64 N/A

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

   4. lower-/.f64 33.4

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

5. Applied rewrites 33.4%

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

7. Applied rewrites 35.4%

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

8. Final simplification 35.4%

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

Developer Target 1: 99.2% 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 2024295 
(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)))