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

Percentage Accurate: 77.4% → 91.6%

Time: 5.2s

Alternatives: 14

Speedup: 0.6×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 91.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-77} \lor \neg \left(y \leq 4 \cdot 10^{-131}\right):\\ \;\;\;\;\left(\left(\left(\frac{t}{a - t} + 1\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -6.4e-77) (not (<= y 4e-131)))
   (* (- (+ (+ (/ t (- a t)) 1.0) (/ x y)) (/ z (- a t))) y)
   (- (+ x y) (/ (* (- z t) y) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.4e-77) || !(y <= 4e-131)) {
		tmp = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y;
	} else {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((y <= (-6.4d-77)) .or. (.not. (y <= 4d-131))) then
        tmp = ((((t / (a - t)) + 1.0d0) + (x / y)) - (z / (a - t))) * y
    else
        tmp = (x + y) - (((z - t) * y) / (a - t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((y <= -6.4e-77) || !(y <= 4e-131)) {
		tmp = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y;
	} else {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (y <= -6.4e-77) or not (y <= 4e-131):
		tmp = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y
	else:
		tmp = (x + y) - (((z - t) * y) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((y <= -6.4e-77) || !(y <= 4e-131))
		tmp = Float64(Float64(Float64(Float64(Float64(t / Float64(a - t)) + 1.0) + Float64(x / y)) - Float64(z / Float64(a - t))) * y);
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((y <= -6.4e-77) || ~((y <= 4e-131)))
		tmp = ((((t / (a - t)) + 1.0) + (x / y)) - (z / (a - t))) * y;
	else
		tmp = (x + y) - (((z - t) * y) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[y, -6.4e-77], N[Not[LessEqual[y, 4e-131]], $MachinePrecision]], N[(N[(N[(N[(N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] - N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.39999999999999999e-77 or 3.9999999999999999e-131 < y

   1. Initial program 63.6%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 91.4

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

   5. Applied rewrites 91.4%

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

   if -6.39999999999999999e-77 < y < 3.9999999999999999e-131

   1. Initial program 96.8%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-77} \lor \neg \left(y \leq 4 \cdot 10^{-131}\right):\\ \;\;\;\;\left(\left(\left(\frac{t}{a - t} + 1\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;\left(1 + \frac{t - z}{a - t}\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;\mathsf{fma}\left(-1, \frac{a - z}{t}, \frac{x}{y}\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y - \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 -1e+306)
     (* (+ 1.0 (/ (- t z) (- a t))) y)
     (if (<= t_1 -5e-230)
       t_1
       (if (<= t_1 0.0)
         (* (fma -1.0 (/ (- a z) t) (/ x y)) y)
         (if (<= t_1 2e+307) t_1 (- y (* (- z t) (/ y (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -1e+306) {
		tmp = (1.0 + ((t - z) / (a - t))) * y;
	} else if (t_1 <= -5e-230) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = fma(-1.0, ((a - z) / t), (x / y)) * y;
	} else if (t_1 <= 2e+307) {
		tmp = t_1;
	} else {
		tmp = y - ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e+306)
		tmp = Float64(Float64(1.0 + Float64(Float64(t - z) / Float64(a - t))) * y);
	elseif (t_1 <= -5e-230)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(fma(-1.0, Float64(Float64(a - z) / t), Float64(x / y)) * y);
	elseif (t_1 <= 2e+307)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+306], N[(N[(1.0 + N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -5e-230], t$95$1, If[LessEqual[t$95$1, 0.0], N[(N[(-1.0 * N[(N[(a - z), $MachinePrecision] / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, 2e+307], t$95$1, N[(y - N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.00000000000000002e306

   1. Initial program 44.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift--.f64 62.9

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

   5. Applied rewrites 62.9%

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

   if -1.00000000000000002e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.00000000000000035e-230 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.99999999999999997e307

   1. Initial program 98.1%

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

   if -5.00000000000000035e-230 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 81.2

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in t around -inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 99.8

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

   8. Applied rewrites 99.8%

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

   if 1.99999999999999997e307 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 39.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower--.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 69.2

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

   5. Applied rewrites 69.2%

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

Alternative 3: 88.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;\left(1 + \frac{t - z}{a - t}\right) \cdot y\\ \mathbf{elif}\;t\_1 \leq -5 \cdot 10^{-230}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y - \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 -1e+306)
     (* (+ 1.0 (/ (- t z) (- a t))) y)
     (if (<= t_1 -5e-230)
       t_1
       (if (<= t_1 0.0)
         (- x (/ (* y (- a z)) t))
         (if (<= t_1 2e+307) t_1 (- y (* (- z t) (/ y (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -1e+306) {
		tmp = (1.0 + ((t - z) / (a - t))) * y;
	} else if (t_1 <= -5e-230) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else if (t_1 <= 2e+307) {
		tmp = t_1;
	} else {
		tmp = y - ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (((z - t) * y) / (a - t))
    if (t_1 <= (-1d+306)) then
        tmp = (1.0d0 + ((t - z) / (a - t))) * y
    else if (t_1 <= (-5d-230)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = x - ((y * (a - z)) / t)
    else if (t_1 <= 2d+307) then
        tmp = t_1
    else
        tmp = y - ((z - t) * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_1 <= -1e+306) {
		tmp = (1.0 + ((t - z) / (a - t))) * y;
	} else if (t_1 <= -5e-230) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else if (t_1 <= 2e+307) {
		tmp = t_1;
	} else {
		tmp = y - ((z - t) * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_1 <= -1e+306:
		tmp = (1.0 + ((t - z) / (a - t))) * y
	elif t_1 <= -5e-230:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = x - ((y * (a - z)) / t)
	elif t_1 <= 2e+307:
		tmp = t_1
	else:
		tmp = y - ((z - t) * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= -1e+306)
		tmp = Float64(Float64(1.0 + Float64(Float64(t - z) / Float64(a - t))) * y);
	elseif (t_1 <= -5e-230)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	elseif (t_1 <= 2e+307)
		tmp = t_1;
	else
		tmp = Float64(y - Float64(Float64(z - t) * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_1 <= -1e+306)
		tmp = (1.0 + ((t - z) / (a - t))) * y;
	elseif (t_1 <= -5e-230)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = x - ((y * (a - z)) / t);
	elseif (t_1 <= 2e+307)
		tmp = t_1;
	else
		tmp = y - ((z - t) * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e+306], N[(N[(1.0 + N[(N[(t - z), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[t$95$1, -5e-230], t$95$1, If[LessEqual[t$95$1, 0.0], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+307], t$95$1, N[(y - N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.00000000000000002e306

   1. Initial program 44.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. associate--l+ N/A

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

      4. lower-+.f64 N/A

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

      5. sub-div N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lift--.f64 62.9

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

   5. Applied rewrites 62.9%

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

   if -1.00000000000000002e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.00000000000000035e-230 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.99999999999999997e307

   1. Initial program 98.1%

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

   if -5.00000000000000035e-230 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 4.7%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 81.2

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

   5. Applied rewrites 81.2%

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

   6. Taylor expanded in t around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 95.2

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

   8. Applied rewrites 95.2%

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

   if 1.99999999999999997e307 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 39.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower--.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 69.2

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

   5. Applied rewrites 69.2%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq -1 \cdot 10^{+306}:\\ \;\;\;\;\left(1 + \frac{t - z}{a - t}\right) \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq -5 \cdot 10^{-230}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq 0:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;y - \left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-230}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \mathbf{elif}\;t\_2 \leq 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y (- a t)))))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -1e+306)
     t_1
     (if (<= t_2 -5e-230)
       (- (+ x y) (/ (* z y) a))
       (if (<= t_2 1e-208) x (if (<= t_2 2e+307) (+ y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -1e+306) {
		tmp = t_1;
	} else if (t_2 <= -5e-230) {
		tmp = (x + y) - ((z * y) / a);
	} else if (t_2 <= 1e-208) {
		tmp = x;
	} else if (t_2 <= 2e+307) {
		tmp = y + x;
	} 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 - (z * (y / (a - t)))
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-1d+306)) then
        tmp = t_1
    else if (t_2 <= (-5d-230)) then
        tmp = (x + y) - ((z * y) / a)
    else if (t_2 <= 1d-208) then
        tmp = x
    else if (t_2 <= 2d+307) then
        tmp = y + x
    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 - (z * (y / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -1e+306) {
		tmp = t_1;
	} else if (t_2 <= -5e-230) {
		tmp = (x + y) - ((z * y) / a);
	} else if (t_2 <= 1e-208) {
		tmp = x;
	} else if (t_2 <= 2e+307) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / (a - t)))
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -1e+306:
		tmp = t_1
	elif t_2 <= -5e-230:
		tmp = (x + y) - ((z * y) / a)
	elif t_2 <= 1e-208:
		tmp = x
	elif t_2 <= 2e+307:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z * Float64(y / Float64(a - t))))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e+306)
		tmp = t_1;
	elseif (t_2 <= -5e-230)
		tmp = Float64(Float64(x + y) - Float64(Float64(z * y) / a));
	elseif (t_2 <= 1e-208)
		tmp = x;
	elseif (t_2 <= 2e+307)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z * (y / (a - t)));
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -1e+306)
		tmp = t_1;
	elseif (t_2 <= -5e-230)
		tmp = (x + y) - ((z * y) / a);
	elseif (t_2 <= 1e-208)
		tmp = x;
	elseif (t_2 <= 2e+307)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+306], t$95$1, If[LessEqual[t$95$2, -5e-230], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e-208], x, If[LessEqual[t$95$2, 2e+307], N[(y + x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.00000000000000002e306 or 1.99999999999999997e307 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 41.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower--.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 66.5

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 64.7%

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

   if -1.00000000000000002e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.00000000000000035e-230

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if -5.00000000000000035e-230 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.0000000000000001e-208

   1. Initial program 26.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 70.5%

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

   if 1.0000000000000001e-208 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.99999999999999997e307

   1. Initial program 97.7%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 83.1

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

   5. Applied rewrites 83.1%

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

Alternative 5: 71.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{a - t}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-230}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_2 \leq 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y (- a t)))))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -1e+306)
     t_1
     (if (<= t_2 -5e-230)
       (+ y x)
       (if (<= t_2 1e-208) x (if (<= t_2 2e+307) (+ y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -1e+306) {
		tmp = t_1;
	} else if (t_2 <= -5e-230) {
		tmp = y + x;
	} else if (t_2 <= 1e-208) {
		tmp = x;
	} else if (t_2 <= 2e+307) {
		tmp = y + x;
	} 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 - (z * (y / (a - t)))
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-1d+306)) then
        tmp = t_1
    else if (t_2 <= (-5d-230)) then
        tmp = y + x
    else if (t_2 <= 1d-208) then
        tmp = x
    else if (t_2 <= 2d+307) then
        tmp = y + x
    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 - (z * (y / (a - t)));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -1e+306) {
		tmp = t_1;
	} else if (t_2 <= -5e-230) {
		tmp = y + x;
	} else if (t_2 <= 1e-208) {
		tmp = x;
	} else if (t_2 <= 2e+307) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / (a - t)))
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -1e+306:
		tmp = t_1
	elif t_2 <= -5e-230:
		tmp = y + x
	elif t_2 <= 1e-208:
		tmp = x
	elif t_2 <= 2e+307:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z * Float64(y / Float64(a - t))))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e+306)
		tmp = t_1;
	elseif (t_2 <= -5e-230)
		tmp = Float64(y + x);
	elseif (t_2 <= 1e-208)
		tmp = x;
	elseif (t_2 <= 2e+307)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z * (y / (a - t)));
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -1e+306)
		tmp = t_1;
	elseif (t_2 <= -5e-230)
		tmp = y + x;
	elseif (t_2 <= 1e-208)
		tmp = x;
	elseif (t_2 <= 2e+307)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+306], t$95$1, If[LessEqual[t$95$2, -5e-230], N[(y + x), $MachinePrecision], If[LessEqual[t$95$2, 1e-208], x, If[LessEqual[t$95$2, 2e+307], N[(y + x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.00000000000000002e306 or 1.99999999999999997e307 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 41.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower--.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 66.5

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 64.7%

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

   if -1.00000000000000002e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.00000000000000035e-230 or 1.0000000000000001e-208 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.99999999999999997e307

   1. Initial program 98.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if -5.00000000000000035e-230 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.0000000000000001e-208

   1. Initial program 26.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 70.5%

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

Alternative 6: 70.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-z}{a - t} \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-230}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_2 \leq 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ (- z) (- a t)) y))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -1e+306)
     t_1
     (if (<= t_2 -5e-230)
       (+ y x)
       (if (<= t_2 1e-208) x (if (<= t_2 2e+307) (+ y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (-z / (a - t)) * y;
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -1e+306) {
		tmp = t_1;
	} else if (t_2 <= -5e-230) {
		tmp = y + x;
	} else if (t_2 <= 1e-208) {
		tmp = x;
	} else if (t_2 <= 2e+307) {
		tmp = y + x;
	} 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 = (-z / (a - t)) * y
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-1d+306)) then
        tmp = t_1
    else if (t_2 <= (-5d-230)) then
        tmp = y + x
    else if (t_2 <= 1d-208) then
        tmp = x
    else if (t_2 <= 2d+307) then
        tmp = y + x
    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 = (-z / (a - t)) * y;
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -1e+306) {
		tmp = t_1;
	} else if (t_2 <= -5e-230) {
		tmp = y + x;
	} else if (t_2 <= 1e-208) {
		tmp = x;
	} else if (t_2 <= 2e+307) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (-z / (a - t)) * y
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -1e+306:
		tmp = t_1
	elif t_2 <= -5e-230:
		tmp = y + x
	elif t_2 <= 1e-208:
		tmp = x
	elif t_2 <= 2e+307:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(-z) / Float64(a - t)) * y)
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e+306)
		tmp = t_1;
	elseif (t_2 <= -5e-230)
		tmp = Float64(y + x);
	elseif (t_2 <= 1e-208)
		tmp = x;
	elseif (t_2 <= 2e+307)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (-z / (a - t)) * y;
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -1e+306)
		tmp = t_1;
	elseif (t_2 <= -5e-230)
		tmp = y + x;
	elseif (t_2 <= 1e-208)
		tmp = x;
	elseif (t_2 <= 2e+307)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[((-z) / N[(a - t), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+306], t$95$1, If[LessEqual[t$95$2, -5e-230], N[(y + x), $MachinePrecision], If[LessEqual[t$95$2, 1e-208], x, If[LessEqual[t$95$2, 2e+307], N[(y + x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.00000000000000002e306 or 1.99999999999999997e307 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 41.5%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 88.9

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

   5. Applied rewrites 88.9%

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

   6. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift--.f64 60.7

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

   8. Applied rewrites 60.7%

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

   if -1.00000000000000002e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.00000000000000035e-230 or 1.0000000000000001e-208 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.99999999999999997e307

   1. Initial program 98.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if -5.00000000000000035e-230 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.0000000000000001e-208

   1. Initial program 26.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 70.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq -1 \cdot 10^{+306}:\\ \;\;\;\;\frac{-z}{a - t} \cdot y\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq -5 \cdot 10^{-230}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{a - t} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - z \cdot \frac{y}{a}\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{+306}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq -5 \cdot 10^{-230}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;t\_2 \leq 10^{-208}:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- y (* z (/ y a)))) (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_2 -1e+306)
     t_1
     (if (<= t_2 -5e-230)
       (+ y x)
       (if (<= t_2 1e-208) x (if (<= t_2 2e+307) (+ y x) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y - (z * (y / a));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -1e+306) {
		tmp = t_1;
	} else if (t_2 <= -5e-230) {
		tmp = y + x;
	} else if (t_2 <= 1e-208) {
		tmp = x;
	} else if (t_2 <= 2e+307) {
		tmp = y + x;
	} 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 - (z * (y / a))
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 <= (-1d+306)) then
        tmp = t_1
    else if (t_2 <= (-5d-230)) then
        tmp = y + x
    else if (t_2 <= 1d-208) then
        tmp = x
    else if (t_2 <= 2d+307) then
        tmp = y + x
    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 - (z * (y / a));
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 <= -1e+306) {
		tmp = t_1;
	} else if (t_2 <= -5e-230) {
		tmp = y + x;
	} else if (t_2 <= 1e-208) {
		tmp = x;
	} else if (t_2 <= 2e+307) {
		tmp = y + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y - (z * (y / a))
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 <= -1e+306:
		tmp = t_1
	elif t_2 <= -5e-230:
		tmp = y + x
	elif t_2 <= 1e-208:
		tmp = x
	elif t_2 <= 2e+307:
		tmp = y + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y - Float64(z * Float64(y / a)))
	t_2 = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= -1e+306)
		tmp = t_1;
	elseif (t_2 <= -5e-230)
		tmp = Float64(y + x);
	elseif (t_2 <= 1e-208)
		tmp = x;
	elseif (t_2 <= 2e+307)
		tmp = Float64(y + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y - (z * (y / a));
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 <= -1e+306)
		tmp = t_1;
	elseif (t_2 <= -5e-230)
		tmp = y + x;
	elseif (t_2 <= 1e-208)
		tmp = x;
	elseif (t_2 <= 2e+307)
		tmp = y + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y - N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e+306], t$95$1, If[LessEqual[t$95$2, -5e-230], N[(y + x), $MachinePrecision], If[LessEqual[t$95$2, 1e-208], x, If[LessEqual[t$95$2, 2e+307], N[(y + x), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -1.00000000000000002e306 or 1.99999999999999997e307 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 41.5%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower--.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 66.5

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in t around 0

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

   8. Applied rewrites 53.5%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 53.8%

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

   if -1.00000000000000002e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -5.00000000000000035e-230 or 1.0000000000000001e-208 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.99999999999999997e307

   1. Initial program 98.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 78.9

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

   5. Applied rewrites 78.9%

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

   if -5.00000000000000035e-230 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 1.0000000000000001e-208

   1. Initial program 26.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 70.5%

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

Alternative 8: 79.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{+72}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-128}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+187}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.28e+72)
   (+ y x)
   (if (<= a -7.6e-128)
     (- x (/ (* (- z t) y) (- a t)))
     (if (<= a 4.8e-63)
       (- x (/ (* y (- a z)) t))
       (if (<= a 2e+187) (- (+ x y) (/ (* z y) a)) (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.28e+72) {
		tmp = y + x;
	} else if (a <= -7.6e-128) {
		tmp = x - (((z - t) * y) / (a - t));
	} else if (a <= 4.8e-63) {
		tmp = x - ((y * (a - z)) / t);
	} else if (a <= 2e+187) {
		tmp = (x + y) - ((z * y) / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.28d+72)) then
        tmp = y + x
    else if (a <= (-7.6d-128)) then
        tmp = x - (((z - t) * y) / (a - t))
    else if (a <= 4.8d-63) then
        tmp = x - ((y * (a - z)) / t)
    else if (a <= 2d+187) then
        tmp = (x + y) - ((z * y) / a)
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.28e+72) {
		tmp = y + x;
	} else if (a <= -7.6e-128) {
		tmp = x - (((z - t) * y) / (a - t));
	} else if (a <= 4.8e-63) {
		tmp = x - ((y * (a - z)) / t);
	} else if (a <= 2e+187) {
		tmp = (x + y) - ((z * y) / a);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.28e+72:
		tmp = y + x
	elif a <= -7.6e-128:
		tmp = x - (((z - t) * y) / (a - t))
	elif a <= 4.8e-63:
		tmp = x - ((y * (a - z)) / t)
	elif a <= 2e+187:
		tmp = (x + y) - ((z * y) / a)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.28e+72)
		tmp = Float64(y + x);
	elseif (a <= -7.6e-128)
		tmp = Float64(x - Float64(Float64(Float64(z - t) * y) / Float64(a - t)));
	elseif (a <= 4.8e-63)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	elseif (a <= 2e+187)
		tmp = Float64(Float64(x + y) - Float64(Float64(z * y) / a));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.28e+72)
		tmp = y + x;
	elseif (a <= -7.6e-128)
		tmp = x - (((z - t) * y) / (a - t));
	elseif (a <= 4.8e-63)
		tmp = x - ((y * (a - z)) / t);
	elseif (a <= 2e+187)
		tmp = (x + y) - ((z * y) / a);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.28e+72], N[(y + x), $MachinePrecision], If[LessEqual[a, -7.6e-128], N[(x - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.8e-63], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2e+187], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.28000000000000009e72 or 1.99999999999999981e187 < a

   1. Initial program 75.0%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 87.9

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

   5. Applied rewrites 87.9%

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

   if -1.28000000000000009e72 < a < -7.6000000000000005e-128

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 78.8%

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

   if -7.6000000000000005e-128 < a < 4.8000000000000001e-63

   1. Initial program 72.1%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 83.8

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

   5. Applied rewrites 83.8%

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

   6. Taylor expanded in t around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 84.7

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

   8. Applied rewrites 84.7%

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

   if 4.8000000000000001e-63 < a < 1.99999999999999981e187

   1. Initial program 70.9%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 74.2

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

   5. Applied rewrites 74.2%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.28 \cdot 10^{+72}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-128}:\\ \;\;\;\;x - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{-63}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+187}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-121} \lor \neg \left(t \leq 0.185\right):\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.85e-121) (not (<= t 0.185)))
   (- x (/ (* y (- a z)) t))
   (- (+ x y) (/ (* z y) a))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.85e-121) || !(t <= 0.185)) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = (x + y) - ((z * y) / a);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-1.85d-121)) .or. (.not. (t <= 0.185d0))) then
        tmp = x - ((y * (a - z)) / t)
    else
        tmp = (x + y) - ((z * y) / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.85e-121) || !(t <= 0.185)) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = (x + y) - ((z * y) / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1.85e-121) or not (t <= 0.185):
		tmp = x - ((y * (a - z)) / t)
	else:
		tmp = (x + y) - ((z * y) / a)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.85e-121) || !(t <= 0.185))
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(z * y) / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -1.85e-121) || ~((t <= 0.185)))
		tmp = x - ((y * (a - z)) / t);
	else
		tmp = (x + y) - ((z * y) / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.85e-121], N[Not[LessEqual[t, 0.185]], $MachinePrecision]], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.8500000000000001e-121 or 0.185 < t

   1. Initial program 64.2%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 74.1

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

   5. Applied rewrites 74.1%

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

   6. Taylor expanded in t around -inf

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

      1. lower-+.f64 N/A

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

      2. mul-1-neg N/A

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

      3. lower-neg.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower--.f64 76.6

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

   8. Applied rewrites 76.6%

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

   if -1.8500000000000001e-121 < t < 0.185

   1. Initial program 92.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. *-commutative N/A

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

      3. lower-*.f64 84.1

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

   5. Applied rewrites 84.1%

      \[\leadsto \left(x + y\right) - \color{blue}{\frac{z \cdot y}{a}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{-121} \lor \neg \left(t \leq 0.185\right):\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9.8 \cdot 10^{-54}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -1.22 \cdot 10^{-179}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-273}:\\ \;\;\;\;\frac{z}{t} \cdot y\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9.8e-54)
   (+ y x)
   (if (<= a -1.22e-179)
     x
     (if (<= a 9.5e-273) (* (/ z t) y) (if (<= a 2.5e+50) x (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.8e-54) {
		tmp = y + x;
	} else if (a <= -1.22e-179) {
		tmp = x;
	} else if (a <= 9.5e-273) {
		tmp = (z / t) * y;
	} else if (a <= 2.5e+50) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9.8d-54)) then
        tmp = y + x
    else if (a <= (-1.22d-179)) then
        tmp = x
    else if (a <= 9.5d-273) then
        tmp = (z / t) * y
    else if (a <= 2.5d+50) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9.8e-54) {
		tmp = y + x;
	} else if (a <= -1.22e-179) {
		tmp = x;
	} else if (a <= 9.5e-273) {
		tmp = (z / t) * y;
	} else if (a <= 2.5e+50) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9.8e-54:
		tmp = y + x
	elif a <= -1.22e-179:
		tmp = x
	elif a <= 9.5e-273:
		tmp = (z / t) * y
	elif a <= 2.5e+50:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9.8e-54)
		tmp = Float64(y + x);
	elseif (a <= -1.22e-179)
		tmp = x;
	elseif (a <= 9.5e-273)
		tmp = Float64(Float64(z / t) * y);
	elseif (a <= 2.5e+50)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9.8e-54)
		tmp = y + x;
	elseif (a <= -1.22e-179)
		tmp = x;
	elseif (a <= 9.5e-273)
		tmp = (z / t) * y;
	elseif (a <= 2.5e+50)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9.8e-54], N[(y + x), $MachinePrecision], If[LessEqual[a, -1.22e-179], x, If[LessEqual[a, 9.5e-273], N[(N[(z / t), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 2.5e+50], x, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.80000000000000042e-54 or 2.5e50 < a

   1. Initial program 75.4%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.1

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

   5. Applied rewrites 77.1%

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

   if -9.80000000000000042e-54 < a < -1.22e-179 or 9.49999999999999925e-273 < a < 2.5e50

   1. Initial program 72.8%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 60.6%

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

   if -1.22e-179 < a < 9.49999999999999925e-273

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. associate-+r+ N/A

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

      5. lower-+.f64 N/A

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

      6. +-commutative N/A

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

      7. lower-+.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lower-/.f64 N/A

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

      12. lift--.f64 87.1

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

   5. Applied rewrites 87.1%

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

   6. Taylor expanded in t around -inf

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

      1. lower-fma.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lift-/.f64 78.0

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

   8. Applied rewrites 78.0%

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

   9. Taylor expanded in z around inf

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

       1. lower-/.f64 58.1

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

   11. Applied rewrites 58.1%

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

Alternative 11: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-51}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-247}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-273}:\\ \;\;\;\;\frac{y \cdot z}{t}\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.1e-51)
   (+ y x)
   (if (<= a -1.8e-247)
     x
     (if (<= a 9.5e-273) (/ (* y z) t) (if (<= a 2.5e+50) x (+ y x))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e-51) {
		tmp = y + x;
	} else if (a <= -1.8e-247) {
		tmp = x;
	} else if (a <= 9.5e-273) {
		tmp = (y * z) / t;
	} else if (a <= 2.5e+50) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.1d-51)) then
        tmp = y + x
    else if (a <= (-1.8d-247)) then
        tmp = x
    else if (a <= 9.5d-273) then
        tmp = (y * z) / t
    else if (a <= 2.5d+50) then
        tmp = x
    else
        tmp = y + x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.1e-51) {
		tmp = y + x;
	} else if (a <= -1.8e-247) {
		tmp = x;
	} else if (a <= 9.5e-273) {
		tmp = (y * z) / t;
	} else if (a <= 2.5e+50) {
		tmp = x;
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.1e-51:
		tmp = y + x
	elif a <= -1.8e-247:
		tmp = x
	elif a <= 9.5e-273:
		tmp = (y * z) / t
	elif a <= 2.5e+50:
		tmp = x
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.1e-51)
		tmp = Float64(y + x);
	elseif (a <= -1.8e-247)
		tmp = x;
	elseif (a <= 9.5e-273)
		tmp = Float64(Float64(y * z) / t);
	elseif (a <= 2.5e+50)
		tmp = x;
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.1e-51)
		tmp = y + x;
	elseif (a <= -1.8e-247)
		tmp = x;
	elseif (a <= 9.5e-273)
		tmp = (y * z) / t;
	elseif (a <= 2.5e+50)
		tmp = x;
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.1e-51], N[(y + x), $MachinePrecision], If[LessEqual[a, -1.8e-247], x, If[LessEqual[a, 9.5e-273], N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision], If[LessEqual[a, 2.5e+50], x, N[(y + x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.0999999999999997e-51 or 2.5e50 < a

   1. Initial program 75.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.7

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

   5. Applied rewrites 77.7%

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

   if -3.0999999999999997e-51 < a < -1.7999999999999998e-247 or 9.49999999999999925e-273 < a < 2.5e50

   1. Initial program 73.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 56.7%

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

   if -1.7999999999999998e-247 < a < 9.49999999999999925e-273

   1. Initial program 79.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-*r/ N/A

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

      2. lower-/.f64 N/A

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

      3. associate-*r* N/A

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

      4. lower-*.f64 N/A

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

      5. mul-1-neg N/A

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

      6. lower-neg.f64 N/A

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

      7. lift--.f64 75.7

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

   5. Applied rewrites 75.7%

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

   6. Taylor expanded in t around inf

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 67.4

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

   8. Applied rewrites 67.4%

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

Alternative 12: 62.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-51} \lor \neg \left(a \leq 2.5 \cdot 10^{+50}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -3.1e-51) (not (<= a 2.5e+50))) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e-51) || !(a <= 2.5e+50)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-3.1d-51)) .or. (.not. (a <= 2.5d+50))) then
        tmp = y + x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -3.1e-51) || !(a <= 2.5e+50)) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -3.1e-51) or not (a <= 2.5e+50):
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -3.1e-51) || !(a <= 2.5e+50))
		tmp = Float64(y + x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -3.1e-51) || ~((a <= 2.5e+50)))
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -3.1e-51], N[Not[LessEqual[a, 2.5e+50]], $MachinePrecision]], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -3.0999999999999997e-51 or 2.5e50 < a

   1. Initial program 75.2%

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

   3. Taylor expanded in a around inf

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

      1. +-commutative N/A

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

      2. lower-+.f64 77.7

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

   5. Applied rewrites 77.7%

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

   if -3.0999999999999997e-51 < a < 2.5e50

   1. Initial program 74.6%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 50.7%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-51} \lor \neg \left(a \leq 2.5 \cdot 10^{+50}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{+103}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y 2.6e+103) x y))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= 2.6e+103) {
		tmp = x;
	} else {
		tmp = 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 (y <= 2.6d+103) then
        tmp = x
    else
        tmp = 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 (y <= 2.6e+103) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= 2.6e+103:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= 2.6e+103)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= 2.6e+103)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, 2.6e+103], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 2.6000000000000002e103

   1. Initial program 79.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 54.7%

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

   if 2.6000000000000002e103 < y

   1. Initial program 53.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower--.f64 N/A

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

      3. associate-/l* N/A

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

      4. lower-*.f64 N/A

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

      5. lift--.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lift--.f64 63.0

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

   5. Applied rewrites 63.0%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 37.2%

      \[\leadsto y \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 50.5% accurate, 29.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.9%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 48.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2025085 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) -13664970889390727/100000000000000000000000) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)) (if (< (- (+ x y) (/ (* (- z t) y) (- a t))) 14754293444577233/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* y (- a z)) (* x t)) (- a t)) (- (+ y x) (* (* (- z t) (/ 1 (- a t))) y)))))

  (- (+ x y) (/ (* (- z t) y) (- a t))))