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

Percentage Accurate: 92.8% → 97.1%

Time: 3.2s

Alternatives: 12

Speedup: 1.0×

• 24.6% 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: 92.8% 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: 97.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a) {
	return x - ((z - t) * (y / 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 - ((z - t) * (y / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.8%

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

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. lower-*.f64 N/A

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

   7. lift--.f64 N/A

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

   8. lower-/.f64 97.1

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

3. Applied rewrites 97.1%

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

Alternative 2: 59.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \frac{y}{a} \cdot t\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+60}:\\ \;\;\;\;y \cdot \frac{t}{a}\\ \mathbf{elif}\;t\_1 \leq 10^{+155}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (* (/ y a) t)))
   (if (<= t_1 -2e+94)
     t_2
     (if (<= t_1 2e-20)
       x
       (if (<= t_1 5e+60) (* y (/ t a)) (if (<= t_1 1e+155) 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 = (y / a) * t;
	double tmp;
	if (t_1 <= -2e+94) {
		tmp = t_2;
	} else if (t_1 <= 2e-20) {
		tmp = x;
	} else if (t_1 <= 5e+60) {
		tmp = y * (t / a);
	} else if (t_1 <= 1e+155) {
		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 = (y / a) * t
    if (t_1 <= (-2d+94)) then
        tmp = t_2
    else if (t_1 <= 2d-20) then
        tmp = x
    else if (t_1 <= 5d+60) then
        tmp = y * (t / a)
    else if (t_1 <= 1d+155) 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 = (y / a) * t;
	double tmp;
	if (t_1 <= -2e+94) {
		tmp = t_2;
	} else if (t_1 <= 2e-20) {
		tmp = x;
	} else if (t_1 <= 5e+60) {
		tmp = y * (t / a);
	} else if (t_1 <= 1e+155) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	t_2 = (y / a) * t
	tmp = 0
	if t_1 <= -2e+94:
		tmp = t_2
	elif t_1 <= 2e-20:
		tmp = x
	elif t_1 <= 5e+60:
		tmp = y * (t / a)
	elif t_1 <= 1e+155:
		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(Float64(y / a) * t)
	tmp = 0.0
	if (t_1 <= -2e+94)
		tmp = t_2;
	elseif (t_1 <= 2e-20)
		tmp = x;
	elseif (t_1 <= 5e+60)
		tmp = Float64(y * Float64(t / a));
	elseif (t_1 <= 1e+155)
		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 = (y / a) * t;
	tmp = 0.0;
	if (t_1 <= -2e+94)
		tmp = t_2;
	elseif (t_1 <= 2e-20)
		tmp = x;
	elseif (t_1 <= 5e+60)
		tmp = y * (t / a);
	elseif (t_1 <= 1e+155)
		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[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+94], t$95$2, If[LessEqual[t$95$1, 2e-20], x, If[LessEqual[t$95$1, 5e+60], N[(y * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+155], x, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2e94 or 1.00000000000000001e155 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 86.2%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 96.9

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

   3. Applied rewrites 96.9%

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

   4. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 51.4

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

   6. Applied rewrites 51.4%

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

   if -2e94 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.99999999999999989e-20 or 4.99999999999999975e60 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.00000000000000001e155

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 70.8%

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

   if 1.99999999999999989e-20 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.99999999999999975e60

   1. Initial program 99.8%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   3. 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 25.5

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

   4. Applied rewrites 25.5%

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

Alternative 3: 56.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := y \cdot \frac{t}{a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+196}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+185}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (* y (/ t a))))
   (if (<= t_1 -5e+196)
     t_2
     (if (<= t_1 2e-20)
       x
       (if (<= t_1 5e+60) t_2 (if (<= t_1 1e+185) 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 = y * (t / a);
	double tmp;
	if (t_1 <= -5e+196) {
		tmp = t_2;
	} else if (t_1 <= 2e-20) {
		tmp = x;
	} else if (t_1 <= 5e+60) {
		tmp = t_2;
	} else if (t_1 <= 1e+185) {
		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 = y * (t / a)
    if (t_1 <= (-5d+196)) then
        tmp = t_2
    else if (t_1 <= 2d-20) then
        tmp = x
    else if (t_1 <= 5d+60) then
        tmp = t_2
    else if (t_1 <= 1d+185) 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 = y * (t / a);
	double tmp;
	if (t_1 <= -5e+196) {
		tmp = t_2;
	} else if (t_1 <= 2e-20) {
		tmp = x;
	} else if (t_1 <= 5e+60) {
		tmp = t_2;
	} else if (t_1 <= 1e+185) {
		tmp = x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	t_2 = y * (t / a)
	tmp = 0
	if t_1 <= -5e+196:
		tmp = t_2
	elif t_1 <= 2e-20:
		tmp = x
	elif t_1 <= 5e+60:
		tmp = t_2
	elif t_1 <= 1e+185:
		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(y * Float64(t / a))
	tmp = 0.0
	if (t_1 <= -5e+196)
		tmp = t_2;
	elseif (t_1 <= 2e-20)
		tmp = x;
	elseif (t_1 <= 5e+60)
		tmp = t_2;
	elseif (t_1 <= 1e+185)
		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 = y * (t / a);
	tmp = 0.0;
	if (t_1 <= -5e+196)
		tmp = t_2;
	elseif (t_1 <= 2e-20)
		tmp = x;
	elseif (t_1 <= 5e+60)
		tmp = t_2;
	elseif (t_1 <= 1e+185)
		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[(y * N[(t / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+196], t$95$2, If[LessEqual[t$95$1, 2e-20], x, If[LessEqual[t$95$1, 5e+60], t$95$2, If[LessEqual[t$95$1, 1e+185], x, t$95$2]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -4.9999999999999998e196 or 1.99999999999999989e-20 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.99999999999999975e60 or 9.9999999999999998e184 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 85.6%

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

   2. Taylor expanded in t around inf

      \[\leadsto \color{blue}{\frac{t \cdot y}{a}} \]
   3. 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 46.6

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

   4. Applied rewrites 46.6%

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

   if -4.9999999999999998e196 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.99999999999999989e-20 or 4.99999999999999975e60 < (/.f64 (*.f64 y (-.f64 z t)) a) < 9.9999999999999998e184

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 65.5%

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

Alternative 4: 85.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-90}:\\ \;\;\;\;x - \frac{z}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (* (- t z) (/ y a))))
   (if (<= t_1 -2e+94)
     t_2
     (if (<= t_1 2e-90)
       (- x (* (/ z a) y))
       (if (<= t_1 1e+106) (fma (/ t a) y 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 - z) * (y / a);
	double tmp;
	if (t_1 <= -2e+94) {
		tmp = t_2;
	} else if (t_1 <= 2e-90) {
		tmp = x - ((z / a) * y);
	} else if (t_1 <= 1e+106) {
		tmp = fma((t / a), y, 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(Float64(t - z) * Float64(y / a))
	tmp = 0.0
	if (t_1 <= -2e+94)
		tmp = t_2;
	elseif (t_1 <= 2e-90)
		tmp = Float64(x - Float64(Float64(z / a) * y));
	elseif (t_1 <= 1e+106)
		tmp = fma(Float64(t / a), y, x);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+94], t$95$2, If[LessEqual[t$95$1, 2e-90], N[(x - N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+106], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2e94 or 1.00000000000000009e106 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 86.9%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a} - \frac{z}{a}\right)} \]
   3. 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 79.3

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

   4. Applied rewrites 79.3%

      \[\leadsto \color{blue}{\frac{\left(t - z\right) \cdot y}{a}} \]
   5. 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

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-/.f64 87.2

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

   6. Applied rewrites 87.2%

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

   if -2e94 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.99999999999999999e-90

   1. Initial program 99.1%

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

   2. Taylor expanded in z around inf

      \[\leadsto x - \color{blue}{\frac{y \cdot z}{a}} \]
   3. 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 87.6

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

   4. Applied rewrites 87.6%

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

   if 1.99999999999999999e-90 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.00000000000000009e106

   1. Initial program 99.7%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{t}{a} - \frac{z}{a}\right)} \]
   3. 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 95.5

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

   4. Applied rewrites 95.5%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 72.9%

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

Alternative 5: 93.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+159}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+187}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t - z}{a}, y, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (* (- t z) (/ y a))))
   (if (<= t_1 -5e+159) t_2 (if (<= t_1 1e+187) (fma (/ (- t z) a) y 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 - z) * (y / a);
	double tmp;
	if (t_1 <= -5e+159) {
		tmp = t_2;
	} else if (t_1 <= 1e+187) {
		tmp = fma(((t - z) / a), y, 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(Float64(t - z) * Float64(y / a))
	tmp = 0.0
	if (t_1 <= -5e+159)
		tmp = t_2;
	elseif (t_1 <= 1e+187)
		tmp = fma(Float64(Float64(t - z) / a), y, x);
	else
		tmp = t_2;
	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]}, Block[{t$95$2 = N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+159], t$95$2, If[LessEqual[t$95$1, 1e+187], N[(N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] * y + x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -5.00000000000000003e159 or 9.99999999999999907e186 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 84.6%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a} - \frac{z}{a}\right)} \]
   3. 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 81.0

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

   4. Applied rewrites 81.0%

      \[\leadsto \color{blue}{\frac{\left(t - z\right) \cdot y}{a}} \]
   5. 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

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-/.f64 90.6

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

   6. Applied rewrites 90.6%

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

   if -5.00000000000000003e159 < (/.f64 (*.f64 y (-.f64 z t)) a) < 9.99999999999999907e186

   1. Initial program 99.3%

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

   2. Taylor expanded in y around 0

      \[\leadsto \color{blue}{x + y \cdot \left(\frac{t}{a} - \frac{z}{a}\right)} \]
   3. 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 95.0

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

   4. Applied rewrites 95.0%

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

Alternative 6: 85.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+127}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 10^{+106}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (* (- t z) (/ y a))))
   (if (<= t_1 -4e+127) t_2 (if (<= t_1 1e+106) (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)) / a;
	double t_2 = (t - z) * (y / a);
	double tmp;
	if (t_1 <= -4e+127) {
		tmp = t_2;
	} else if (t_1 <= 1e+106) {
		tmp = fma((y / a), t, 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(Float64(t - z) * Float64(y / a))
	tmp = 0.0
	if (t_1 <= -4e+127)
		tmp = t_2;
	elseif (t_1 <= 1e+106)
		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[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+127], t$95$2, If[LessEqual[t$95$1, 1e+106], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -3.99999999999999982e127 or 1.00000000000000009e106 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 86.4%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a} - \frac{z}{a}\right)} \]
   3. 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 79.9

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

   4. Applied rewrites 79.9%

      \[\leadsto \color{blue}{\frac{\left(t - z\right) \cdot y}{a}} \]
   5. 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

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

      5. lower-*.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-/.f64 88.0

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

   6. Applied rewrites 88.0%

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

   if -3.99999999999999982e127 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.00000000000000009e106

   1. Initial program 99.3%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x - -1 \cdot \frac{t \cdot y}{a}} \]
   3. 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 83.0

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

   4. Applied rewrites 83.0%

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

Alternative 7: 57.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+94}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 -2e+94) (* (/ y a) t) (if (<= t_1 2e-20) x (/ (* t 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 <= -2e+94) {
		tmp = (y / a) * t;
	} else if (t_1 <= 2e-20) {
		tmp = x;
	} else {
		tmp = (t * y) / a;
	}
	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 = (y * (z - t)) / a
    if (t_1 <= (-2d+94)) then
        tmp = (y / a) * t
    else if (t_1 <= 2d-20) then
        tmp = x
    else
        tmp = (t * 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 <= -2e+94) {
		tmp = (y / a) * t;
	} else if (t_1 <= 2e-20) {
		tmp = x;
	} else {
		tmp = (t * y) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -2e+94:
		tmp = (y / a) * t
	elif t_1 <= 2e-20:
		tmp = x
	else:
		tmp = (t * 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 <= -2e+94)
		tmp = Float64(Float64(y / a) * t);
	elseif (t_1 <= 2e-20)
		tmp = x;
	else
		tmp = Float64(Float64(t * 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 <= -2e+94)
		tmp = (y / a) * t;
	elseif (t_1 <= 2e-20)
		tmp = x;
	else
		tmp = (t * 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[LessEqual[t$95$1, -2e+94], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2e-20], x, N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -2e94

   1. Initial program 86.7%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 96.8

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

   3. Applied rewrites 96.8%

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

   4. Taylor expanded in t around inf

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lift-/.f64 49.1

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

   6. Applied rewrites 49.1%

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

   if -2e94 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.99999999999999989e-20

   1. Initial program 99.2%

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

   2. Taylor expanded in x around inf

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

   4. Applied rewrites 75.5%

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

   if 1.99999999999999989e-20 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 89.8%

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

   2. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{t}{a} - \frac{z}{a}\right)} \]
   3. 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 75.1

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

   4. Applied rewrites 75.1%

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

   5. Taylor expanded in z around 0

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

   7. Applied rewrites 43.0%

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

Alternative 8: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - z \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{+21}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (* z (/ y a)))))
   (if (<= z -1.5e+24) t_1 (if (<= z 6.5e+21) (fma (/ y a) t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - (z * (y / a));
	double tmp;
	if (z <= -1.5e+24) {
		tmp = t_1;
	} else if (z <= 6.5e+21) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(z * Float64(y / a)))
	tmp = 0.0
	if (z <= -1.5e+24)
		tmp = t_1;
	elseif (z <= 6.5e+21)
		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[(x - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e+24], t$95$1, If[LessEqual[z, 6.5e+21], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.49999999999999997e24 or 6.5e21 < z

   1. Initial program 90.3%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 98.0

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

   3. Applied rewrites 98.0%

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

   4. Taylor expanded in z around inf

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

   6. Applied rewrites 84.7%

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

   if -1.49999999999999997e24 < z < 6.5e21

   1. Initial program 94.9%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x - -1 \cdot \frac{t \cdot y}{a}} \]
   3. 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 87.9

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

   4. Applied rewrites 87.9%

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

Alternative 9: 76.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-z\right) \cdot \frac{y}{a}\\ \mathbf{if}\;z \leq -6.5 \cdot 10^{+171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (- z) (/ y a))))
   (if (<= z -6.5e+171) t_1 (if (<= z 4.9e+86) (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 <= -6.5e+171) {
		tmp = t_1;
	} else if (z <= 4.9e+86) {
		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 <= -6.5e+171)
		tmp = t_1;
	elseif (z <= 4.9e+86)
		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, -6.5e+171], t$95$1, If[LessEqual[z, 4.9e+86], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5e171 or 4.8999999999999999e86 < z

   1. Initial program 89.5%

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

   2. Taylor expanded in z around inf

      \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot z}{a}} \]
   3. 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 62.7

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

   4. Applied rewrites 62.7%

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

   if -6.5e171 < z < 4.8999999999999999e86

   1. Initial program 94.2%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x - -1 \cdot \frac{t \cdot y}{a}} \]
   3. 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 82.4

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

   4. Applied rewrites 82.4%

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

Alternative 10: 74.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -y \cdot \frac{z}{a}\\ \mathbf{if}\;z \leq -4.4 \cdot 10^{+102}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.9 \cdot 10^{+86}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* y (/ z a)))))
   (if (<= z -4.4e+102) t_1 (if (<= z 4.9e+86) (fma (/ y a) t x) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -(y * (z / a));
	double tmp;
	if (z <= -4.4e+102) {
		tmp = t_1;
	} else if (z <= 4.9e+86) {
		tmp = fma((y / a), t, x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(-Float64(y * Float64(z / a)))
	tmp = 0.0
	if (z <= -4.4e+102)
		tmp = t_1;
	elseif (z <= 4.9e+86)
		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[(y * N[(z / a), $MachinePrecision]), $MachinePrecision])}, If[LessEqual[z, -4.4e+102], t$95$1, If[LessEqual[z, 4.9e+86], N[(N[(y / a), $MachinePrecision] * t + x), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000015e102 or 4.8999999999999999e86 < z

   1. Initial program 89.1%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 97.7

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

   3. Applied rewrites 97.7%

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

   4. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

         \[\leadsto -1 \cdot \frac{y \cdot z}{a} \]

      2. *-commutative N/A

         \[\leadsto -1 \cdot \frac{y \cdot z}{a} \]

      3. mul-1-neg N/A

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

      4. lower-neg.f64 N/A

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

      5. associate-/l* N/A

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

      6. lower-*.f64 N/A

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

      7. lower-/.f64 56.2

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

   6. Applied rewrites 56.2%

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

   if -4.40000000000000015e102 < z < 4.8999999999999999e86

   1. Initial program 94.8%

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

   2. Taylor expanded in z around 0

      \[\leadsto \color{blue}{x - -1 \cdot \frac{t \cdot y}{a}} \]
   3. 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 84.7

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

   4. Applied rewrites 84.7%

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

Alternative 11: 71.4% 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 92.8%

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

2. Taylor expanded in z around 0

   \[\leadsto \color{blue}{x - -1 \cdot \frac{t \cdot y}{a}} \]
3. 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 71.4

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

4. Applied rewrites 71.4%

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

Alternative 12: 40.0% 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 92.8%

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

2. Taylor expanded in x around inf

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

4. Applied rewrites 40.0%

   \[\leadsto \color{blue}{x} \]
5. 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

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 2025093 
(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)))