Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B

Percentage Accurate: 98.1% → 99.8%

Time: 1.7min

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

Derivation

1. Initial program 98.1%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-/.f64 N/A

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

   4. mult-flip N/A

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

   5. *-commutative N/A

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

   6. associate-*l* N/A

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

   7. *-commutative N/A

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

   8. lift--.f64 N/A

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

   9. sub-flip N/A

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

   10. distribute-rgt-in N/A

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

   11. *-commutative N/A

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

   12. distribute-rgt-neg-out N/A

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

   13. sub-flip-reverse N/A

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

   14. lower-134-z0z1z2z3z4 N/A

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

   15. frac-2neg N/A

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

   16. metadata-eval N/A

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

   17. lower-/.f64 N/A

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

   18. lift--.f64 N/A

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

   19. sub-negate-rev N/A

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

   20. lower--.f64 99.8%

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

3. Applied rewrites 99.8%

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

Alternative 2: 96.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t\_1 \leq -1000000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \frac{3022314549036573}{151115727451828646838272}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{elif}\;t\_1 \leq \frac{4505851427184181}{4503599627370496}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (+ x (* y (/ z (- a t))))))
  (if (<= t_1 -1000000)
    t_2
    (if (<= t_1 3022314549036573/151115727451828646838272)
      (+ x (* y (/ (- z t) a)))
      (if (<= t_1 4505851427184181/4503599627370496) (+ x y) t_2)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = x + (y * (z / (a - t)));
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 2e-8) {
		tmp = x + (y * ((z - t) / a));
	} else if (t_1 <= 1.0005) {
		tmp = x + 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 = (z - t) / (a - t)
    t_2 = x + (y * (z / (a - t)))
    if (t_1 <= (-1000000.0d0)) then
        tmp = t_2
    else if (t_1 <= 2d-8) then
        tmp = x + (y * ((z - t) / a))
    else if (t_1 <= 1.0005d0) then
        tmp = x + 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 = (z - t) / (a - t);
	double t_2 = x + (y * (z / (a - t)));
	double tmp;
	if (t_1 <= -1000000.0) {
		tmp = t_2;
	} else if (t_1 <= 2e-8) {
		tmp = x + (y * ((z - t) / a));
	} else if (t_1 <= 1.0005) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = x + (y * (z / (a - t)))
	tmp = 0
	if t_1 <= -1000000.0:
		tmp = t_2
	elif t_1 <= 2e-8:
		tmp = x + (y * ((z - t) / a))
	elif t_1 <= 1.0005:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(x + Float64(y * Float64(z / Float64(a - t))))
	tmp = 0.0
	if (t_1 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 2e-8)
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / a)));
	elseif (t_1 <= 1.0005)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = x + (y * (z / (a - t)));
	tmp = 0.0;
	if (t_1 <= -1000000.0)
		tmp = t_2;
	elseif (t_1 <= 2e-8)
		tmp = x + (y * ((z - t) / a));
	elseif (t_1 <= 1.0005)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1000000], t$95$2, If[LessEqual[t$95$1, 3022314549036573/151115727451828646838272], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 4505851427184181/4503599627370496], N[(x + y), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -1e6 or 1.0004999999999999 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 76.8%

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

   4. Applied rewrites 76.8%

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

   if -1e6 < (/.f64 (-.f64 z t) (-.f64 a t)) < 2e-8

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 60.2%

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

   if 2e-8 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0004999999999999

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

Alternative 3: 91.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := x + y \cdot \frac{z}{a - t}\\ \mathbf{if}\;t\_1 \leq \frac{8034690221294951}{803469022129495137770981046170581301261101496891396417650688}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \frac{4505851427184181}{4503599627370496}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (+ x (* y (/ z (- a t))))))
  (if (<=
       t_1
       8034690221294951/803469022129495137770981046170581301261101496891396417650688)
    t_2
    (if (<= t_1 4505851427184181/4503599627370496) (+ x y) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = x + (y * (z / (a - t)));
	double tmp;
	if (t_1 <= 1e-44) {
		tmp = t_2;
	} else if (t_1 <= 1.0005) {
		tmp = x + 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 = (z - t) / (a - t)
    t_2 = x + (y * (z / (a - t)))
    if (t_1 <= 1d-44) then
        tmp = t_2
    else if (t_1 <= 1.0005d0) then
        tmp = x + 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 = (z - t) / (a - t);
	double t_2 = x + (y * (z / (a - t)));
	double tmp;
	if (t_1 <= 1e-44) {
		tmp = t_2;
	} else if (t_1 <= 1.0005) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = x + (y * (z / (a - t)))
	tmp = 0
	if t_1 <= 1e-44:
		tmp = t_2
	elif t_1 <= 1.0005:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(x + Float64(y * Float64(z / Float64(a - t))))
	tmp = 0.0
	if (t_1 <= 1e-44)
		tmp = t_2;
	elseif (t_1 <= 1.0005)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = x + (y * (z / (a - t)));
	tmp = 0.0;
	if (t_1 <= 1e-44)
		tmp = t_2;
	elseif (t_1 <= 1.0005)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 8034690221294951/803469022129495137770981046170581301261101496891396417650688], t$95$2, If[LessEqual[t$95$1, 4505851427184181/4503599627370496], N[(x + y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 9.9999999999999995e-45 or 1.0004999999999999 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 76.8%

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

   4. Applied rewrites 76.8%

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

   if 9.9999999999999995e-45 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0004999999999999

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

Alternative 4: 88.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := x + \frac{y \cdot z}{a - t}\\ \mathbf{if}\;t\_1 \leq \frac{8034690221294951}{803469022129495137770981046170581301261101496891396417650688}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \frac{2254051613498933}{2251799813685248}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (+ x (/ (* y z) (- a t)))))
  (if (<=
       t_1
       8034690221294951/803469022129495137770981046170581301261101496891396417650688)
    t_2
    (if (<= t_1 2254051613498933/2251799813685248) (+ x y) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = x + ((y * z) / (a - t));
	double tmp;
	if (t_1 <= 1e-44) {
		tmp = t_2;
	} else if (t_1 <= 1.001) {
		tmp = x + 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 = (z - t) / (a - t)
    t_2 = x + ((y * z) / (a - t))
    if (t_1 <= 1d-44) then
        tmp = t_2
    else if (t_1 <= 1.001d0) then
        tmp = x + 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 = (z - t) / (a - t);
	double t_2 = x + ((y * z) / (a - t));
	double tmp;
	if (t_1 <= 1e-44) {
		tmp = t_2;
	} else if (t_1 <= 1.001) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = x + ((y * z) / (a - t))
	tmp = 0
	if t_1 <= 1e-44:
		tmp = t_2
	elif t_1 <= 1.001:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(x + Float64(Float64(y * z) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= 1e-44)
		tmp = t_2;
	elseif (t_1 <= 1.001)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = x + ((y * z) / (a - t));
	tmp = 0.0;
	if (t_1 <= 1e-44)
		tmp = t_2;
	elseif (t_1 <= 1.001)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 8034690221294951/803469022129495137770981046170581301261101496891396417650688], t$95$2, If[LessEqual[t$95$1, 2254051613498933/2251799813685248], N[(x + y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < 9.9999999999999995e-45 or 1.0009999999999999 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.8%

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

   4. Applied rewrites 73.8%

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

   if 9.9999999999999995e-45 < (/.f64 (-.f64 z t) (-.f64 a t)) < 1.0009999999999999

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

Alternative 5: 80.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -50000000000000003814884920545943501647482485473280:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \mathbf{elif}\;t\_1 \leq \frac{8034690221294951}{803469022129495137770981046170581301261101496891396417650688}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \mathbf{elif}\;t\_1 \leq 9999999999999999673560075006595519222746403606649979913266024618633003221909504:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (- z t) (- a t))))
  (if (<= t_1 -50000000000000003814884920545943501647482485473280)
    (* (/ y (- a t)) z)
    (if (<=
         t_1
         8034690221294951/803469022129495137770981046170581301261101496891396417650688)
      (+ x (* y (/ z a)))
      (if (<=
           t_1
           9999999999999999673560075006595519222746403606649979913266024618633003221909504)
        (+ x y)
        (+ x (/ (* y z) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+49) {
		tmp = (y / (a - t)) * z;
	} else if (t_1 <= 1e-44) {
		tmp = x + (y * (z / a));
	} else if (t_1 <= 1e+79) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / 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 = (z - t) / (a - t)
    if (t_1 <= (-5d+49)) then
        tmp = (y / (a - t)) * z
    else if (t_1 <= 1d-44) then
        tmp = x + (y * (z / a))
    else if (t_1 <= 1d+79) then
        tmp = x + y
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+49) {
		tmp = (y / (a - t)) * z;
	} else if (t_1 <= 1e-44) {
		tmp = x + (y * (z / a));
	} else if (t_1 <= 1e+79) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e+49:
		tmp = (y / (a - t)) * z
	elif t_1 <= 1e-44:
		tmp = x + (y * (z / a))
	elif t_1 <= 1e+79:
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e+49)
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	elseif (t_1 <= 1e-44)
		tmp = Float64(x + Float64(y * Float64(z / a)));
	elseif (t_1 <= 1e+79)
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -5e+49)
		tmp = (y / (a - t)) * z;
	elseif (t_1 <= 1e-44)
		tmp = x + (y * (z / a));
	elseif (t_1 <= 1e+79)
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000000003814884920545943501647482485473280], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 8034690221294951/803469022129495137770981046170581301261101496891396417650688], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 9999999999999999673560075006595519222746403606649979913266024618633003221909504], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.0000000000000004e49

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.3%

      \[\leadsto y \]

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.7%

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

   10. Applied rewrites 26.7%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lift-/.f64 N/A

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

       5. lift-*.f64 29.0%

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

   12. Applied rewrites 29.0%

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

   if -5.0000000000000004e49 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.9999999999999995e-45

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 61.1%

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

   4. Applied rewrites 61.1%

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

   if 9.9999999999999995e-45 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.9999999999999997e78

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if 9.9999999999999997e78 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.5%

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

   4. Applied rewrites 59.5%

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

Alternative 6: 80.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq -50000000000000003814884920545943501647482485473280:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \mathbf{elif}\;t\_1 \leq \frac{8034690221294951}{803469022129495137770981046170581301261101496891396417650688}:\\ \;\;\;\;x + \frac{y}{a} \cdot z\\ \mathbf{elif}\;t\_1 \leq 9999999999999999673560075006595519222746403606649979913266024618633003221909504:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (- z t) (- a t))))
  (if (<= t_1 -50000000000000003814884920545943501647482485473280)
    (* (/ y (- a t)) z)
    (if (<=
         t_1
         8034690221294951/803469022129495137770981046170581301261101496891396417650688)
      (+ x (* (/ y a) z))
      (if (<=
           t_1
           9999999999999999673560075006595519222746403606649979913266024618633003221909504)
        (+ x y)
        (+ x (/ (* y z) a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+49) {
		tmp = (y / (a - t)) * z;
	} else if (t_1 <= 1e-44) {
		tmp = x + ((y / a) * z);
	} else if (t_1 <= 1e+79) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / 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 = (z - t) / (a - t)
    if (t_1 <= (-5d+49)) then
        tmp = (y / (a - t)) * z
    else if (t_1 <= 1d-44) then
        tmp = x + ((y / a) * z)
    else if (t_1 <= 1d+79) then
        tmp = x + y
    else
        tmp = x + ((y * z) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -5e+49) {
		tmp = (y / (a - t)) * z;
	} else if (t_1 <= 1e-44) {
		tmp = x + ((y / a) * z);
	} else if (t_1 <= 1e+79) {
		tmp = x + y;
	} else {
		tmp = x + ((y * z) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -5e+49:
		tmp = (y / (a - t)) * z
	elif t_1 <= 1e-44:
		tmp = x + ((y / a) * z)
	elif t_1 <= 1e+79:
		tmp = x + y
	else:
		tmp = x + ((y * z) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -5e+49)
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	elseif (t_1 <= 1e-44)
		tmp = Float64(x + Float64(Float64(y / a) * z));
	elseif (t_1 <= 1e+79)
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(Float64(y * z) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -5e+49)
		tmp = (y / (a - t)) * z;
	elseif (t_1 <= 1e-44)
		tmp = x + ((y / a) * z);
	elseif (t_1 <= 1e+79)
		tmp = x + y;
	else
		tmp = x + ((y * z) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -50000000000000003814884920545943501647482485473280], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 8034690221294951/803469022129495137770981046170581301261101496891396417650688], N[(x + N[(N[(y / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 9999999999999999673560075006595519222746403606649979913266024618633003221909504], N[(x + y), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.0000000000000004e49

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.3%

      \[\leadsto y \]

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.7%

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

   10. Applied rewrites 26.7%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lift-/.f64 N/A

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

       5. lift-*.f64 29.0%

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

   12. Applied rewrites 29.0%

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

   if -5.0000000000000004e49 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.9999999999999995e-45

   1. Initial program 98.1%

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

      1. lift-*.f64 N/A

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

      2. *-commutative N/A

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

      3. lift-/.f64 N/A

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

      4. mult-flip N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

      8. lift--.f64 N/A

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

      9. sub-flip N/A

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

      10. distribute-rgt-in N/A

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

      11. *-commutative N/A

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

      12. distribute-rgt-neg-out N/A

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

      13. sub-flip-reverse N/A

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

      14. lower-134-z0z1z2z3z4 N/A

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

      15. frac-2neg N/A

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

      16. metadata-eval N/A

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

      17. lower-/.f64 N/A

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

      18. lift--.f64 N/A

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

      19. sub-negate-rev N/A

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

      20. lower--.f64 99.8%

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

   3. Applied rewrites 99.8%

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

   4. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.5%

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

   6. Applied rewrites 59.5%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. lower-/.f64 61.4%

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

   8. Applied rewrites 61.4%

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

   if 9.9999999999999995e-45 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.9999999999999997e78

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if 9.9999999999999997e78 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.5%

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

   4. Applied rewrites 59.5%

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

Alternative 7: 78.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{y \cdot z}{a}\\ t_2 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_2 \leq -50000000000000003814884920545943501647482485473280:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \mathbf{elif}\;t\_2 \leq \frac{8034690221294951}{803469022129495137770981046170581301261101496891396417650688}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 9999999999999999673560075006595519222746403606649979913266024618633003221909504:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (/ (* y z) a))) (t_2 (/ (- z t) (- a t))))
  (if (<= t_2 -50000000000000003814884920545943501647482485473280)
    (* (/ y (- a t)) z)
    (if (<=
         t_2
         8034690221294951/803469022129495137770981046170581301261101496891396417650688)
      t_1
      (if (<=
           t_2
           9999999999999999673560075006595519222746403606649979913266024618633003221909504)
        (+ x y)
        t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((y * z) / a);
	double t_2 = (z - t) / (a - t);
	double tmp;
	if (t_2 <= -5e+49) {
		tmp = (y / (a - t)) * z;
	} else if (t_2 <= 1e-44) {
		tmp = t_1;
	} else if (t_2 <= 1e+79) {
		tmp = x + y;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = x + ((y * z) / a)
    t_2 = (z - t) / (a - t)
    if (t_2 <= (-5d+49)) then
        tmp = (y / (a - t)) * z
    else if (t_2 <= 1d-44) then
        tmp = t_1
    else if (t_2 <= 1d+79) then
        tmp = x + y
    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 + ((y * z) / a);
	double t_2 = (z - t) / (a - t);
	double tmp;
	if (t_2 <= -5e+49) {
		tmp = (y / (a - t)) * z;
	} else if (t_2 <= 1e-44) {
		tmp = t_1;
	} else if (t_2 <= 1e+79) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((y * z) / a)
	t_2 = (z - t) / (a - t)
	tmp = 0
	if t_2 <= -5e+49:
		tmp = (y / (a - t)) * z
	elif t_2 <= 1e-44:
		tmp = t_1
	elif t_2 <= 1e+79:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(y * z) / a))
	t_2 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_2 <= -5e+49)
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	elseif (t_2 <= 1e-44)
		tmp = t_1;
	elseif (t_2 <= 1e+79)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((y * z) / a);
	t_2 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_2 <= -5e+49)
		tmp = (y / (a - t)) * z;
	elseif (t_2 <= 1e-44)
		tmp = t_1;
	elseif (t_2 <= 1e+79)
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -50000000000000003814884920545943501647482485473280], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$2, 8034690221294951/803469022129495137770981046170581301261101496891396417650688], t$95$1, If[LessEqual[t$95$2, 9999999999999999673560075006595519222746403606649979913266024618633003221909504], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -5.0000000000000004e49

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.3%

      \[\leadsto y \]

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.7%

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

   10. Applied rewrites 26.7%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lift-/.f64 N/A

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

       5. lift-*.f64 29.0%

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

   12. Applied rewrites 29.0%

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

   if -5.0000000000000004e49 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.9999999999999995e-45 or 9.9999999999999997e78 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.5%

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

   4. Applied rewrites 59.5%

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

   if 9.9999999999999995e-45 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.9999999999999997e78

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

Alternative 8: 71.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ \mathbf{if}\;t\_1 \leq \frac{-2535301200456459}{2535301200456458802993406410752}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \mathbf{elif}\;t\_1 \leq 500000000000000016999495856501412297471987359856449023856715357418937635861600416646370808190366722960654336:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a - t}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (- z t) (- a t))))
  (if (<= t_1 -2535301200456459/2535301200456458802993406410752)
    (* (/ y (- a t)) z)
    (if (<=
         t_1
         500000000000000016999495856501412297471987359856449023856715357418937635861600416646370808190366722960654336)
      (+ x y)
      (/ (* y z) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -1e-15) {
		tmp = (y / (a - t)) * z;
	} else if (t_1 <= 5e+107) {
		tmp = x + y;
	} else {
		tmp = (y * z) / (a - 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 = (z - t) / (a - t)
    if (t_1 <= (-1d-15)) then
        tmp = (y / (a - t)) * z
    else if (t_1 <= 5d+107) then
        tmp = x + y
    else
        tmp = (y * z) / (a - 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 = (z - t) / (a - t);
	double tmp;
	if (t_1 <= -1e-15) {
		tmp = (y / (a - t)) * z;
	} else if (t_1 <= 5e+107) {
		tmp = x + y;
	} else {
		tmp = (y * z) / (a - t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	tmp = 0
	if t_1 <= -1e-15:
		tmp = (y / (a - t)) * z
	elif t_1 <= 5e+107:
		tmp = x + y
	else:
		tmp = (y * z) / (a - t)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	tmp = 0.0
	if (t_1 <= -1e-15)
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	elseif (t_1 <= 5e+107)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y * z) / Float64(a - t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	tmp = 0.0;
	if (t_1 <= -1e-15)
		tmp = (y / (a - t)) * z;
	elseif (t_1 <= 5e+107)
		tmp = x + y;
	else
		tmp = (y * z) / (a - t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2535301200456459/2535301200456458802993406410752], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[t$95$1, 500000000000000016999495856501412297471987359856449023856715357418937635861600416646370808190366722960654336], N[(x + y), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -1.0000000000000001e-15

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.3%

      \[\leadsto y \]

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.7%

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

   10. Applied rewrites 26.7%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lift-/.f64 N/A

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

       5. lift-*.f64 29.0%

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

   12. Applied rewrites 29.0%

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

   if -1.0000000000000001e-15 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5.0000000000000002e107

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if 5.0000000000000002e107 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.3%

      \[\leadsto y \]

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.7%

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

   10. Applied rewrites 26.7%

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

Alternative 9: 70.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{y}{a - t} \cdot z\\ \mathbf{if}\;t\_1 \leq \frac{-2535301200456459}{2535301200456458802993406410752}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 9999999999999999455752309870428160:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (* (/ y (- a t)) z)))
  (if (<= t_1 -2535301200456459/2535301200456458802993406410752)
    t_2
    (if (<= t_1 9999999999999999455752309870428160) (+ x y) t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (y / (a - t)) * z;
	double tmp;
	if (t_1 <= -1e-15) {
		tmp = t_2;
	} else if (t_1 <= 1e+34) {
		tmp = x + 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 = (z - t) / (a - t)
    t_2 = (y / (a - t)) * z
    if (t_1 <= (-1d-15)) then
        tmp = t_2
    else if (t_1 <= 1d+34) then
        tmp = x + 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 = (z - t) / (a - t);
	double t_2 = (y / (a - t)) * z;
	double tmp;
	if (t_1 <= -1e-15) {
		tmp = t_2;
	} else if (t_1 <= 1e+34) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = (y / (a - t)) * z
	tmp = 0
	if t_1 <= -1e-15:
		tmp = t_2
	elif t_1 <= 1e+34:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(y / Float64(a - t)) * z)
	tmp = 0.0
	if (t_1 <= -1e-15)
		tmp = t_2;
	elseif (t_1 <= 1e+34)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = (y / (a - t)) * z;
	tmp = 0.0;
	if (t_1 <= -1e-15)
		tmp = t_2;
	elseif (t_1 <= 1e+34)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[t$95$1, -2535301200456459/2535301200456458802993406410752], t$95$2, If[LessEqual[t$95$1, 9999999999999999455752309870428160], N[(x + y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -1.0000000000000001e-15 or 9.9999999999999995e33 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.3%

      \[\leadsto y \]

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.7%

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

   10. Applied rewrites 26.7%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-*l/ N/A

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

       4. lift-/.f64 N/A

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

       5. lift-*.f64 29.0%

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

   12. Applied rewrites 29.0%

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

   if -1.0000000000000001e-15 < (/.f64 (-.f64 z t) (-.f64 a t)) < 9.9999999999999995e33

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

Alternative 10: 64.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} t_1 := \frac{z - t}{a - t}\\ t_2 := \frac{y \cdot z}{a}\\ \mathbf{if}\;t\_1 \leq -400000000000000009427747005668102333299813118022752745251965015707312667386464693039323744636979804104925642752:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 500000000000000016999495856501412297471987359856449023856715357418937635861600416646370808190366722960654336:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (- z t) (- a t))) (t_2 (/ (* y z) a)))
  (if (<=
       t_1
       -400000000000000009427747005668102333299813118022752745251965015707312667386464693039323744636979804104925642752)
    t_2
    (if (<=
         t_1
         500000000000000016999495856501412297471987359856449023856715357418937635861600416646370808190366722960654336)
      (+ x y)
      t_2))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (z - t) / (a - t);
	double t_2 = (y * z) / a;
	double tmp;
	if (t_1 <= -4e+110) {
		tmp = t_2;
	} else if (t_1 <= 5e+107) {
		tmp = x + 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 = (z - t) / (a - t)
    t_2 = (y * z) / a
    if (t_1 <= (-4d+110)) then
        tmp = t_2
    else if (t_1 <= 5d+107) then
        tmp = x + 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 = (z - t) / (a - t);
	double t_2 = (y * z) / a;
	double tmp;
	if (t_1 <= -4e+110) {
		tmp = t_2;
	} else if (t_1 <= 5e+107) {
		tmp = x + y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (z - t) / (a - t)
	t_2 = (y * z) / a
	tmp = 0
	if t_1 <= -4e+110:
		tmp = t_2
	elif t_1 <= 5e+107:
		tmp = x + y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(z - t) / Float64(a - t))
	t_2 = Float64(Float64(y * z) / a)
	tmp = 0.0
	if (t_1 <= -4e+110)
		tmp = t_2;
	elseif (t_1 <= 5e+107)
		tmp = Float64(x + y);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (z - t) / (a - t);
	t_2 = (y * z) / a;
	tmp = 0.0;
	if (t_1 <= -4e+110)
		tmp = t_2;
	elseif (t_1 <= 5e+107)
		tmp = x + y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -400000000000000009427747005668102333299813118022752745251965015707312667386464693039323744636979804104925642752], t$95$2, If[LessEqual[t$95$1, 500000000000000016999495856501412297471987359856449023856715357418937635861600416646370808190366722960654336], N[(x + y), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 z t) (-.f64 a t)) < -4.0000000000000001e110 or 5.0000000000000002e107 < (/.f64 (-.f64 z t) (-.f64 a t))

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in x around 0

      \[\leadsto y \]
   6. Step-by-step derivation

   7. Applied rewrites 18.3%

      \[\leadsto y \]

   8. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.7%

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

   10. Applied rewrites 26.7%

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

   11. Taylor expanded in t around 0

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

   13. Applied rewrites 18.4%

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

   if -4.0000000000000001e110 < (/.f64 (-.f64 z t) (-.f64 a t)) < 5.0000000000000002e107

   1. Initial program 98.1%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

Alternative 11: 59.4% accurate, 6.5× speedup

Math

\[x + y \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

2. Taylor expanded in t around inf

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

   1. lower-+.f64 59.4%

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

4. Applied rewrites 59.4%

   \[\leadsto \color{blue}{x + y} \]
5. Add Preprocessing

Alternative 12: 18.3% accurate, 26.0× speedup

Math

\[y \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.1%

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

2. Taylor expanded in t around inf

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

   1. lower-+.f64 59.4%

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

4. Applied rewrites 59.4%

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

5. Taylor expanded in x around 0

   \[\leadsto y \]
6. Step-by-step derivation

7. Applied rewrites 18.3%

   \[\leadsto y \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64
  (+ x (* y (/ (- z t) (- a t)))))