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

Percentage Accurate: 93.1% → 96.5%

Time: 3.5s

Alternatives: 8

Speedup: 0.3×

• 24.5% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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: 93.1% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - z}{a}\\ t_2 := x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(t\_1, y, x\right)\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- t z) a)) (t_2 (- x (/ (* y (- z t)) a))))
   (if (<= t_2 (- INFINITY))
     (fma t_1 y x)
     (if (<= t_2 INFINITY) t_2 (* t_1 y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t - z) / a;
	double t_2 = x - ((y * (z - t)) / a);
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = fma(t_1, y, x);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = t_1 * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t - z) / a)
	t_2 = Float64(x - Float64(Float64(y * Float64(z - t)) / a))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = fma(t_1, y, x);
	elseif (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(t_1 * y);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 3 regimes

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

   1. Initial program 78.5%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 99.9

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

   5. Applied rewrites 99.9%

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

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

   1. Initial program 95.8%

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

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

   1. Initial program 93.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. sub-div N/A

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

      3. associate-*l/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 56.9

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

   5. Applied rewrites 56.9%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 56.4

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

   7. Applied rewrites 56.4%

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

Alternative 2: 59.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := t \cdot \frac{y}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (* t (/ y a))))
   (if (<= t_1 -2e+37) t_2 (if (<= t_1 1e+114) x t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double t_2 = t * (y / a);
	double tmp;
	if (t_1 <= -2e+37) {
		tmp = t_2;
	} else if (t_1 <= 1e+114) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 = (y * (z - t)) / a
    t_2 = t * (y / a)
    if (t_1 <= (-2d+37)) then
        tmp = t_2
    else if (t_1 <= 1d+114) then
        tmp = x
    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 = (y * (z - t)) / a;
	double t_2 = t * (y / a);
	double tmp;
	if (t_1 <= -2e+37) {
		tmp = t_2;
	} else if (t_1 <= 1e+114) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	t_2 = t * (y / a)
	tmp = 0
	if t_1 <= -2e+37:
		tmp = t_2
	elif t_1 <= 1e+114:
		tmp = x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	t_2 = Float64(t * Float64(y / a))
	tmp = 0.0
	if (t_1 <= -2e+37)
		tmp = t_2;
	elseif (t_1 <= 1e+114)
		tmp = x;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	t_2 = t * (y / a);
	tmp = 0.0;
	if (t_1 <= -2e+37)
		tmp = t_2;
	elseif (t_1 <= 1e+114)
		tmp = x;
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+37], t$95$2, If[LessEqual[t$95$1, 1e+114], x, t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -1.99999999999999991e37 or 1e114 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 88.0%

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

   3. Taylor expanded in t around inf

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

      1. *-commutative N/A

         \[\leadsto \frac{y \cdot t}{a} \]

      2. associate-/l* N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 44.7

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

   5. Applied rewrites 44.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

         \[\leadsto \frac{t \cdot y}{a} \]

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 50.7

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

   7. Applied rewrites 50.7%

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

   if -1.99999999999999991e37 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1e114

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   4. Step-by-step derivation

   5. Applied rewrites 70.5%

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

Alternative 3: 79.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ t_2 := \frac{t - z}{a} \cdot y\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+168}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+68}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))) (t_2 (* (/ (- t z) a) y)))
   (if (<= t_1 -2e+168) t_2 (if (<= t_1 5e+68) (fma (/ y a) t x) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double t_2 = ((t - z) / a) * y;
	double tmp;
	if (t_1 <= -2e+168) {
		tmp = t_2;
	} else if (t_1 <= 5e+68) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	t_2 = Float64(Float64(Float64(t - z) / a) * y)
	tmp = 0.0
	if (t_1 <= -2e+168)
		tmp = t_2;
	elseif (t_1 <= 5e+68)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+168], t$95$2, If[LessEqual[t$95$1, 5e+68], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -1.9999999999999999e168 or 5.0000000000000004e68 < (*.f64 y (-.f64 z t))

   1. Initial program 86.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. sub-div N/A

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

      3. associate-*l/ N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 73.4

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

   5. Applied rewrites 73.4%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-*l/ N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift--.f64 82.3

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

   7. Applied rewrites 82.3%

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

   if -1.9999999999999999e168 < (*.f64 y (-.f64 z t)) < 5.0000000000000004e68

   1. Initial program 99.4%

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

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

      2. associate-/l* N/A

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

      3. distribute-lft-neg-in N/A

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

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

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

      5. associate-/l* N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 77.6

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

   5. Applied rewrites 77.6%

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

Alternative 4: 92.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+211}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+82}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) t x)))
   (if (<= t -4.5e+211) t_1 (if (<= t 1.2e+82) (fma (/ (- t z) a) y x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), t, x);
	double tmp;
	if (t <= -4.5e+211) {
		tmp = t_1;
	} else if (t <= 1.2e+82) {
		tmp = fma(((t - z) / a), y, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), t, x)
	tmp = 0.0
	if (t <= -4.5e+211)
		tmp = t_1;
	elseif (t <= 1.2e+82)
		tmp = fma(Float64(Float64(t - z) / a), y, 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 + x), $MachinePrecision]}, If[LessEqual[t, -4.5e+211], t$95$1, If[LessEqual[t, 1.2e+82], N[(N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5e211 or 1.19999999999999999e82 < t

   1. Initial program 89.9%

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

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

      2. associate-/l* N/A

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

      3. distribute-lft-neg-in N/A

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

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

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

      5. associate-/l* N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 89.6

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

   5. Applied rewrites 89.6%

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

   if -4.5e211 < t < 1.19999999999999999e82

   1. Initial program 94.3%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. sub-div N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 94.0

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

   5. Applied rewrites 94.0%

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

Alternative 5: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.7 \cdot 10^{-6}:\\ \;\;\;\;x - \frac{z}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (fma (/ y a) t x)))
   (if (<= t -2.9e+40) t_1 (if (<= t 1.7e-6) (- x (* (/ z a) y)) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = fma((y / a), t, x);
	double tmp;
	if (t <= -2.9e+40) {
		tmp = t_1;
	} else if (t <= 1.7e-6) {
		tmp = x - ((z / a) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = fma(Float64(y / a), t, x)
	tmp = 0.0
	if (t <= -2.9e+40)
		tmp = t_1;
	elseif (t <= 1.7e-6)
		tmp = Float64(x - Float64(Float64(z / 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] * t + x), $MachinePrecision]}, If[LessEqual[t, -2.9e+40], t$95$1, If[LessEqual[t, 1.7e-6], N[(x - N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.90000000000000017e40 or 1.70000000000000003e-6 < t

   1. Initial program 90.7%

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

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

      2. associate-/l* N/A

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

      3. distribute-lft-neg-in N/A

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

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

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

      5. associate-/l* N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 84.3

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

   5. Applied rewrites 84.3%

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

   if -2.90000000000000017e40 < t < 1.70000000000000003e-6

   1. Initial program 95.4%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 84.7

         \[\leadsto x - \frac{z}{a} \cdot y \]

   5. Applied rewrites 84.7%

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

Alternative 6: 77.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+144}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z) (/ y a))))
   (if (<= z -3.1e+144) t_1 (if (<= z 8e+80) (fma (/ y a) t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -z * (y / a);
	double tmp;
	if (z <= -3.1e+144) {
		tmp = t_1;
	} else if (z <= 8e+80) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-z) * Float64(y / a))
	tmp = 0.0
	if (z <= -3.1e+144)
		tmp = t_1;
	elseif (z <= 8e+80)
		tmp = fma(Float64(y / a), t, x);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-z) * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+144], t$95$1, If[LessEqual[z, 8e+80], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1000000000000002e144 or 8e80 < z

   1. Initial program 89.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. mul-1-neg N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 62.4

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

   5. Applied rewrites 62.4%

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

   if -3.1000000000000002e144 < z < 8e80

   1. Initial program 94.8%

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

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

      2. associate-/l* N/A

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

      3. distribute-lft-neg-in N/A

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

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

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

      5. associate-/l* N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 83.9

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

   5. Applied rewrites 83.9%

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

Alternative 7: 71.9% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 93.1%

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

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

   2. associate-/l* N/A

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

   3. distribute-lft-neg-in N/A

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

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

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

   5. associate-/l* N/A

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

   6. +-commutative N/A

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

   7. *-commutative N/A

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

   8. associate-*l/ N/A

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

   9. lower-fma.f64 N/A

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

   10. lower-/.f64 71.9

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

5. Applied rewrites 71.9%

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

Alternative 8: 39.3% accurate, 23.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.1%

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

3. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
4. Step-by-step derivation

5. Applied rewrites 39.3%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 99.3% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    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 2025089 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :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)))