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

Percentage Accurate: 93.7% → 99.6%

Time: 5.8s

Alternatives: 12

Speedup: 1.1×

• 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: 93.7% 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: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+270}:\\ \;\;\;\;\mathsf{fma}\left(t - z, \frac{y}{a}, x\right)\\ \mathbf{elif}\;t\_1 \leq 3 \cdot 10^{+259}:\\ \;\;\;\;x - \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a}, -y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (<= t_1 -4e+270)
     (fma (- t z) (/ y a) x)
     (if (<= t_1 3e+259) (- x (/ t_1 a)) (fma (/ (- z t) a) (- y) x)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -4e+270) {
		tmp = fma((t - z), (y / a), x);
	} else if (t_1 <= 3e+259) {
		tmp = x - (t_1 / a);
	} else {
		tmp = fma(((z - t) / a), -y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -4e+270)
		tmp = fma(Float64(t - z), Float64(y / a), x);
	elseif (t_1 <= 3e+259)
		tmp = Float64(x - Float64(t_1 / a));
	else
		tmp = fma(Float64(Float64(z - t) / a), Float64(-y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+270], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[t$95$1, 3e+259], N[(x - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * (-y) + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -4.0000000000000002e270

   1. Initial program 67.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.8%

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

   if -4.0000000000000002e270 < (*.f64 y (-.f64 z t)) < 3.00000000000000013e259

   1. Initial program 99.4%

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

   if 3.00000000000000013e259 < (*.f64 y (-.f64 z t))

   1. Initial program 70.4%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

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

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

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

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

      8. *-commutative N/A

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

      9. associate-/l* N/A

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

      10. lift-*.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. +-commutative N/A

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

      13. lift-/.f64 N/A

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

      14. lift-*.f64 N/A

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

      15. associate-/l* N/A

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

      16. *-commutative N/A

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

      17. distribute-rgt-neg-in N/A

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

      18. lower-fma.f64 N/A

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

      19. lower-/.f64 N/A

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

      20. lower-neg.f64 99.9

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

   4. Applied rewrites 99.9%

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

Alternative 2: 84.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+269}:\\ \;\;\;\;\frac{t - z}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq -0.02:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;t\_1 \leq 500:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (<= t_1 -5e+269)
     (* (/ (- t z) a) y)
     (if (<= t_1 -0.02)
       (- x (/ (* y z) a))
       (if (<= t_1 500.0) (+ (* (/ t a) y) x) (* (- t z) (/ y a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -5e+269) {
		tmp = ((t - z) / a) * y;
	} else if (t_1 <= -0.02) {
		tmp = x - ((y * z) / a);
	} else if (t_1 <= 500.0) {
		tmp = ((t / a) * y) + x;
	} else {
		tmp = (t - z) * (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 <= (-5d+269)) then
        tmp = ((t - z) / a) * y
    else if (t_1 <= (-0.02d0)) then
        tmp = x - ((y * z) / a)
    else if (t_1 <= 500.0d0) then
        tmp = ((t / a) * y) + x
    else
        tmp = (t - z) * (y / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if (t_1 <= -5e+269) {
		tmp = ((t - z) / a) * y;
	} else if (t_1 <= -0.02) {
		tmp = x - ((y * z) / a);
	} else if (t_1 <= 500.0) {
		tmp = ((t / a) * y) + x;
	} else {
		tmp = (t - z) * (y / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if t_1 <= -5e+269:
		tmp = ((t - z) / a) * y
	elif t_1 <= -0.02:
		tmp = x - ((y * z) / a)
	elif t_1 <= 500.0:
		tmp = ((t / a) * y) + x
	else:
		tmp = (t - z) * (y / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if (t_1 <= -5e+269)
		tmp = Float64(Float64(Float64(t - z) / a) * y);
	elseif (t_1 <= -0.02)
		tmp = Float64(x - Float64(Float64(y * z) / a));
	elseif (t_1 <= 500.0)
		tmp = Float64(Float64(Float64(t / a) * y) + x);
	else
		tmp = Float64(Float64(t - z) * Float64(y / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y * (z - t)) / a;
	tmp = 0.0;
	if (t_1 <= -5e+269)
		tmp = ((t - z) / a) * y;
	elseif (t_1 <= -0.02)
		tmp = x - ((y * z) / a);
	elseif (t_1 <= 500.0)
		tmp = ((t / a) * y) + x;
	else
		tmp = (t - z) * (y / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+269], N[(N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -0.02], N[(x - N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 500.0], N[(N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -5.0000000000000002e269

   1. Initial program 73.8%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 94.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 92.0%

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

   if -5.0000000000000002e269 < (/.f64 (*.f64 y (-.f64 z t)) a) < -0.0200000000000000004

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 81.8%

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

   if -0.0200000000000000004 < (/.f64 (*.f64 y (-.f64 z t)) a) < 500

   1. Initial program 99.0%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 92.1%

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

   7. Applied rewrites 92.1%

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

   if 500 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 86.5%

      \[\leadsto \color{blue}{\left(t - z\right) \cdot \frac{y}{a}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -5 \cdot 10^{+269}:\\ \;\;\;\;\frac{t - z}{a} \cdot y\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq -0.02:\\ \;\;\;\;x - \frac{y \cdot z}{a}\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a} \leq 500:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \mathbf{else}:\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+75} \lor \neg \left(t\_1 \leq 500\right):\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -4e+75) (not (<= t_1 500.0)))
     (* (- t z) (/ y a))
     (+ (* (/ t a) y) x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -4e+75) || !(t_1 <= 500.0)) {
		tmp = (t - z) * (y / a);
	} else {
		tmp = ((t / a) * y) + x;
	}
	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 <= (-4d+75)) .or. (.not. (t_1 <= 500.0d0))) then
        tmp = (t - z) * (y / a)
    else
        tmp = ((t / a) * y) + x
    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 <= -4e+75) || !(t_1 <= 500.0)) {
		tmp = (t - z) * (y / a);
	} else {
		tmp = ((t / a) * y) + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if (t_1 <= -4e+75) or not (t_1 <= 500.0):
		tmp = (t - z) * (y / a)
	else:
		tmp = ((t / a) * y) + x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -4e+75) || !(t_1 <= 500.0))
		tmp = Float64(Float64(t - z) * Float64(y / a));
	else
		tmp = Float64(Float64(Float64(t / a) * y) + x);
	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 <= -4e+75) || ~((t_1 <= 500.0)))
		tmp = (t - z) * (y / a);
	else
		tmp = ((t / a) * y) + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+75], N[Not[LessEqual[t$95$1, 500.0]], $MachinePrecision]], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -3.99999999999999971e75 or 500 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 86.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 86.3%

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

   if -3.99999999999999971e75 < (/.f64 (*.f64 y (-.f64 z t)) a) < 500

   1. Initial program 99.1%

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

   5. Applied rewrites 88.7%

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

   7. Applied rewrites 88.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -4 \cdot 10^{+75} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 500\right):\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a} \cdot y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+75} \lor \neg \left(t\_1 \leq 500\right):\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -4e+75) (not (<= t_1 500.0)))
     (* (- t z) (/ y a))
     (fma (/ t a) y x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -4e+75) || !(t_1 <= 500.0)) {
		tmp = (t - z) * (y / a);
	} else {
		tmp = fma((t / a), y, x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -4e+75) || !(t_1 <= 500.0))
		tmp = Float64(Float64(t - z) * Float64(y / a));
	else
		tmp = fma(Float64(t / a), y, x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+75], N[Not[LessEqual[t$95$1, 500.0]], $MachinePrecision]], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(N[(t / a), $MachinePrecision] * y + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -3.99999999999999971e75 or 500 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 86.3%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 86.3%

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

   if -3.99999999999999971e75 < (/.f64 (*.f64 y (-.f64 z t)) a) < 500

   1. Initial program 99.1%

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

   5. Applied rewrites 88.7%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -4 \cdot 10^{+75} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 500\right):\\ \;\;\;\;\left(t - z\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{t}{a}, y, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+107} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+183}\right):\\ \;\;\;\;\frac{t - z}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -5e+107) (not (<= t_1 2e+183)))
     (* (/ (- t z) a) y)
     (fma t (/ y a) x))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -5e+107) || !(t_1 <= 2e+183)) {
		tmp = ((t - z) / a) * y;
	} else {
		tmp = fma(t, (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -5e+107) || !(t_1 <= 2e+183))
		tmp = Float64(Float64(Float64(t - z) / a) * y);
	else
		tmp = fma(t, Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e+107], N[Not[LessEqual[t$95$1, 2e+183]], $MachinePrecision]], N[(N[(N[(t - z), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -5.0000000000000002e107 or 1.99999999999999989e183 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 83.5%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 95.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 86.0%

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

   if -5.0000000000000002e107 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.99999999999999989e183

   1. Initial program 99.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 97.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 82.9%

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

4. Final simplification 84.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -5 \cdot 10^{+107} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 2 \cdot 10^{+183}\right):\\ \;\;\;\;\frac{t - z}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 57.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+75} \lor \neg \left(t\_1 \leq 2 \cdot 10^{+183}\right):\\ \;\;\;\;\frac{t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -4e+75) (not (<= t_1 2e+183))) (* (/ t a) y) x)))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -4e+75) || !(t_1 <= 2e+183)) {
		tmp = (t / a) * y;
	} else {
		tmp = x;
	}
	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 <= (-4d+75)) .or. (.not. (t_1 <= 2d+183))) then
        tmp = (t / a) * y
    else
        tmp = x
    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 <= -4e+75) || !(t_1 <= 2e+183)) {
		tmp = (t / a) * y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if (t_1 <= -4e+75) or not (t_1 <= 2e+183):
		tmp = (t / a) * y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -4e+75) || !(t_1 <= 2e+183))
		tmp = Float64(Float64(t / a) * y);
	else
		tmp = x;
	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 <= -4e+75) || ~((t_1 <= 2e+183)))
		tmp = (t / a) * y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+75], N[Not[LessEqual[t$95$1, 2e+183]], $MachinePrecision]], N[(N[(t / a), $MachinePrecision] * y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -3.99999999999999971e75 or 1.99999999999999989e183 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 84.1%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 47.8%

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

   if -3.99999999999999971e75 < (/.f64 (*.f64 y (-.f64 z t)) a) < 1.99999999999999989e183

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 66.8%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -4 \cdot 10^{+75} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 2 \cdot 10^{+183}\right):\\ \;\;\;\;\frac{t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+75} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-29}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (* y (- z t)) a)))
   (if (or (<= t_1 -4e+75) (not (<= t_1 5e-29))) (* t (/ y a)) x)))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y * (z - t)) / a;
	double tmp;
	if ((t_1 <= -4e+75) || !(t_1 <= 5e-29)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	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 <= (-4d+75)) .or. (.not. (t_1 <= 5d-29))) then
        tmp = t * (y / a)
    else
        tmp = x
    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 <= -4e+75) || !(t_1 <= 5e-29)) {
		tmp = t * (y / a);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	tmp = 0
	if (t_1 <= -4e+75) or not (t_1 <= 5e-29):
		tmp = t * (y / a)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y * Float64(z - t)) / a)
	tmp = 0.0
	if ((t_1 <= -4e+75) || !(t_1 <= 5e-29))
		tmp = Float64(t * Float64(y / a));
	else
		tmp = x;
	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 <= -4e+75) || ~((t_1 <= 5e-29)))
		tmp = t * (y / a);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+75], N[Not[LessEqual[t$95$1, 5e-29]], $MachinePrecision]], N[(t * N[(y / a), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -3.99999999999999971e75 or 4.99999999999999986e-29 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 86.7%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 43.1%

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

   7. Applied rewrites 43.8%

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

   if -3.99999999999999971e75 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.99999999999999986e-29

   1. Initial program 99.0%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 75.0%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \leq -4 \cdot 10^{+75} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \leq 5 \cdot 10^{-29}\right):\\ \;\;\;\;t \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+270} \lor \neg \left(t\_1 \leq 5 \cdot 10^{+195}\right):\\ \;\;\;\;\mathsf{fma}\left(t - z, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (- z t))))
   (if (or (<= t_1 -4e+270) (not (<= t_1 5e+195)))
     (fma (- t z) (/ y a) x)
     (- x (/ t_1 a)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if ((t_1 <= -4e+270) || !(t_1 <= 5e+195)) {
		tmp = fma((t - z), (y / a), x);
	} else {
		tmp = x - (t_1 / a);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if ((t_1 <= -4e+270) || !(t_1 <= 5e+195))
		tmp = fma(Float64(t - z), Float64(y / a), x);
	else
		tmp = Float64(x - Float64(t_1 / a));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -4e+270], N[Not[LessEqual[t$95$1, 5e+195]], $MachinePrecision]], N[(N[(t - z), $MachinePrecision] * N[(y / a), $MachinePrecision] + x), $MachinePrecision], N[(x - N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 y (-.f64 z t)) < -4.0000000000000002e270 or 4.9999999999999998e195 < (*.f64 y (-.f64 z t))

   1. Initial program 73.2%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 99.8%

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

   if -4.0000000000000002e270 < (*.f64 y (-.f64 z t)) < 4.9999999999999998e195

   1. Initial program 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \leq -4 \cdot 10^{+270} \lor \neg \left(y \cdot \left(z - t\right) \leq 5 \cdot 10^{+195}\right):\\ \;\;\;\;\mathsf{fma}\left(t - z, \frac{y}{a}, x\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+215} \lor \neg \left(z \leq 2.9 \cdot 10^{+142}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -1.9e+215) (not (<= z 2.9e+142)))
   (* (- z) (/ y a))
   (fma t (/ y a) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -1.9e+215) || !(z <= 2.9e+142)) {
		tmp = -z * (y / a);
	} else {
		tmp = fma(t, (y / a), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -1.9e+215) || !(z <= 2.9e+142))
		tmp = Float64(Float64(-z) * Float64(y / a));
	else
		tmp = fma(t, Float64(y / a), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -1.9e+215], N[Not[LessEqual[z, 2.9e+142]], $MachinePrecision]], N[((-z) * N[(y / a), $MachinePrecision]), $MachinePrecision], N[(t * N[(y / a), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.89999999999999984e215 or 2.90000000000000013e142 < z

   1. Initial program 82.5%

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

   5. Applied rewrites 63.9%

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

   7. Applied rewrites 73.8%

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

   if -1.89999999999999984e215 < z < 2.90000000000000013e142

   1. Initial program 94.9%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 95.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 78.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+215} \lor \neg \left(z \leq 2.9 \cdot 10^{+142}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{y}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t, \frac{y}{a}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 96.3%

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

Alternative 11: 71.5% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 91.8%

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

3. Taylor expanded in x around 0

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

5. Applied rewrites 96.3%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 66.9%

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

Alternative 12: 40.4% 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 91.8%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 37.2%

   \[\leadsto \color{blue}{x} \]
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 2025019 
(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)))