Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Percentage Accurate: 85.1% → 98.1%

Time: 38.8s

Alternatives: 13

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.1%

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

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. associate-*l* N/A

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

   6. *-commutative N/A

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

   7. lower-*.f64 N/A

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

   8. mult-flip-rev N/A

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

   9. frac-2neg N/A

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

   10. lift--.f64 N/A

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

   11. sub-negate-rev N/A

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

   12. lower-/.f64 N/A

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

   13. lower--.f64 N/A

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

   14. lift--.f64 N/A

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

   15. sub-negate-rev N/A

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

   16. lower--.f64 98.1%

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

3. Applied rewrites 98.1%

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

Alternative 2: 87.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -420000000000000001878680817402491437056:\\ \;\;\;\;x + \frac{z}{z - a} \cdot t\\ \mathbf{elif}\;z \leq \frac{4242751136953197}{18446744073709551616}:\\ \;\;\;\;x + \frac{t \cdot y}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z - y}{z} \cdot t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -420000000000000001878680817402491437056)
  (+ x (* (/ z (- z a)) t))
  (if (<= z 4242751136953197/18446744073709551616)
    (+ x (/ (* t y) (- a z)))
    (+ x (* (/ (- z y) z) t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+38) {
		tmp = x + ((z / (z - a)) * t);
	} else if (z <= 0.00023) {
		tmp = x + ((t * y) / (a - z));
	} else {
		tmp = x + (((z - y) / 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) :: tmp
    if (z <= (-4.2d+38)) then
        tmp = x + ((z / (z - a)) * t)
    else if (z <= 0.00023d0) then
        tmp = x + ((t * y) / (a - z))
    else
        tmp = x + (((z - y) / z) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.2e+38) {
		tmp = x + ((z / (z - a)) * t);
	} else if (z <= 0.00023) {
		tmp = x + ((t * y) / (a - z));
	} else {
		tmp = x + (((z - y) / z) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.2e+38:
		tmp = x + ((z / (z - a)) * t)
	elif z <= 0.00023:
		tmp = x + ((t * y) / (a - z))
	else:
		tmp = x + (((z - y) / z) * t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.2e+38)
		tmp = Float64(x + Float64(Float64(z / Float64(z - a)) * t));
	elseif (z <= 0.00023)
		tmp = Float64(x + Float64(Float64(t * y) / Float64(a - z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(z - y) / z) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.2e+38)
		tmp = x + ((z / (z - a)) * t);
	elseif (z <= 0.00023)
		tmp = x + ((t * y) / (a - z));
	else
		tmp = x + (((z - y) / z) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -420000000000000001878680817402491437056], N[(x + N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4242751136953197/18446744073709551616], N[(x + N[(N[(t * y), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(z - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.2e38

   1. Initial program 85.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 98.1%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 71.8%

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

   if -4.2e38 < z < 2.3000000000000001e-4

   1. Initial program 85.1%

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

   2. Taylor expanded in y around inf

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

      1. lower-*.f64 73.4%

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

   4. Applied rewrites 73.4%

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

   if 2.3000000000000001e-4 < z

   1. Initial program 85.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 98.1%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 67.0%

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

   6. Applied rewrites 67.0%

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

Alternative 3: 83.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq \frac{-6338253001141147}{316912650057057350374175801344}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t\_1 \leq 2000000000000000047490864717302210714817315855657364374946929977340474859084041145136355256432166588258691938267680232151586826339780163146874880:\\ \;\;\;\;x + \frac{z}{z - a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* (- y z) t) (- a z))))
  (if (<= t_1 -6338253001141147/316912650057057350374175801344)
    (* (/ (- y z) (- a z)) t)
    (if (<=
         t_1
         2000000000000000047490864717302210714817315855657364374946929977340474859084041145136355256432166588258691938267680232151586826339780163146874880)
      (+ x (* (/ z (- z a)) t))
      (* (/ t (- a z)) (- y z))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -2e-14) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (t_1 <= 2e+144) {
		tmp = x + ((z / (z - a)) * t);
	} else {
		tmp = (t / (a - z)) * (y - 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) / (a - z)
    if (t_1 <= (-2d-14)) then
        tmp = ((y - z) / (a - z)) * t
    else if (t_1 <= 2d+144) then
        tmp = x + ((z / (z - a)) * t)
    else
        tmp = (t / (a - z)) * (y - 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) / (a - z);
	double tmp;
	if (t_1 <= -2e-14) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (t_1 <= 2e+144) {
		tmp = x + ((z / (z - a)) * t);
	} else {
		tmp = (t / (a - z)) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -2e-14:
		tmp = ((y - z) / (a - z)) * t
	elif t_1 <= 2e+144:
		tmp = x + ((z / (z - a)) * t)
	else:
		tmp = (t / (a - z)) * (y - z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= -2e-14)
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	elseif (t_1 <= 2e+144)
		tmp = Float64(x + Float64(Float64(z / Float64(z - a)) * t));
	else
		tmp = Float64(Float64(t / Float64(a - z)) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -2e-14)
		tmp = ((y - z) / (a - z)) * t;
	elseif (t_1 <= 2e+144)
		tmp = x + ((z / (z - a)) * t);
	else
		tmp = (t / (a - z)) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -6338253001141147/316912650057057350374175801344], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, 2000000000000000047490864717302210714817315855657364374946929977340474859084041145136355256432166588258691938267680232151586826339780163146874880], N[(x + N[(N[(z / N[(z - a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -2e-14

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.3%

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

   4. Applied rewrites 39.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l/ N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lift-/.f64 N/A

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

      18. distribute-frac-neg2 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower-/.f64 N/A

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

      22. lift--.f64 47.4%

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

   6. Applied rewrites 47.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. frac-2neg-rev N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 49.7%

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

   8. Applied rewrites 49.7%

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

   if -2e-14 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 2e144

   1. Initial program 85.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 98.1%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in y around 0

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

   6. Applied rewrites 71.8%

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

   if 2e144 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.3%

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

   4. Applied rewrites 39.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l/ N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lift-/.f64 N/A

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

      18. distribute-frac-neg2 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower-/.f64 N/A

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

      22. lift--.f64 47.4%

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

   6. Applied rewrites 47.4%

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

Alternative 4: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{z - y}{z} \cdot t\\ \mathbf{if}\;z \leq \frac{-8256342791959349}{485667223056432267729865476705879726660601709763034880312953102434726071301302124544}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{8235557476827325}{200867255532373784442745261542645325315275374222849104412672}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (/ (- z y) z) t))))
  (if (<=
       z
       -8256342791959349/485667223056432267729865476705879726660601709763034880312953102434726071301302124544)
    t_1
    (if (<=
         z
         8235557476827325/200867255532373784442745261542645325315275374222849104412672)
      (+ x (/ (* t y) a))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((z - y) / z) * t);
	double tmp;
	if (z <= -1.7e-68) {
		tmp = t_1;
	} else if (z <= 4.1e-44) {
		tmp = x + ((t * y) / 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 - y) / z) * t)
    if (z <= (-1.7d-68)) then
        tmp = t_1
    else if (z <= 4.1d-44) then
        tmp = x + ((t * y) / 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 - y) / z) * t);
	double tmp;
	if (z <= -1.7e-68) {
		tmp = t_1;
	} else if (z <= 4.1e-44) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((z - y) / z) * t)
	tmp = 0
	if z <= -1.7e-68:
		tmp = t_1
	elif z <= 4.1e-44:
		tmp = x + ((t * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(z - y) / z) * t))
	tmp = 0.0
	if (z <= -1.7e-68)
		tmp = t_1;
	elseif (z <= 4.1e-44)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((z - y) / z) * t);
	tmp = 0.0;
	if (z <= -1.7e-68)
		tmp = t_1;
	elseif (z <= 4.1e-44)
		tmp = x + ((t * y) / 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 - y), $MachinePrecision] / z), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8256342791959349/485667223056432267729865476705879726660601709763034880312953102434726071301302124544], t$95$1, If[LessEqual[z, 8235557476827325/200867255532373784442745261542645325315275374222849104412672], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.7000000000000001e-68 or 4.0999999999999999e-44 < z

   1. Initial program 85.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 98.1%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower--.f64 67.0%

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

   6. Applied rewrites 67.0%

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

   if -1.7000000000000001e-68 < z < 4.0999999999999999e-44

   1. Initial program 85.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 60.1%

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

   4. Applied rewrites 60.1%

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

Alternative 5: 80.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_1 \leq \frac{-6338253001141147}{316912650057057350374175801344}:\\ \;\;\;\;\frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t\_1 \leq \frac{-3334007216439927}{1667003608219963568519962947680314449286189580578977040099064452941009309454408017880358050217888572685732477648358310111472200413529841270090839013082707511523789394878503639615769571477953506182241254033971650495422687009369115322790969344}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_1 \leq \frac{6183260036827613}{123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;t\_1 \leq 500000000000000021922921522538098677317023825920:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{a - z} \cdot \left(y - z\right)\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (/ (* (- y z) t) (- a z))))
  (if (<= t_1 -6338253001141147/316912650057057350374175801344)
    (* (/ (- y z) (- a z)) t)
    (if (<=
         t_1
         -3334007216439927/1667003608219963568519962947680314449286189580578977040099064452941009309454408017880358050217888572685732477648358310111472200413529841270090839013082707511523789394878503639615769571477953506182241254033971650495422687009369115322790969344)
      (+ x t)
      (if (<=
           t_1
           6183260036827613/123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568)
        (+ x (/ (* t y) a))
        (if (<= t_1 500000000000000021922921522538098677317023825920)
          (+ x t)
          (* (/ t (- a z)) (- y z))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_1 <= -2e-14) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (t_1 <= -2e-225) {
		tmp = x + t;
	} else if (t_1 <= 5e-158) {
		tmp = x + ((t * y) / a);
	} else if (t_1 <= 5e+47) {
		tmp = x + t;
	} else {
		tmp = (t / (a - z)) * (y - 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) / (a - z)
    if (t_1 <= (-2d-14)) then
        tmp = ((y - z) / (a - z)) * t
    else if (t_1 <= (-2d-225)) then
        tmp = x + t
    else if (t_1 <= 5d-158) then
        tmp = x + ((t * y) / a)
    else if (t_1 <= 5d+47) then
        tmp = x + t
    else
        tmp = (t / (a - z)) * (y - 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) / (a - z);
	double tmp;
	if (t_1 <= -2e-14) {
		tmp = ((y - z) / (a - z)) * t;
	} else if (t_1 <= -2e-225) {
		tmp = x + t;
	} else if (t_1 <= 5e-158) {
		tmp = x + ((t * y) / a);
	} else if (t_1 <= 5e+47) {
		tmp = x + t;
	} else {
		tmp = (t / (a - z)) * (y - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_1 <= -2e-14:
		tmp = ((y - z) / (a - z)) * t
	elif t_1 <= -2e-225:
		tmp = x + t
	elif t_1 <= 5e-158:
		tmp = x + ((t * y) / a)
	elif t_1 <= 5e+47:
		tmp = x + t
	else:
		tmp = (t / (a - z)) * (y - z)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_1 <= -2e-14)
		tmp = Float64(Float64(Float64(y - z) / Float64(a - z)) * t);
	elseif (t_1 <= -2e-225)
		tmp = Float64(x + t);
	elseif (t_1 <= 5e-158)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (t_1 <= 5e+47)
		tmp = Float64(x + t);
	else
		tmp = Float64(Float64(t / Float64(a - z)) * Float64(y - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_1 <= -2e-14)
		tmp = ((y - z) / (a - z)) * t;
	elseif (t_1 <= -2e-225)
		tmp = x + t;
	elseif (t_1 <= 5e-158)
		tmp = x + ((t * y) / a);
	elseif (t_1 <= 5e+47)
		tmp = x + t;
	else
		tmp = (t / (a - z)) * (y - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -6338253001141147/316912650057057350374175801344], N[(N[(N[(y - z), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[t$95$1, -3334007216439927/1667003608219963568519962947680314449286189580578977040099064452941009309454408017880358050217888572685732477648358310111472200413529841270090839013082707511523789394878503639615769571477953506182241254033971650495422687009369115322790969344], N[(x + t), $MachinePrecision], If[LessEqual[t$95$1, 6183260036827613/123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 500000000000000021922921522538098677317023825920], N[(x + t), $MachinePrecision], N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -2e-14

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.3%

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

   4. Applied rewrites 39.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l/ N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lift-/.f64 N/A

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

      18. distribute-frac-neg2 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower-/.f64 N/A

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

      22. lift--.f64 47.4%

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

   6. Applied rewrites 47.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. frac-2neg-rev N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 49.7%

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

   8. Applied rewrites 49.7%

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

   if -2e-14 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -1.9999999999999999e-225 or 4.9999999999999997e-158 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 5.0000000000000002e47

   1. Initial program 85.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.5%

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

   if -1.9999999999999999e-225 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.9999999999999997e-158

   1. Initial program 85.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 60.1%

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

   4. Applied rewrites 60.1%

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

   if 5.0000000000000002e47 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.3%

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

   4. Applied rewrites 39.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l/ N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lift-/.f64 N/A

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

      18. distribute-frac-neg2 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower-/.f64 N/A

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

      22. lift--.f64 47.4%

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

   6. Applied rewrites 47.4%

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

Alternative 6: 77.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{t}{a - z} \cdot \left(y - z\right)\\ t_2 := \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{if}\;t\_2 \leq \frac{-6338253001141147}{316912650057057350374175801344}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq \frac{-3334007216439927}{1667003608219963568519962947680314449286189580578977040099064452941009309454408017880358050217888572685732477648358310111472200413529841270090839013082707511523789394878503639615769571477953506182241254033971650495422687009369115322790969344}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;t\_2 \leq \frac{6183260036827613}{123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{elif}\;t\_2 \leq 500000000000000021922921522538098677317023825920:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (/ t (- a z)) (- y z)))
       (t_2 (/ (* (- y z) t) (- a z))))
  (if (<= t_2 -6338253001141147/316912650057057350374175801344)
    t_1
    (if (<=
         t_2
         -3334007216439927/1667003608219963568519962947680314449286189580578977040099064452941009309454408017880358050217888572685732477648358310111472200413529841270090839013082707511523789394878503639615769571477953506182241254033971650495422687009369115322790969344)
      (+ x t)
      (if (<=
           t_2
           6183260036827613/123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568)
        (+ x (/ (* t y) a))
        (if (<= t_2 500000000000000021922921522538098677317023825920)
          (+ x t)
          t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (t / (a - z)) * (y - z);
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -2e-14) {
		tmp = t_1;
	} else if (t_2 <= -2e-225) {
		tmp = x + t;
	} else if (t_2 <= 5e-158) {
		tmp = x + ((t * y) / a);
	} else if (t_2 <= 5e+47) {
		tmp = x + t;
	} 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 = (t / (a - z)) * (y - z)
    t_2 = ((y - z) * t) / (a - z)
    if (t_2 <= (-2d-14)) then
        tmp = t_1
    else if (t_2 <= (-2d-225)) then
        tmp = x + t
    else if (t_2 <= 5d-158) then
        tmp = x + ((t * y) / a)
    else if (t_2 <= 5d+47) then
        tmp = x + t
    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 = (t / (a - z)) * (y - z);
	double t_2 = ((y - z) * t) / (a - z);
	double tmp;
	if (t_2 <= -2e-14) {
		tmp = t_1;
	} else if (t_2 <= -2e-225) {
		tmp = x + t;
	} else if (t_2 <= 5e-158) {
		tmp = x + ((t * y) / a);
	} else if (t_2 <= 5e+47) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (t / (a - z)) * (y - z)
	t_2 = ((y - z) * t) / (a - z)
	tmp = 0
	if t_2 <= -2e-14:
		tmp = t_1
	elif t_2 <= -2e-225:
		tmp = x + t
	elif t_2 <= 5e-158:
		tmp = x + ((t * y) / a)
	elif t_2 <= 5e+47:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(t / Float64(a - z)) * Float64(y - z))
	t_2 = Float64(Float64(Float64(y - z) * t) / Float64(a - z))
	tmp = 0.0
	if (t_2 <= -2e-14)
		tmp = t_1;
	elseif (t_2 <= -2e-225)
		tmp = Float64(x + t);
	elseif (t_2 <= 5e-158)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	elseif (t_2 <= 5e+47)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (t / (a - z)) * (y - z);
	t_2 = ((y - z) * t) / (a - z);
	tmp = 0.0;
	if (t_2 <= -2e-14)
		tmp = t_1;
	elseif (t_2 <= -2e-225)
		tmp = x + t;
	elseif (t_2 <= 5e-158)
		tmp = x + ((t * y) / a);
	elseif (t_2 <= 5e+47)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(t / N[(a - z), $MachinePrecision]), $MachinePrecision] * N[(y - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y - z), $MachinePrecision] * t), $MachinePrecision] / N[(a - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -6338253001141147/316912650057057350374175801344], t$95$1, If[LessEqual[t$95$2, -3334007216439927/1667003608219963568519962947680314449286189580578977040099064452941009309454408017880358050217888572685732477648358310111472200413529841270090839013082707511523789394878503639615769571477953506182241254033971650495422687009369115322790969344], N[(x + t), $MachinePrecision], If[LessEqual[t$95$2, 6183260036827613/123665200736552267030251260509823595017565674550605919957031528046448612553265933585158200530621522494798835713008069669675682517153375604983773077550946583958303386074349568], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 500000000000000021922921522538098677317023825920], N[(x + t), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -2e-14 or 5.0000000000000002e47 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.3%

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

   4. Applied rewrites 39.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l/ N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lift-/.f64 N/A

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

      18. distribute-frac-neg2 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower-/.f64 N/A

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

      22. lift--.f64 47.4%

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

   6. Applied rewrites 47.4%

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

   if -2e-14 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < -1.9999999999999999e-225 or 4.9999999999999997e-158 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 5.0000000000000002e47

   1. Initial program 85.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.5%

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

   if -1.9999999999999999e-225 < (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)) < 4.9999999999999997e-158

   1. Initial program 85.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 60.1%

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

   4. Applied rewrites 60.1%

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

Alternative 7: 77.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := x + \frac{t}{z} \cdot \left(z - y\right)\\ \mathbf{if}\;z \leq \frac{-4613838619036107}{242833611528216133864932738352939863330300854881517440156476551217363035650651062272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq \frac{1318191364431203}{6277101735386680763835789423207666416102355444464034512896}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (+ x (* (/ t z) (- z y)))))
  (if (<=
       z
       -4613838619036107/242833611528216133864932738352939863330300854881517440156476551217363035650651062272)
    t_1
    (if (<=
         z
         1318191364431203/6277101735386680763835789423207666416102355444464034512896)
      (+ x (/ (* t y) a))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + ((t / z) * (z - y));
	double tmp;
	if (z <= -1.9e-68) {
		tmp = t_1;
	} else if (z <= 2.1e-43) {
		tmp = x + ((t * y) / 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 + ((t / z) * (z - y))
    if (z <= (-1.9d-68)) then
        tmp = t_1
    else if (z <= 2.1d-43) then
        tmp = x + ((t * y) / 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 + ((t / z) * (z - y));
	double tmp;
	if (z <= -1.9e-68) {
		tmp = t_1;
	} else if (z <= 2.1e-43) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + ((t / z) * (z - y))
	tmp = 0
	if z <= -1.9e-68:
		tmp = t_1
	elif z <= 2.1e-43:
		tmp = x + ((t * y) / a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(t / z) * Float64(z - y)))
	tmp = 0.0
	if (z <= -1.9e-68)
		tmp = t_1;
	elseif (z <= 2.1e-43)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + ((t / z) * (z - y));
	tmp = 0.0;
	if (z <= -1.9e-68)
		tmp = t_1;
	elseif (z <= 2.1e-43)
		tmp = x + ((t * y) / 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[(t / z), $MachinePrecision] * N[(z - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4613838619036107/242833611528216133864932738352939863330300854881517440156476551217363035650651062272], t$95$1, If[LessEqual[z, 1318191364431203/6277101735386680763835789423207666416102355444464034512896], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1.9000000000000002e-68 or 2.1000000000000001e-43 < z

   1. Initial program 85.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 98.1%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in a around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 58.7%

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

   6. Applied rewrites 58.7%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift--.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-*l* N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. mult-flip-rev N/A

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

      10. lower-/.f64 N/A

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

      11. lift--.f64 65.6%

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

   8. Applied rewrites 65.6%

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

   if -1.9000000000000002e-68 < z < 2.1000000000000001e-43

   1. Initial program 85.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 60.1%

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

   4. Applied rewrites 60.1%

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

Alternative 8: 77.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -4799999999999999953829101568:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq 26000000000000000:\\ \;\;\;\;x + \frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -4799999999999999953829101568)
  (+ x t)
  (if (<= z 26000000000000000) (+ x (* (/ y a) t)) (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+27) {
		tmp = x + t;
	} else if (z <= 2.6e+16) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x + 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) :: tmp
    if (z <= (-4.8d+27)) then
        tmp = x + t
    else if (z <= 2.6d+16) then
        tmp = x + ((y / a) * t)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -4.8e+27) {
		tmp = x + t;
	} else if (z <= 2.6e+16) {
		tmp = x + ((y / a) * t);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -4.8e+27:
		tmp = x + t
	elif z <= 2.6e+16:
		tmp = x + ((y / a) * t)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -4.8e+27)
		tmp = Float64(x + t);
	elseif (z <= 2.6e+16)
		tmp = Float64(x + Float64(Float64(y / a) * t));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -4.8e+27)
		tmp = x + t;
	elseif (z <= 2.6e+16)
		tmp = x + ((y / a) * t);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4799999999999999953829101568], N[(x + t), $MachinePrecision], If[LessEqual[z, 26000000000000000], N[(x + N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e27 or 2.6e16 < z

   1. Initial program 85.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.5%

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

   if -4.8e27 < z < 2.6e16

   1. Initial program 85.1%

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

      1. lift-/.f64 N/A

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

      2. mult-flip N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. mult-flip-rev N/A

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

      9. frac-2neg N/A

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

      10. lift--.f64 N/A

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

      11. sub-negate-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower--.f64 98.1%

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

   3. Applied rewrites 98.1%

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

   4. Taylor expanded in z around 0

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

      1. lower-/.f64 61.5%

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

   6. Applied rewrites 61.5%

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

Alternative 9: 76.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq -4999999999999999791559868416:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq \frac{1590140912926291}{649037107316853453566312041152512}:\\ \;\;\;\;x + \frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= z -4999999999999999791559868416)
  (+ x t)
  (if (<= z 1590140912926291/649037107316853453566312041152512)
    (+ x (/ (* t y) a))
    (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+27) {
		tmp = x + t;
	} else if (z <= 2.45e-18) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x + 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) :: tmp
    if (z <= (-5d+27)) then
        tmp = x + t
    else if (z <= 2.45d-18) then
        tmp = x + ((t * y) / a)
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -5e+27) {
		tmp = x + t;
	} else if (z <= 2.45e-18) {
		tmp = x + ((t * y) / a);
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -5e+27:
		tmp = x + t
	elif z <= 2.45e-18:
		tmp = x + ((t * y) / a)
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -5e+27)
		tmp = Float64(x + t);
	elseif (z <= 2.45e-18)
		tmp = Float64(x + Float64(Float64(t * y) / a));
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -5e+27)
		tmp = x + t;
	elseif (z <= 2.45e-18)
		tmp = x + ((t * y) / a);
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -4999999999999999791559868416], N[(x + t), $MachinePrecision], If[LessEqual[z, 1590140912926291/649037107316853453566312041152512], N[(x + N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -4.9999999999999998e27 or 2.4500000000000001e-18 < z

   1. Initial program 85.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.5%

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

   if -4.9999999999999998e27 < z < 2.4500000000000001e-18

   1. Initial program 85.1%

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

   2. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 60.1%

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

   4. Applied rewrites 60.1%

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

Alternative 10: 64.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} t_1 := \frac{y}{a - z} \cdot t\\ \mathbf{if}\;y \leq -125000000000000004714848161632068786467724214271375990583792072320444331735548805624202380779518698661634426763635923712456941447904364351344500703752365677891099149098885108365277599999000415576260608:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6500000000000000106196004345803255164756849025361838451046535828149741892512568564695125575801263618109502173149575593363745726195467295895700360130074478143777178143768408366629599996836639792909642313474686134012229284104994296318231092133888:\\ \;\;\;\;x + t\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (/ y (- a z)) t)))
  (if (<=
       y
       -125000000000000004714848161632068786467724214271375990583792072320444331735548805624202380779518698661634426763635923712456941447904364351344500703752365677891099149098885108365277599999000415576260608)
    t_1
    (if (<=
         y
         6500000000000000106196004345803255164756849025361838451046535828149741892512568564695125575801263618109502173149575593363745726195467295895700360130074478143777178143768408366629599996836639792909642313474686134012229284104994296318231092133888)
      (+ x t)
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (a - z)) * t;
	double tmp;
	if (y <= -1.25e+200) {
		tmp = t_1;
	} else if (y <= 6.5e+243) {
		tmp = x + t;
	} 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 = (y / (a - z)) * t
    if (y <= (-1.25d+200)) then
        tmp = t_1
    else if (y <= 6.5d+243) then
        tmp = x + t
    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 = (y / (a - z)) * t;
	double tmp;
	if (y <= -1.25e+200) {
		tmp = t_1;
	} else if (y <= 6.5e+243) {
		tmp = x + t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (a - z)) * t
	tmp = 0
	if y <= -1.25e+200:
		tmp = t_1
	elif y <= 6.5e+243:
		tmp = x + t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(a - z)) * t)
	tmp = 0.0
	if (y <= -1.25e+200)
		tmp = t_1;
	elseif (y <= 6.5e+243)
		tmp = Float64(x + t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (a - z)) * t;
	tmp = 0.0;
	if (y <= -1.25e+200)
		tmp = t_1;
	elseif (y <= 6.5e+243)
		tmp = x + t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / N[(a - z), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[y, -125000000000000004714848161632068786467724214271375990583792072320444331735548805624202380779518698661634426763635923712456941447904364351344500703752365677891099149098885108365277599999000415576260608], t$95$1, If[LessEqual[y, 6500000000000000106196004345803255164756849025361838451046535828149741892512568564695125575801263618109502173149575593363745726195467295895700360130074478143777178143768408366629599996836639792909642313474686134012229284104994296318231092133888], N[(x + t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25e200 or 6.5000000000000001e243 < y

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.3%

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

   4. Applied rewrites 39.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l/ N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lift-/.f64 N/A

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

      18. distribute-frac-neg2 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower-/.f64 N/A

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

      22. lift--.f64 47.4%

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

   6. Applied rewrites 47.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. frac-2neg-rev N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 49.7%

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

   8. Applied rewrites 49.7%

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

   9. Taylor expanded in y around inf

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

       1. lower-/.f64 N/A

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

       2. lower--.f64 28.5%

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

   11. Applied rewrites 28.5%

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

   if -1.25e200 < y < 6.5000000000000001e243

   1. Initial program 85.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.5%

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

Alternative 11: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq \frac{-8338720222318261}{94758184344525691842589080106353915726128296943157752144717531617800961467674370503593652882607817257720198406807316479868870852301929589321550737002025216015896910157522577243058183937475491017166931103132108688408987234729984}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq \frac{-7540071506325551}{377003575316277553052632783947358479815640765734281611362288441560101396530857955835685848633641608981764089063400052322800846281248691448694119974860434438887084693231743502178167752441192448774799271819130974018130465379775860716808779827596916922071594850183201524526501846714374614008118077197384100897810808832}:\\ \;\;\;\;\frac{t \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     z
     -8338720222318261/94758184344525691842589080106353915726128296943157752144717531617800961467674370503593652882607817257720198406807316479868870852301929589321550737002025216015896910157522577243058183937475491017166931103132108688408987234729984)
  (+ x t)
  (if (<=
       z
       -7540071506325551/377003575316277553052632783947358479815640765734281611362288441560101396530857955835685848633641608981764089063400052322800846281248691448694119974860434438887084693231743502178167752441192448774799271819130974018130465379775860716808779827596916922071594850183201524526501846714374614008118077197384100897810808832)
    (/ (* t y) a)
    (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e-212) {
		tmp = x + t;
	} else if (z <= -2e-299) {
		tmp = (t * y) / a;
	} else {
		tmp = x + 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) :: tmp
    if (z <= (-8.8d-212)) then
        tmp = x + t
    else if (z <= (-2d-299)) then
        tmp = (t * y) / a
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e-212) {
		tmp = x + t;
	} else if (z <= -2e-299) {
		tmp = (t * y) / a;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e-212:
		tmp = x + t
	elif z <= -2e-299:
		tmp = (t * y) / a
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e-212)
		tmp = Float64(x + t);
	elseif (z <= -2e-299)
		tmp = Float64(Float64(t * y) / a);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e-212)
		tmp = x + t;
	elseif (z <= -2e-299)
		tmp = (t * y) / a;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8338720222318261/94758184344525691842589080106353915726128296943157752144717531617800961467674370503593652882607817257720198406807316479868870852301929589321550737002025216015896910157522577243058183937475491017166931103132108688408987234729984], N[(x + t), $MachinePrecision], If[LessEqual[z, -7540071506325551/377003575316277553052632783947358479815640765734281611362288441560101396530857955835685848633641608981764089063400052322800846281248691448694119974860434438887084693231743502178167752441192448774799271819130974018130465379775860716808779827596916922071594850183201524526501846714374614008118077197384100897810808832], N[(N[(t * y), $MachinePrecision] / a), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000001e-212 or -2e-299 < z

   1. Initial program 85.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.5%

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

   if -8.8000000000000001e-212 < z < -2e-299

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.3%

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

   4. Applied rewrites 39.3%

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

   5. Taylor expanded in y around inf

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

      1. lower-*.f64 26.5%

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

   7. Applied rewrites 26.5%

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

   8. Taylor expanded in z around 0

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

   10. Applied rewrites 18.4%

       \[\leadsto \frac{t \cdot y}{a} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 12: 60.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq \frac{-8338720222318261}{94758184344525691842589080106353915726128296943157752144717531617800961467674370503593652882607817257720198406807316479868870852301929589321550737002025216015896910157522577243058183937475491017166931103132108688408987234729984}:\\ \;\;\;\;x + t\\ \mathbf{elif}\;z \leq \frac{-7540071506325551}{377003575316277553052632783947358479815640765734281611362288441560101396530857955835685848633641608981764089063400052322800846281248691448694119974860434438887084693231743502178167752441192448774799271819130974018130465379775860716808779827596916922071594850183201524526501846714374614008118077197384100897810808832}:\\ \;\;\;\;\frac{y}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + t\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     z
     -8338720222318261/94758184344525691842589080106353915726128296943157752144717531617800961467674370503593652882607817257720198406807316479868870852301929589321550737002025216015896910157522577243058183937475491017166931103132108688408987234729984)
  (+ x t)
  (if (<=
       z
       -7540071506325551/377003575316277553052632783947358479815640765734281611362288441560101396530857955835685848633641608981764089063400052322800846281248691448694119974860434438887084693231743502178167752441192448774799271819130974018130465379775860716808779827596916922071594850183201524526501846714374614008118077197384100897810808832)
    (* (/ y a) t)
    (+ x t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e-212) {
		tmp = x + t;
	} else if (z <= -2e-299) {
		tmp = (y / a) * t;
	} else {
		tmp = x + 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) :: tmp
    if (z <= (-8.8d-212)) then
        tmp = x + t
    else if (z <= (-2d-299)) then
        tmp = (y / a) * t
    else
        tmp = x + t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= -8.8e-212) {
		tmp = x + t;
	} else if (z <= -2e-299) {
		tmp = (y / a) * t;
	} else {
		tmp = x + t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= -8.8e-212:
		tmp = x + t
	elif z <= -2e-299:
		tmp = (y / a) * t
	else:
		tmp = x + t
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= -8.8e-212)
		tmp = Float64(x + t);
	elseif (z <= -2e-299)
		tmp = Float64(Float64(y / a) * t);
	else
		tmp = Float64(x + t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= -8.8e-212)
		tmp = x + t;
	elseif (z <= -2e-299)
		tmp = (y / a) * t;
	else
		tmp = x + t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, -8338720222318261/94758184344525691842589080106353915726128296943157752144717531617800961467674370503593652882607817257720198406807316479868870852301929589321550737002025216015896910157522577243058183937475491017166931103132108688408987234729984], N[(x + t), $MachinePrecision], If[LessEqual[z, -7540071506325551/377003575316277553052632783947358479815640765734281611362288441560101396530857955835685848633641608981764089063400052322800846281248691448694119974860434438887084693231743502178167752441192448774799271819130974018130465379775860716808779827596916922071594850183201524526501846714374614008118077197384100897810808832], N[(N[(y / a), $MachinePrecision] * t), $MachinePrecision], N[(x + t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.8000000000000001e-212 or -2e-299 < z

   1. Initial program 85.1%

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

   2. Taylor expanded in z around inf

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

   4. Applied rewrites 60.5%

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

   if -8.8000000000000001e-212 < z < -2e-299

   1. Initial program 85.1%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.3%

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

   4. Applied rewrites 39.3%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. *-commutative N/A

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

      5. lift-*.f64 N/A

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

      6. sub-negate-rev N/A

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

      7. lift--.f64 N/A

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

      8. distribute-neg-frac2 N/A

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

      9. lift-*.f64 N/A

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

      10. *-commutative N/A

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

      11. associate-*l/ N/A

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

      12. lift-/.f64 N/A

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

      13. lift-*.f64 N/A

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

      14. lift-*.f64 N/A

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

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

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

      16. lower-*.f64 N/A

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

      17. lift-/.f64 N/A

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

      18. distribute-frac-neg2 N/A

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

      19. lift--.f64 N/A

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

      20. sub-negate-rev N/A

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

      21. lower-/.f64 N/A

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

      22. lift--.f64 47.4%

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

   6. Applied rewrites 47.4%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. associate-*l/ N/A

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

      5. associate-/l* N/A

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

      6. frac-2neg-rev N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. sub-negate-rev N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-negate-rev N/A

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

      13. lift--.f64 N/A

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

      14. sub-negate-rev N/A

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

      15. frac-2neg-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 49.7%

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

   8. Applied rewrites 49.7%

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

   9. Taylor expanded in z around 0

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

       1. lower-/.f64 20.0%

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

   11. Applied rewrites 20.0%

       \[\leadsto \frac{y}{a} \cdot t \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 60.5% accurate, 6.5× speedup

Math

\[x + t \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.1%

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

2. Taylor expanded in z around inf

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

4. Applied rewrites 60.5%

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

Reproduce

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