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

Percentage Accurate: 85.7% → 99.8%

Time: 1.8min

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (a - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 85.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (a - t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

Derivation

1. Initial program 85.7%

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

   1. lift-/.f64 N/A

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

   2. mult-flip N/A

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

   3. *-commutative N/A

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

   4. lift-*.f64 N/A

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

   5. lift--.f64 N/A

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

   6. sub-flip N/A

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

   7. distribute-lft-in N/A

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

   8. *-commutative N/A

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

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

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

   10. sub-flip-reverse N/A

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

   11. lower-134-z0z1z2z3z4 N/A

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

   12. frac-2neg N/A

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

   13. metadata-eval N/A

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

   14. lower-/.f64 N/A

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

   15. lift--.f64 N/A

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

   16. sub-negate-rev N/A

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

   17. lower--.f64 99.8%

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

3. Applied rewrites 99.8%

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

Alternative 2: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((t - z) / (t - a)) * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. associate-/l* N/A

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

   4. *-commutative N/A

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

   5. lower-*.f64 N/A

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

   6. lift--.f64 N/A

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

   7. sub-negate-rev N/A

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

   8. distribute-frac-neg N/A

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

   9. distribute-neg-frac2 N/A

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

   10. lower-/.f64 N/A

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

   11. lower--.f64 N/A

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

   12. lift--.f64 N/A

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

   13. sub-negate-rev N/A

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

   14. lower--.f64 98.1%

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

3. Applied rewrites 98.1%

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

Alternative 3: 86.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} t_1 := x - \frac{t}{a - t} \cdot y\\ \mathbf{if}\;t \leq -390000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq \frac{2535301200456459}{158456325028528675187087900672}:\\ \;\;\;\;x - \frac{z}{t - a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (- x (* (/ t (- a t)) y))))
  (if (<= t -390000)
    t_1
    (if (<= t 2535301200456459/158456325028528675187087900672)
      (- x (* (/ z (- t a)) y))
      t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t / (a - t)) * y);
	double tmp;
	if (t <= -390000.0) {
		tmp = t_1;
	} else if (t <= 1.6e-14) {
		tmp = x - ((z / (t - a)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((t / (a - t)) * y)
    if (t <= (-390000.0d0)) then
        tmp = t_1
    else if (t <= 1.6d-14) then
        tmp = x - ((z / (t - a)) * y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((t / (a - t)) * y);
	double tmp;
	if (t <= -390000.0) {
		tmp = t_1;
	} else if (t <= 1.6e-14) {
		tmp = x - ((z / (t - a)) * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((t / (a - t)) * y)
	tmp = 0
	if t <= -390000.0:
		tmp = t_1
	elif t <= 1.6e-14:
		tmp = x - ((z / (t - a)) * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(t / Float64(a - t)) * y))
	tmp = 0.0
	if (t <= -390000.0)
		tmp = t_1;
	elseif (t <= 1.6e-14)
		tmp = Float64(x - Float64(Float64(z / Float64(t - a)) * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((t / (a - t)) * y);
	tmp = 0.0;
	if (t <= -390000.0)
		tmp = t_1;
	elseif (t <= 1.6e-14)
		tmp = x - ((z / (t - a)) * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -390000], t$95$1, If[LessEqual[t, 2535301200456459/158456325028528675187087900672], N[(x - N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.9e5 or 1.6000000000000001e-14 < t

   1. Initial program 85.7%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 95.8%

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

   3. Applied rewrites 95.8%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift--.f64 N/A

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

      8. sub-negate-rev N/A

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

      9. lift--.f64 N/A

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

      10. sub-negate-rev N/A

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

      11. frac-2neg-rev N/A

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

      12. lower-/.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lift--.f64 98.1%

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

   5. Applied rewrites 98.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 71.1%

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

   if -3.9e5 < t < 1.6000000000000001e-14

   1. Initial program 85.7%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 95.8%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.8%

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

   6. Applied rewrites 73.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 76.8%

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

   8. Applied rewrites 76.8%

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

Alternative 4: 84.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -3000000:\\ \;\;\;\;x - \frac{y}{t} \cdot \left(z - t\right)\\ \mathbf{elif}\;t \leq 27999999999999998718775726159859284263970005195775618603481361310393122879981161303240436092695688073577940461915432855327377195008:\\ \;\;\;\;x - \frac{z}{t - a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= t -3000000)
  (- x (* (/ y t) (- z t)))
  (if (<=
       t
       27999999999999998718775726159859284263970005195775618603481361310393122879981161303240436092695688073577940461915432855327377195008)
    (- x (* (/ z (- t a)) y))
    (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3000000.0) {
		tmp = x - ((y / t) * (z - t));
	} else if (t <= 2.8e+130) {
		tmp = x - ((z / (t - a)) * y);
	} else {
		tmp = x + y;
	}
	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 (t <= (-3000000.0d0)) then
        tmp = x - ((y / t) * (z - t))
    else if (t <= 2.8d+130) then
        tmp = x - ((z / (t - a)) * y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3000000.0) {
		tmp = x - ((y / t) * (z - t));
	} else if (t <= 2.8e+130) {
		tmp = x - ((z / (t - a)) * y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -3000000.0:
		tmp = x - ((y / t) * (z - t))
	elif t <= 2.8e+130:
		tmp = x - ((z / (t - a)) * y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3000000.0)
		tmp = Float64(x - Float64(Float64(y / t) * Float64(z - t)));
	elseif (t <= 2.8e+130)
		tmp = Float64(x - Float64(Float64(z / Float64(t - a)) * y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -3000000.0)
		tmp = x - ((y / t) * (z - t));
	elseif (t <= 2.8e+130)
		tmp = x - ((z / (t - a)) * y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3000000], N[(x - N[(N[(y / t), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 27999999999999998718775726159859284263970005195775618603481361310393122879981161303240436092695688073577940461915432855327377195008], N[(x - N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3e6

   1. Initial program 85.7%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 95.8%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in t around inf

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

      1. lower-/.f64 64.3%

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

   6. Applied rewrites 64.3%

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

   if -3e6 < t < 2.7999999999999999e130

   1. Initial program 85.7%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 95.8%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.8%

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

   6. Applied rewrites 73.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 76.8%

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

   8. Applied rewrites 76.8%

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

   if 2.7999999999999999e130 < t

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

Alternative 5: 83.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -2800000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 27999999999999998718775726159859284263970005195775618603481361310393122879981161303240436092695688073577940461915432855327377195008:\\ \;\;\;\;x - \frac{z}{t - a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= t -2800000)
  (+ x y)
  (if (<=
       t
       27999999999999998718775726159859284263970005195775618603481361310393122879981161303240436092695688073577940461915432855327377195008)
    (- x (* (/ z (- t a)) y))
    (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2800000.0) {
		tmp = x + y;
	} else if (t <= 2.8e+130) {
		tmp = x - ((z / (t - a)) * y);
	} else {
		tmp = x + y;
	}
	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 (t <= (-2800000.0d0)) then
        tmp = x + y
    else if (t <= 2.8d+130) then
        tmp = x - ((z / (t - a)) * y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -2800000.0) {
		tmp = x + y;
	} else if (t <= 2.8e+130) {
		tmp = x - ((z / (t - a)) * y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -2800000.0:
		tmp = x + y
	elif t <= 2.8e+130:
		tmp = x - ((z / (t - a)) * y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -2800000.0)
		tmp = Float64(x + y);
	elseif (t <= 2.8e+130)
		tmp = Float64(x - Float64(Float64(z / Float64(t - a)) * y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -2800000.0)
		tmp = x + y;
	elseif (t <= 2.8e+130)
		tmp = x - ((z / (t - a)) * y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -2800000], N[(x + y), $MachinePrecision], If[LessEqual[t, 27999999999999998718775726159859284263970005195775618603481361310393122879981161303240436092695688073577940461915432855327377195008], N[(x - N[(N[(z / N[(t - a), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8e6 or 2.7999999999999999e130 < t

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if -2.8e6 < t < 2.7999999999999999e130

   1. Initial program 85.7%

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

      1. lift-+.f64 N/A

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

      2. add-flip N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. *-commutative N/A

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

      10. lower-*.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. sub-negate-rev N/A

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

      14. lower--.f64 95.8%

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

   3. Applied rewrites 95.8%

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

   4. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 73.8%

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

   6. Applied rewrites 73.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 76.8%

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

   8. Applied rewrites 76.8%

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

Alternative 6: 81.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -700000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 23000000000000002113798415841583634489255369458070367475338738167367743897258102483121572000025882191942560861254112410265809059840:\\ \;\;\;\;x + \frac{y \cdot z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= t -700000)
  (+ x y)
  (if (<=
       t
       23000000000000002113798415841583634489255369458070367475338738167367743897258102483121572000025882191942560861254112410265809059840)
    (+ x (/ (* y z) (- a t)))
    (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -700000.0) {
		tmp = x + y;
	} else if (t <= 2.3e+130) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + y;
	}
	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 (t <= (-700000.0d0)) then
        tmp = x + y
    else if (t <= 2.3d+130) then
        tmp = x + ((y * z) / (a - t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -700000.0) {
		tmp = x + y;
	} else if (t <= 2.3e+130) {
		tmp = x + ((y * z) / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -700000.0:
		tmp = x + y
	elif t <= 2.3e+130:
		tmp = x + ((y * z) / (a - t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -700000.0)
		tmp = Float64(x + y);
	elseif (t <= 2.3e+130)
		tmp = Float64(x + Float64(Float64(y * z) / Float64(a - t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -700000.0)
		tmp = x + y;
	elseif (t <= 2.3e+130)
		tmp = x + ((y * z) / (a - t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -700000], N[(x + y), $MachinePrecision], If[LessEqual[t, 23000000000000002113798415841583634489255369458070367475338738167367743897258102483121572000025882191942560861254112410265809059840], N[(x + N[(N[(y * z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -7e5 or 2.3000000000000002e130 < t

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if -7e5 < t < 2.3000000000000002e130

   1. Initial program 85.7%

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

   2. Taylor expanded in z around inf

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

      1. lower-*.f64 73.8%

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

   4. Applied rewrites 73.8%

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

Alternative 7: 77.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -11500:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 8600000000000000000000:\\ \;\;\;\;x + \frac{z - t}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= t -11500)
  (+ x y)
  (if (<= t 8600000000000000000000)
    (+ x (* (/ (- z t) a) y))
    (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -11500.0) {
		tmp = x + y;
	} else if (t <= 8.6e+21) {
		tmp = x + (((z - t) / a) * y);
	} else {
		tmp = x + y;
	}
	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 (t <= (-11500.0d0)) then
        tmp = x + y
    else if (t <= 8.6d+21) then
        tmp = x + (((z - t) / a) * y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -11500.0) {
		tmp = x + y;
	} else if (t <= 8.6e+21) {
		tmp = x + (((z - t) / a) * y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -11500.0:
		tmp = x + y
	elif t <= 8.6e+21:
		tmp = x + (((z - t) / a) * y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -11500.0)
		tmp = Float64(x + y);
	elseif (t <= 8.6e+21)
		tmp = Float64(x + Float64(Float64(Float64(z - t) / a) * y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -11500.0)
		tmp = x + y;
	elseif (t <= 8.6e+21)
		tmp = x + (((z - t) / a) * y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -11500], N[(x + y), $MachinePrecision], If[LessEqual[t, 8600000000000000000000], N[(x + N[(N[(N[(z - t), $MachinePrecision] / a), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -11500 or 8.6e21 < t

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if -11500 < t < 8.6e21

   1. Initial program 85.7%

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

   2. Taylor expanded in t around 0

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

   4. Applied rewrites 57.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 60.2%

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

   6. Applied rewrites 60.2%

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

Alternative 8: 76.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} t_1 := \frac{y}{a - t} \cdot \left(z - t\right)\\ t_2 := \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{if}\;t\_2 \leq -999999999999999966484112715463900049825186092620125502979674597309179755437379230686511104:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq \frac{20240225330731}{202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{elif}\;t\_2 \leq 4999999999999999797083622281751813657459980448242257198348695049033519614754772127580160:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (let* ((t_1 (* (/ y (- a t)) (- z t)))
       (t_2 (/ (* y (- z t)) (- a t))))
  (if (<=
       t_2
       -999999999999999966484112715463900049825186092620125502979674597309179755437379230686511104)
    t_1
    (if (<=
         t_2
         20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784)
      (+ x (/ (* y z) a))
      (if (<=
           t_2
           4999999999999999797083622281751813657459980448242257198348695049033519614754772127580160)
        (+ x y)
        t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (a - t)) * (z - t);
	double t_2 = (y * (z - t)) / (a - t);
	double tmp;
	if (t_2 <= -1e+90) {
		tmp = t_1;
	} else if (t_2 <= 1e-310) {
		tmp = x + ((y * z) / a);
	} else if (t_2 <= 5e+87) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / (a - t)) * (z - t)
    t_2 = (y * (z - t)) / (a - t)
    if (t_2 <= (-1d+90)) then
        tmp = t_1
    else if (t_2 <= 1d-310) then
        tmp = x + ((y * z) / a)
    else if (t_2 <= 5d+87) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / (a - t)) * (z - t);
	double t_2 = (y * (z - t)) / (a - t);
	double tmp;
	if (t_2 <= -1e+90) {
		tmp = t_1;
	} else if (t_2 <= 1e-310) {
		tmp = x + ((y * z) / a);
	} else if (t_2 <= 5e+87) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / (a - t)) * (z - t)
	t_2 = (y * (z - t)) / (a - t)
	tmp = 0
	if t_2 <= -1e+90:
		tmp = t_1
	elif t_2 <= 1e-310:
		tmp = x + ((y * z) / a)
	elif t_2 <= 5e+87:
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / Float64(a - t)) * Float64(z - t))
	t_2 = Float64(Float64(y * Float64(z - t)) / Float64(a - t))
	tmp = 0.0
	if (t_2 <= -1e+90)
		tmp = t_1;
	elseif (t_2 <= 1e-310)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	elseif (t_2 <= 5e+87)
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / (a - t)) * (z - t);
	t_2 = (y * (z - t)) / (a - t);
	tmp = 0.0;
	if (t_2 <= -1e+90)
		tmp = t_1;
	elseif (t_2 <= 1e-310)
		tmp = x + ((y * z) / a);
	elseif (t_2 <= 5e+87)
		tmp = x + y;
	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 - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -999999999999999966484112715463900049825186092620125502979674597309179755437379230686511104], t$95$1, If[LessEqual[t$95$2, 20240225330731/202402253307310618352495346718917307049556649764142118356901358027430339567995346891960383701437124495187077864316811911389808737385793476867013399940738509921517424276566361364466907742093216341239767678472745068562007483424692698618103355649159556340810056512358769552333414615230502532186327508646006263307707741093494784], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 4999999999999999797083622281751813657459980448242257198348695049033519614754772127580160], N[(x + y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < -9.9999999999999997e89 or 4.9999999999999998e87 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 85.7%

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

   2. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower--.f64 39.7%

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

   4. Applied rewrites 39.7%

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

      1. lift--.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift--.f64 N/A

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

      6. associate-*l/ N/A

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

      7. sub-negate-rev N/A

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

      8. lift--.f64 N/A

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

      9. distribute-neg-frac2 N/A

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

      10. lift-/.f64 N/A

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

      11. lower-*.f64 N/A

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

      12. lift-/.f64 N/A

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

      13. distribute-neg-frac2 N/A

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

      14. lift--.f64 N/A

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

      15. sub-negate-rev N/A

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

      16. lower-/.f64 N/A

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

      17. lift--.f64 47.5%

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

   6. Applied rewrites 47.5%

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

   if -9.9999999999999997e89 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 9.9999999999999694e-311

   1. Initial program 85.7%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.5%

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

   4. Applied rewrites 59.5%

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

   if 9.9999999999999694e-311 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 4.9999999999999998e87

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

Alternative 9: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \mathbf{if}\;t \leq -590000:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq \frac{4951760157141521}{2475880078570760549798248448}:\\ \;\;\;\;x + \frac{y \cdot z}{a}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<= t -590000)
  (+ x y)
  (if (<= t 4951760157141521/2475880078570760549798248448)
    (+ x (/ (* y z) a))
    (+ x y))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -590000.0) {
		tmp = x + y;
	} else if (t <= 2e-12) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	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 (t <= (-590000.0d0)) then
        tmp = x + y
    else if (t <= 2d-12) then
        tmp = x + ((y * z) / a)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -590000.0) {
		tmp = x + y;
	} else if (t <= 2e-12) {
		tmp = x + ((y * z) / a);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -590000.0:
		tmp = x + y
	elif t <= 2e-12:
		tmp = x + ((y * z) / a)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -590000.0)
		tmp = Float64(x + y);
	elseif (t <= 2e-12)
		tmp = Float64(x + Float64(Float64(y * z) / a));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -590000.0)
		tmp = x + y;
	elseif (t <= 2e-12)
		tmp = x + ((y * z) / a);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -590000], N[(x + y), $MachinePrecision], If[LessEqual[t, 4951760157141521/2475880078570760549798248448], N[(x + N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -5.9e5 or 2e-12 < t

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if -5.9e5 < t < 2e-12

   1. Initial program 85.7%

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

   2. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 59.5%

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

   4. Applied rewrites 59.5%

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

Alternative 10: 61.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} \leq 49999999999999999884518512257185400348306273996201919460278431983048793274064838238955966239342592:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a - t} \cdot z\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     (/ (* y (- z t)) (- a t))
     49999999999999999884518512257185400348306273996201919460278431983048793274064838238955966239342592)
  (+ x y)
  (* (/ y (- a t)) z)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((y * (z - t)) / (a - t)) <= 5e+97) {
		tmp = x + y;
	} else {
		tmp = (y / (a - t)) * z;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((y * (z - t)) / (a - t)) <= 5d+97) then
        tmp = x + y
    else
        tmp = (y / (a - t)) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((y * (z - t)) / (a - t)) <= 5e+97) {
		tmp = x + y;
	} else {
		tmp = (y / (a - t)) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if ((y * (z - t)) / (a - t)) <= 5e+97:
		tmp = x + y
	else:
		tmp = (y / (a - t)) * z
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(Float64(y * Float64(z - t)) / Float64(a - t)) <= 5e+97)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y / Float64(a - t)) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((y * (z - t)) / (a - t)) <= 5e+97)
		tmp = x + y;
	else
		tmp = (y / (a - t)) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], 49999999999999999884518512257185400348306273996201919460278431983048793274064838238955966239342592], N[(x + y), $MachinePrecision], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)) < 5e97

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if 5e97 < (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.7%

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

   7. Applied rewrites 26.7%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 29.0%

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

   9. Applied rewrites 29.0%

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

       1. lift-*.f64 N/A

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

       2. lift--.f64 N/A

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

       3. lift-/.f64 N/A

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

       4. associate-*l/ N/A

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

       5. associate-/l* N/A

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

       6. *-commutative N/A

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

       7. lower-*.f64 N/A

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

       8. lower-/.f64 N/A

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

       9. lift--.f64 29.0%

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

   11. Applied rewrites 29.0%

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

Alternative 11: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq 195000000000000013423086018547400826322037102352529376490127476942746493577204858317007062682042928858068800774948149770500210948420271766960380875352257810703753010192511781284796122612829243604576830292428928369807154637679269281644300321474793929847322181632:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot z}{a}\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     z
     195000000000000013423086018547400826322037102352529376490127476942746493577204858317007062682042928858068800774948149770500210948420271766960380875352257810703753010192511781284796122612829243604576830292428928369807154637679269281644300321474793929847322181632)
  (+ x y)
  (/ (* y z) a)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.95e+260) {
		tmp = x + y;
	} else {
		tmp = (y * z) / a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (z <= 1.95d+260) then
        tmp = x + y
    else
        tmp = (y * z) / a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.95e+260) {
		tmp = x + y;
	} else {
		tmp = (y * z) / a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.95e+260:
		tmp = x + y
	else:
		tmp = (y * z) / a
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.95e+260)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(y * z) / a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.95e+260)
		tmp = x + y;
	else
		tmp = (y * z) / a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 195000000000000013423086018547400826322037102352529376490127476942746493577204858317007062682042928858068800774948149770500210948420271766960380875352257810703753010192511781284796122612829243604576830292428928369807154637679269281644300321474793929847322181632], N[(x + y), $MachinePrecision], N[(N[(y * z), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.9500000000000001e260

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if 1.9500000000000001e260 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.7%

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

   7. Applied rewrites 26.7%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 18.4%

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

Alternative 12: 59.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \mathbf{if}\;z \leq 195000000000000013423086018547400826322037102352529376490127476942746493577204858317007062682042928858068800774948149770500210948420271766960380875352257810703753010192511781284796122612829243604576830292428928369807154637679269281644300321474793929847322181632:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z}{a} \cdot y\\ \end{array} \]

FPCore

(FPCore (x y z t a)
  :precision binary64
  (if (<=
     z
     195000000000000013423086018547400826322037102352529376490127476942746493577204858317007062682042928858068800774948149770500210948420271766960380875352257810703753010192511781284796122612829243604576830292428928369807154637679269281644300321474793929847322181632)
  (+ x y)
  (* (/ z a) y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (z <= 1.95e+260) {
		tmp = x + y;
	} else {
		tmp = (z / a) * y;
	}
	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 <= 1.95d+260) then
        tmp = x + y
    else
        tmp = (z / a) * y
    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 <= 1.95e+260) {
		tmp = x + y;
	} else {
		tmp = (z / a) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if z <= 1.95e+260:
		tmp = x + y
	else:
		tmp = (z / a) * y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (z <= 1.95e+260)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(z / a) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (z <= 1.95e+260)
		tmp = x + y;
	else
		tmp = (z / a) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[z, 195000000000000013423086018547400826322037102352529376490127476942746493577204858317007062682042928858068800774948149770500210948420271766960380875352257810703753010192511781284796122612829243604576830292428928369807154637679269281644300321474793929847322181632], N[(x + y), $MachinePrecision], N[(N[(z / a), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.9500000000000001e260

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   if 1.9500000000000001e260 < z

   1. Initial program 85.7%

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

   2. Taylor expanded in t around inf

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

      1. lower-+.f64 59.4%

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

   4. Applied rewrites 59.4%

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

   5. Taylor expanded in z around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 26.7%

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

   7. Applied rewrites 26.7%

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

   8. Taylor expanded in t around 0

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

   10. Applied rewrites 18.4%

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 N/A

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

       3. associate-/l* N/A

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

       4. *-commutative N/A

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

       5. lower-*.f64 N/A

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

       6. lower-/.f64 20.2%

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

   12. Applied rewrites 20.2%

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

Alternative 13: 59.4% accurate, 6.5× speedup

Math

\[x + y \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

2. Taylor expanded in t around inf

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

   1. lower-+.f64 59.4%

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

4. Applied rewrites 59.4%

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

Alternative 14: 18.3% accurate, 26.0× speedup

Math

\[y \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.7%

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

2. Taylor expanded in t around inf

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

   1. lower-+.f64 59.4%

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

4. Applied rewrites 59.4%

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

5. Taylor expanded in x around 0

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

7. Applied rewrites 18.3%

   \[\leadsto y \]
8. Add Preprocessing

Reproduce

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