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

Percentage Accurate: 93.6% → 99.8%

Time: 1.9min

Alternatives: 9

Speedup: 1.0×

• 74.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 93.6% accurate, 1.0× speedup

Math

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

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: 99.8% accurate, 0.7× speedup

Math

\[\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a}\right), x, a, \left(t - z\right), y\right) \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (134-z0z1z2z3z4 (/ 1 a) x a (- t z) y))

Derivation

1. Initial program 93.6%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
2. 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. add-to-fraction N/A

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

   4. mult-flip N/A

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

   5. *-commutative N/A

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

   6. *-rgt-identity N/A

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

   7. associate-*l* N/A

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

   8. *-commutative N/A

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

   9. *-rgt-identity N/A

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

   10. lift-*.f64 N/A

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

   11. *-commutative N/A

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

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

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

   13. lift--.f64 N/A

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

   14. sub-negate-rev N/A

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

   15. lower-134-z0z1z2z3z4 N/A

       \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a}\right), x, a, \left(t - z\right), y\right)} \]

   16. lower-/.f64 N/A

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{1}{a}\right)}, x, a, \left(t - z\right), y\right) \]

   17. lower--.f64 99.8%

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a}\right), x, a, \color{blue}{\left(t - z\right)}, y\right) \]

3. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a}\right), x, a, \left(t - z\right), y\right)} \]
4. Add Preprocessing

Alternative 2: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -19999999999999999022865849278470264106778320922372433398933167781147023447499918366556775778344680456191750897534276513413896506501104986185271471852552907987540733076746850001554473076458172448768:\\ \;\;\;\;x + \frac{z - t}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 1999999999999999876516601650563957080654054728944248956588832425077742983649199427273641055007816510603264:\\ \;\;\;\;x + \frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* y (- z t))))
  (if (<=
       t_1
       -19999999999999999022865849278470264106778320922372433398933167781147023447499918366556775778344680456191750897534276513413896506501104986185271471852552907987540733076746850001554473076458172448768)
    (+ x (* (/ (- z t) a) y))
    (if (<=
         t_1
         1999999999999999876516601650563957080654054728944248956588832425077742983649199427273641055007816510603264)
      (+ x (/ t_1 a))
      (- x (* (/ y a) (- t z)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -2e+196) {
		tmp = x + (((z - t) / a) * y);
	} else if (t_1 <= 2e+105) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x - ((y / a) * (t - z));
	}
	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)
    if (t_1 <= (-2d+196)) then
        tmp = x + (((z - t) / a) * y)
    else if (t_1 <= 2d+105) then
        tmp = x + (t_1 / a)
    else
        tmp = x - ((y / a) * (t - z))
    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);
	double tmp;
	if (t_1 <= -2e+196) {
		tmp = x + (((z - t) / a) * y);
	} else if (t_1 <= 2e+105) {
		tmp = x + (t_1 / a);
	} else {
		tmp = x - ((y / a) * (t - z));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -2e+196:
		tmp = x + (((z - t) / a) * y)
	elif t_1 <= 2e+105:
		tmp = x + (t_1 / a)
	else:
		tmp = x - ((y / a) * (t - z))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+196)
		tmp = Float64(x + Float64(Float64(Float64(z - t) / a) * y));
	elseif (t_1 <= 2e+105)
		tmp = Float64(x + Float64(t_1 / a));
	else
		tmp = Float64(x - Float64(Float64(y / a) * Float64(t - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+196)
		tmp = x + (((z - t) / a) * y);
	elseif (t_1 <= 2e+105)
		tmp = x + (t_1 / a);
	else
		tmp = x - ((y / a) * (t - z));
	end
	tmp_2 = 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, -19999999999999999022865849278470264106778320922372433398933167781147023447499918366556775778344680456191750897534276513413896506501104986185271471852552907987540733076746850001554473076458172448768], N[(x + N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1999999999999999876516601650563957080654054728944248956588832425077742983649199427273641055007816510603264], N[(x + N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -1.9999999999999999e196

   1. Initial program 93.6%

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

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 93.6%

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

   3. Applied rewrites 93.6%

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

   if -1.9999999999999999e196 < (*.f64 y (-.f64 z t)) < 1.9999999999999999e105

   1. Initial program 93.6%

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

   if 1.9999999999999999e105 < (*.f64 y (-.f64 z t))

   1. Initial program 93.6%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. mult-flip-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 97.2%

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

   3. Applied rewrites 97.2%

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

Alternative 3: 98.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{z - t}{a} \cdot y\\ \mathbf{if}\;a \leq \frac{-2535301200456459}{2535301200456458802993406410752}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq \frac{5993757216606705}{199791907220223502808422222706762643567910281130558153654986045416023791284464999687699590596063486154228923591770023865308670443474450259602571264}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (/ (- z t) a) y))))
  (if (<= a -2535301200456459/2535301200456458802993406410752)
    t_1
    (if (<=
         a
         5993757216606705/199791907220223502808422222706762643567910281130558153654986045416023791284464999687699590596063486154228923591770023865308670443474450259602571264)
      (+ x (/ (* y (- z t)) a))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((z - t) / a) * y);
	double tmp;
	if (a <= -1e-15) {
		tmp = t_1;
	} else if (a <= 3e-131) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = 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 = x + (((z - t) / a) * y)
    if (a <= (-1d-15)) then
        tmp = t_1
    else if (a <= 3d-131) then
        tmp = x + ((y * (z - t)) / a)
    else
        tmp = 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 = x + (((z - t) / a) * y);
	double tmp;
	if (a <= -1e-15) {
		tmp = t_1;
	} else if (a <= 3e-131) {
		tmp = x + ((y * (z - t)) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((z - t) / a) * y)
	tmp = 0
	if a <= -1e-15:
		tmp = t_1
	elif a <= 3e-131:
		tmp = x + ((y * (z - t)) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(z - t) / a) * y))
	tmp = 0.0
	if (a <= -1e-15)
		tmp = t_1;
	elseif (a <= 3e-131)
		tmp = Float64(x + Float64(Float64(y * Float64(z - t)) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((z - t) / a) * y);
	tmp = 0.0;
	if (a <= -1e-15)
		tmp = t_1;
	elseif (a <= 3e-131)
		tmp = x + ((y * (z - t)) / a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2535301200456459/2535301200456458802993406410752], t$95$1, If[LessEqual[a, 5993757216606705/199791907220223502808422222706762643567910281130558153654986045416023791284464999687699590596063486154228923591770023865308670443474450259602571264], N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.0000000000000001e-15 or 3e-131 < a

   1. Initial program 93.6%

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

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 93.6%

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

   3. Applied rewrites 93.6%

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

   if -1.0000000000000001e-15 < a < 3e-131

   1. Initial program 93.6%

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

Alternative 4: 93.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) / a) * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 93.6%

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

3. Applied rewrites 93.6%

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

Alternative 5: 86.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -999999999999999967336168804116691273849533185806555472917961779471295845921727862608739868455469056:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \frac{-375375841440235}{3753758414402350114985578847754628430655879796774751768338949695381315781309615853973705099290165690424277009592352731309591345333151121630880730453319952580019863461295451288668314174944572706159989883958951313077165169522342308559632306943619798833037312}:\\ \;\;\;\;x - \frac{y}{a} \cdot t\\ \mathbf{elif}\;t\_1 \leq 4999999999999999817033982815443287105513571612636783896840181921713543250771443712:\\ \;\;\;\;x + \frac{z}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (* (/ y a) (- z t))))
  (if (<=
       t_1
       -999999999999999967336168804116691273849533185806555472917961779471295845921727862608739868455469056)
    t_2
    (if (<=
         t_1
         -375375841440235/3753758414402350114985578847754628430655879796774751768338949695381315781309615853973705099290165690424277009592352731309591345333151121630880730453319952580019863461295451288668314174944572706159989883958951313077165169522342308559632306943619798833037312)
      (- x (* (/ y a) t))
      (if (<=
           t_1
           4999999999999999817033982815443287105513571612636783896840181921713543250771443712)
        (+ x (* (/ z a) y))
        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) * (z - t);
	double tmp;
	if (t_1 <= -1e+99) {
		tmp = t_2;
	} else if (t_1 <= -1e-241) {
		tmp = x - ((y / a) * t);
	} else if (t_1 <= 5e+81) {
		tmp = x + ((z / a) * y);
	} 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) * (z - t)
    if (t_1 <= (-1d+99)) then
        tmp = t_2
    else if (t_1 <= (-1d-241)) then
        tmp = x - ((y / a) * t)
    else if (t_1 <= 5d+81) then
        tmp = x + ((z / a) * y)
    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) * (z - t);
	double tmp;
	if (t_1 <= -1e+99) {
		tmp = t_2;
	} else if (t_1 <= -1e-241) {
		tmp = x - ((y / a) * t);
	} else if (t_1 <= 5e+81) {
		tmp = x + ((z / a) * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	t_2 = (y / a) * (z - t)
	tmp = 0
	if t_1 <= -1e+99:
		tmp = t_2
	elif t_1 <= -1e-241:
		tmp = x - ((y / a) * t)
	elif t_1 <= 5e+81:
		tmp = x + ((z / a) * y)
	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) * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -1e+99)
		tmp = t_2;
	elseif (t_1 <= -1e-241)
		tmp = Float64(x - Float64(Float64(y / a) * t));
	elseif (t_1 <= 5e+81)
		tmp = Float64(x + Float64(Float64(z / a) * y));
	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) * (z - t);
	tmp = 0.0;
	if (t_1 <= -1e+99)
		tmp = t_2;
	elseif (t_1 <= -1e-241)
		tmp = x - ((y / a) * t);
	elseif (t_1 <= 5e+81)
		tmp = x + ((z / a) * y);
	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] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -999999999999999967336168804116691273849533185806555472917961779471295845921727862608739868455469056], t$95$2, If[LessEqual[t$95$1, -375375841440235/3753758414402350114985578847754628430655879796774751768338949695381315781309615853973705099290165690424277009592352731309591345333151121630880730453319952580019863461295451288668314174944572706159989883958951313077165169522342308559632306943619798833037312], N[(x - N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4999999999999999817033982815443287105513571612636783896840181921713543250771443712], N[(x + N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -9.9999999999999997e98 or 4.9999999999999998e81 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 93.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.9%

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

   4. Applied rewrites 56.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 59.7%

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

   6. Applied rewrites 59.7%

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

   if -9.9999999999999997e98 < (/.f64 (*.f64 y (-.f64 z t)) a) < -9.9999999999999997e-242

   1. Initial program 93.6%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. mult-flip N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

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

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. *-commutative N/A

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

      13. lower-*.f64 N/A

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

      14. mult-flip-rev N/A

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

      15. lower-/.f64 N/A

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

      16. lower--.f64 97.2%

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

   3. Applied rewrites 97.2%

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

   4. Taylor expanded in z around 0

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

   6. Applied rewrites 71.1%

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

   if -9.9999999999999997e-242 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.9999999999999998e81

   1. Initial program 93.6%

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

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 93.6%

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

   3. Applied rewrites 93.6%

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

   4. Taylor expanded in z around inf

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

      1. lower-/.f64 68.9%

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

   6. Applied rewrites 68.9%

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

Alternative 6: 86.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{y \cdot \left(z - t\right)}{a}\\ t_2 := \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -40000000000000001215144113708014667563008:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 4999999999999999817033982815443287105513571612636783896840181921713543250771443712:\\ \;\;\;\;x + \frac{z}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* y (- z t)) a)) (t_2 (* (/ y a) (- z t))))
  (if (<= t_1 -40000000000000001215144113708014667563008)
    t_2
    (if (<=
         t_1
         4999999999999999817033982815443287105513571612636783896840181921713543250771443712)
      (+ x (* (/ z a) y))
      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) * (z - t);
	double tmp;
	if (t_1 <= -4e+40) {
		tmp = t_2;
	} else if (t_1 <= 5e+81) {
		tmp = x + ((z / a) * y);
	} 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) * (z - t)
    if (t_1 <= (-4d+40)) then
        tmp = t_2
    else if (t_1 <= 5d+81) then
        tmp = x + ((z / a) * y)
    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) * (z - t);
	double tmp;
	if (t_1 <= -4e+40) {
		tmp = t_2;
	} else if (t_1 <= 5e+81) {
		tmp = x + ((z / a) * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y * (z - t)) / a
	t_2 = (y / a) * (z - t)
	tmp = 0
	if t_1 <= -4e+40:
		tmp = t_2
	elif t_1 <= 5e+81:
		tmp = x + ((z / a) * y)
	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) * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -4e+40)
		tmp = t_2;
	elseif (t_1 <= 5e+81)
		tmp = Float64(x + Float64(Float64(z / a) * y));
	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) * (z - t);
	tmp = 0.0;
	if (t_1 <= -4e+40)
		tmp = t_2;
	elseif (t_1 <= 5e+81)
		tmp = x + ((z / a) * y);
	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] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -40000000000000001215144113708014667563008], t$95$2, If[LessEqual[t$95$1, 4999999999999999817033982815443287105513571612636783896840181921713543250771443712], N[(x + N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) a) < -4.0000000000000001e40 or 4.9999999999999998e81 < (/.f64 (*.f64 y (-.f64 z t)) a)

   1. Initial program 93.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.9%

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

   4. Applied rewrites 56.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 59.7%

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

   6. Applied rewrites 59.7%

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

   if -4.0000000000000001e40 < (/.f64 (*.f64 y (-.f64 z t)) a) < 4.9999999999999998e81

   1. Initial program 93.6%

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

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 93.6%

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

   3. Applied rewrites 93.6%

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

   4. Taylor expanded in z around inf

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

      1. lower-/.f64 68.9%

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

   6. Applied rewrites 68.9%

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

Alternative 7: 61.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} t_1 := y \cdot \left(z - t\right)\\ \mathbf{if}\;t\_1 \leq -19999999999999999022865849278470264106778320922372433398933167781147023447499918366556775778344680456191750897534276513413896506501104986185271471852552907987540733076746850001554473076458172448768:\\ \;\;\;\;\frac{z - t}{a} \cdot y\\ \mathbf{elif}\;t\_1 \leq 4999999999999999650599673463152198642336665750694884246307948430823614916415456951880981793447127233788614017024:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(z - t\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* y (- z t))))
  (if (<=
       t_1
       -19999999999999999022865849278470264106778320922372433398933167781147023447499918366556775778344680456191750897534276513413896506501104986185271471852552907987540733076746850001554473076458172448768)
    (* (/ (- z t) a) y)
    (if (<=
         t_1
         4999999999999999650599673463152198642336665750694884246307948430823614916415456951880981793447127233788614017024)
      (/ t_1 a)
      (* (/ y a) (- z t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z - t);
	double tmp;
	if (t_1 <= -2e+196) {
		tmp = ((z - t) / a) * y;
	} else if (t_1 <= 5e+111) {
		tmp = t_1 / a;
	} else {
		tmp = (y / a) * (z - t);
	}
	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)
    if (t_1 <= (-2d+196)) then
        tmp = ((z - t) / a) * y
    else if (t_1 <= 5d+111) then
        tmp = t_1 / a
    else
        tmp = (y / a) * (z - t)
    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);
	double tmp;
	if (t_1 <= -2e+196) {
		tmp = ((z - t) / a) * y;
	} else if (t_1 <= 5e+111) {
		tmp = t_1 / a;
	} else {
		tmp = (y / a) * (z - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z - t)
	tmp = 0
	if t_1 <= -2e+196:
		tmp = ((z - t) / a) * y
	elif t_1 <= 5e+111:
		tmp = t_1 / a
	else:
		tmp = (y / a) * (z - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z - t))
	tmp = 0.0
	if (t_1 <= -2e+196)
		tmp = Float64(Float64(Float64(z - t) / a) * y);
	elseif (t_1 <= 5e+111)
		tmp = Float64(t_1 / a);
	else
		tmp = Float64(Float64(y / a) * Float64(z - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z - t);
	tmp = 0.0;
	if (t_1 <= -2e+196)
		tmp = ((z - t) / a) * y;
	elseif (t_1 <= 5e+111)
		tmp = t_1 / a;
	else
		tmp = (y / a) * (z - t);
	end
	tmp_2 = 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, -19999999999999999022865849278470264106778320922372433398933167781147023447499918366556775778344680456191750897534276513413896506501104986185271471852552907987540733076746850001554473076458172448768], N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 4999999999999999650599673463152198642336665750694884246307948430823614916415456951880981793447127233788614017024], N[(t$95$1 / a), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 y (-.f64 z t)) < -1.9999999999999999e196

   1. Initial program 93.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.9%

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

   4. Applied rewrites 56.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-/l* N/A

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

      6. lift-/.f64 N/A

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

      7. *-commutative N/A

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

      8. lift-*.f64 57.1%

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

   6. Applied rewrites 57.1%

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

   if -1.9999999999999999e196 < (*.f64 y (-.f64 z t)) < 4.9999999999999997e111

   1. Initial program 93.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.9%

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

   4. Applied rewrites 56.9%

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

   if 4.9999999999999997e111 < (*.f64 y (-.f64 z t))

   1. Initial program 93.6%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 56.9%

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

   4. Applied rewrites 56.9%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift--.f64 N/A

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

      4. lift--.f64 N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 59.7%

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

   6. Applied rewrites 59.7%

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

Alternative 8: 59.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 = (y / a) * (z - t)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

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

2. Taylor expanded in x around 0

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 56.9%

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

4. Applied rewrites 56.9%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift--.f64 N/A

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

   4. lift--.f64 N/A

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

   5. associate-*l/ N/A

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

   6. lift-/.f64 N/A

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

   7. lower-*.f64 59.7%

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

6. Applied rewrites 59.7%

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

Alternative 9: 35.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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 = (y / a) * z
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.6%

   \[x + \frac{y \cdot \left(z - t\right)}{a} \]
2. 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. add-to-fraction N/A

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

   4. mult-flip N/A

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

   5. *-commutative N/A

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

   6. *-rgt-identity N/A

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

   7. associate-*l* N/A

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

   8. *-commutative N/A

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

   9. *-rgt-identity N/A

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

   10. lift-*.f64 N/A

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

   11. *-commutative N/A

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

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

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

   13. lift--.f64 N/A

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

   14. sub-negate-rev N/A

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

   15. lower-134-z0z1z2z3z4 N/A

       \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a}\right), x, a, \left(t - z\right), y\right)} \]

   16. lower-/.f64 N/A

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\color{blue}{\left(\frac{1}{a}\right)}, x, a, \left(t - z\right), y\right) \]

   17. lower--.f64 99.8%

       \[\leadsto \mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a}\right), x, a, \color{blue}{\left(t - z\right)}, y\right) \]

3. Applied rewrites 99.8%

   \[\leadsto \color{blue}{\mathsf{134\_z0z1z2z3z4}\left(\left(\frac{1}{a}\right), x, a, \left(t - z\right), y\right)} \]

4. Taylor expanded in z around inf

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

   1. lower-/.f64 N/A

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

   2. lower-*.f64 32.3%

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

6. Applied rewrites 32.3%

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

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. lift-/.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-*.f64 N/A

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

   6. associate-*r* N/A

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

   7. lift-*.f64 N/A

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

   8. lower-*.f64 35.0%

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

   9. lift-*.f64 N/A

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

   10. *-commutative N/A

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

   11. lift-/.f64 N/A

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

   12. mult-flip N/A

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

   13. lift-/.f64 35.0%

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

8. Applied rewrites 35.0%

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

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64
  (+ x (/ (* y (- z t)) a)))