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

Percentage Accurate: 76.8% → 92.5%

Time: 4.9s

Alternatives: 9

Speedup: 0.8×

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: 76.8% 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: 92.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{a - t}\\ t_2 := \frac{t}{a - t}\\ t_3 := t\_2 - 1\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+17}:\\ \;\;\;\;\left(\left(\left(t\_2 - -1\right) + \frac{x}{y}\right) - t\_1\right) \cdot y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-87}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\frac{{t\_2}^{2}}{t\_3} - \frac{1}{t\_3}\right) + \frac{x}{y}\right) - t\_1\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (- a t))) (t_2 (/ t (- a t))) (t_3 (- t_2 1.0)))
   (if (<= y -1.6e+17)
     (* (- (+ (- t_2 -1.0) (/ x y)) t_1) y)
     (if (<= y 1.2e-87)
       (- (+ x y) (/ (* (- z t) y) (- a t)))
       (* (- (+ (- (/ (pow t_2 2.0) t_3) (/ 1.0 t_3)) (/ x y)) t_1) y)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (a - t);
	double t_2 = t / (a - t);
	double t_3 = t_2 - 1.0;
	double tmp;
	if (y <= -1.6e+17) {
		tmp = (((t_2 - -1.0) + (x / y)) - t_1) * y;
	} else if (y <= 1.2e-87) {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	} else {
		tmp = ((((pow(t_2, 2.0) / t_3) - (1.0 / t_3)) + (x / y)) - t_1) * 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) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = z / (a - t)
    t_2 = t / (a - t)
    t_3 = t_2 - 1.0d0
    if (y <= (-1.6d+17)) then
        tmp = (((t_2 - (-1.0d0)) + (x / y)) - t_1) * y
    else if (y <= 1.2d-87) then
        tmp = (x + y) - (((z - t) * y) / (a - t))
    else
        tmp = (((((t_2 ** 2.0d0) / t_3) - (1.0d0 / t_3)) + (x / y)) - t_1) * y
    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);
	double t_2 = t / (a - t);
	double t_3 = t_2 - 1.0;
	double tmp;
	if (y <= -1.6e+17) {
		tmp = (((t_2 - -1.0) + (x / y)) - t_1) * y;
	} else if (y <= 1.2e-87) {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	} else {
		tmp = ((((Math.pow(t_2, 2.0) / t_3) - (1.0 / t_3)) + (x / y)) - t_1) * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (a - t)
	t_2 = t / (a - t)
	t_3 = t_2 - 1.0
	tmp = 0
	if y <= -1.6e+17:
		tmp = (((t_2 - -1.0) + (x / y)) - t_1) * y
	elif y <= 1.2e-87:
		tmp = (x + y) - (((z - t) * y) / (a - t))
	else:
		tmp = ((((math.pow(t_2, 2.0) / t_3) - (1.0 / t_3)) + (x / y)) - t_1) * y
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(a - t))
	t_2 = Float64(t / Float64(a - t))
	t_3 = Float64(t_2 - 1.0)
	tmp = 0.0
	if (y <= -1.6e+17)
		tmp = Float64(Float64(Float64(Float64(t_2 - -1.0) + Float64(x / y)) - t_1) * y);
	elseif (y <= 1.2e-87)
		tmp = Float64(Float64(x + y) - Float64(Float64(Float64(z - t) * y) / Float64(a - t)));
	else
		tmp = Float64(Float64(Float64(Float64(Float64((t_2 ^ 2.0) / t_3) - Float64(1.0 / t_3)) + Float64(x / y)) - t_1) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (a - t);
	t_2 = t / (a - t);
	t_3 = t_2 - 1.0;
	tmp = 0.0;
	if (y <= -1.6e+17)
		tmp = (((t_2 - -1.0) + (x / y)) - t_1) * y;
	elseif (y <= 1.2e-87)
		tmp = (x + y) - (((z - t) * y) / (a - t));
	else
		tmp = (((((t_2 ^ 2.0) / t_3) - (1.0 / t_3)) + (x / y)) - t_1) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - 1.0), $MachinePrecision]}, If[LessEqual[y, -1.6e+17], N[(N[(N[(N[(t$95$2 - -1.0), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 1.2e-87], N[(N[(x + y), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(N[(N[Power[t$95$2, 2.0], $MachinePrecision] / t$95$3), $MachinePrecision] - N[(1.0 / t$95$3), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision] * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6e17

   1. Initial program 49.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 88.6

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

   5. Applied rewrites 88.6%

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

   if -1.6e17 < y < 1.2e-87

   1. Initial program 97.5%

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

   if 1.2e-87 < y

   1. Initial program 71.1%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 96.8

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

   5. Applied rewrites 96.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. flip-+ N/A

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

      5. lower-/.f64 N/A

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

      6. metadata-eval N/A

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

      7. lower--.f64 N/A

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

      8. lower-*.f64 N/A

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

      9. lift-/.f64 N/A

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

      10. lift--.f64 N/A

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

      11. lift-/.f64 N/A

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

      12. lift--.f64 N/A

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

      13. lower--.f64 N/A

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

      14. lift-/.f64 N/A

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

      15. lift--.f64 96.8

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

   7. Applied rewrites 96.8%

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

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift--.f64 N/A

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

      7. lift-/.f64 N/A

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

      8. lift--.f64 N/A

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

      9. lift--.f64 N/A

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

      10. lift-/.f64 N/A

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

      11. div-sub N/A

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

      12. lower--.f64 N/A

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

   9. Applied rewrites 96.9%

      \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - {\left(\frac{t}{a - t} - 1\right)}^{-1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]
   10. Step-by-step derivation

       1. lift-pow.f64 N/A

          \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - {\left(\frac{t}{a - t} - 1\right)}^{-1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]

       2. lift--.f64 N/A

          \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - {\left(\frac{t}{a - t} - 1\right)}^{-1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]

       3. lift--.f64 N/A

          \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - {\left(\frac{t}{a - t} - 1\right)}^{-1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]

       4. lift-/.f64 N/A

          \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - {\left(\frac{t}{a - t} - 1\right)}^{-1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]

       5. inv-pow N/A

          \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - \frac{1}{\frac{t}{a - t} - 1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]

       6. lower-/.f64 N/A

          \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - \frac{1}{\frac{t}{a - t} - 1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]

       7. lift-/.f64 N/A

          \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - \frac{1}{\frac{t}{a - t} - 1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]

       8. lift--.f64 N/A

          \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - \frac{1}{\frac{t}{a - t} - 1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]

       9. lift--.f64 96.9

          \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - \frac{1}{\frac{t}{a - t} - 1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]

   11. Applied rewrites 96.9%

       \[\leadsto \left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - \frac{1}{\frac{t}{a - t} - 1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y \]
3. Recombined 3 regimes into one program.

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+17}:\\ \;\;\;\;\left(\left(\left(\frac{t}{a - t} - -1\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-87}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\frac{{\left(\frac{t}{a - t}\right)}^{2}}{\frac{t}{a - t} - 1} - \frac{1}{\frac{t}{a - t} - 1}\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+17} \lor \neg \left(y \leq 1.2 \cdot 10^{-87}\right):\\ \;\;\;\;\left(\left(\left(\frac{t}{a - t} - -1\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= y -1.6e+17) (not (<= y 1.2e-87)))
   (* (- (+ (- (/ 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 <= -1.6e+17) || !(y <= 1.2e-87)) {
		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 <= (-1.6d+17)) .or. (.not. (y <= 1.2d-87))) 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 <= -1.6e+17) || !(y <= 1.2e-87)) {
		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 <= -1.6e+17) or not (y <= 1.2e-87):
		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 <= -1.6e+17) || !(y <= 1.2e-87))
		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 <= -1.6e+17) || ~((y <= 1.2e-87)))
		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, -1.6e+17], N[Not[LessEqual[y, 1.2e-87]], $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 < -1.6e17 or 1.2e-87 < y

   1. Initial program 60.9%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 93.0

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

   5. Applied rewrites 93.0%

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

   if -1.6e17 < y < 1.2e-87

   1. Initial program 97.5%

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

4. Final simplification 95.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+17} \lor \neg \left(y \leq 1.2 \cdot 10^{-87}\right):\\ \;\;\;\;\left(\left(\left(\frac{t}{a - t} - -1\right) + \frac{x}{y}\right) - \frac{z}{a - t}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{a - t}\\ \mathbf{if}\;a \leq -1.8 \cdot 10^{+99} \lor \neg \left(a \leq 45\right):\\ \;\;\;\;\left(x + y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;x - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ z (- a t)))))
   (if (or (<= a -1.8e+99) (not (<= a 45.0))) (- (+ x y) t_1) (- x t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * (z / (a - t));
	double tmp;
	if ((a <= -1.8e+99) || !(a <= 45.0)) {
		tmp = (x + y) - t_1;
	} else {
		tmp = x - t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / (a - t))
    if ((a <= (-1.8d+99)) .or. (.not. (a <= 45.0d0))) then
        tmp = (x + y) - t_1
    else
        tmp = x - 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 / (a - t));
	double tmp;
	if ((a <= -1.8e+99) || !(a <= 45.0)) {
		tmp = (x + y) - t_1;
	} else {
		tmp = x - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * (z / (a - t))
	tmp = 0
	if (a <= -1.8e+99) or not (a <= 45.0):
		tmp = (x + y) - t_1
	else:
		tmp = x - t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(z / Float64(a - t)))
	tmp = 0.0
	if ((a <= -1.8e+99) || !(a <= 45.0))
		tmp = Float64(Float64(x + y) - t_1);
	else
		tmp = Float64(x - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * (z / (a - t));
	tmp = 0.0;
	if ((a <= -1.8e+99) || ~((a <= 45.0)))
		tmp = (x + y) - t_1;
	else
		tmp = x - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -1.8e+99], N[Not[LessEqual[a, 45.0]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - t$95$1), $MachinePrecision], N[(x - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -1.8000000000000001e99 or 45 < a

   1. Initial program 79.2%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 94.1

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

   5. Applied rewrites 94.1%

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

   if -1.8000000000000001e99 < a < 45

   1. Initial program 76.7%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 78.7

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

   5. Applied rewrites 78.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 89.7%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+99} \lor \neg \left(a \leq 45\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+126}:\\ \;\;\;\;y + x\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-76}:\\ \;\;\;\;x - y \cdot \frac{z}{a}\\ \mathbf{elif}\;a \leq 42:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;y + x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2e+126)
   (+ y x)
   (if (<= a -4.2e-76)
     (- x (* y (/ z a)))
     (if (<= a 42.0) (+ x (/ (* y z) t)) (+ y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2e+126) {
		tmp = y + x;
	} else if (a <= -4.2e-76) {
		tmp = x - (y * (z / a));
	} else if (a <= 42.0) {
		tmp = x + ((y * z) / t);
	} 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 <= (-2d+126)) then
        tmp = y + x
    else if (a <= (-4.2d-76)) then
        tmp = x - (y * (z / a))
    else if (a <= 42.0d0) then
        tmp = x + ((y * z) / t)
    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 <= -2e+126) {
		tmp = y + x;
	} else if (a <= -4.2e-76) {
		tmp = x - (y * (z / a));
	} else if (a <= 42.0) {
		tmp = x + ((y * z) / t);
	} else {
		tmp = y + x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2e+126:
		tmp = y + x
	elif a <= -4.2e-76:
		tmp = x - (y * (z / a))
	elif a <= 42.0:
		tmp = x + ((y * z) / t)
	else:
		tmp = y + x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2e+126)
		tmp = Float64(y + x);
	elseif (a <= -4.2e-76)
		tmp = Float64(x - Float64(y * Float64(z / a)));
	elseif (a <= 42.0)
		tmp = Float64(x + Float64(Float64(y * z) / t));
	else
		tmp = Float64(y + x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2e+126)
		tmp = y + x;
	elseif (a <= -4.2e-76)
		tmp = x - (y * (z / a));
	elseif (a <= 42.0)
		tmp = x + ((y * z) / t);
	else
		tmp = y + x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2e+126], N[(y + x), $MachinePrecision], If[LessEqual[a, -4.2e-76], N[(x - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 42.0], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(y + x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.99999999999999985e126 or 42 < a

   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 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 -1.99999999999999985e126 < a < -4.19999999999999985e-76

   1. Initial program 71.9%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 78.8

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

   5. Applied rewrites 78.8%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 77.7%

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

   9. Taylor expanded in t around 0

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

   11. Applied rewrites 62.5%

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

   if -4.19999999999999985e-76 < a < 42

   1. Initial program 78.8%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 81.6

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

   8. Applied rewrites 81.6%

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

   9. Taylor expanded in z around inf

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 80.7

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

   11. Applied rewrites 80.7%

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

Alternative 5: 84.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+126} \lor \neg \left(a \leq 1.55 \cdot 10^{+73}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2e+126) (not (<= a 1.55e+73)))
   (+ y x)
   (- x (* y (/ z (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e+126) || !(a <= 1.55e+73)) {
		tmp = y + x;
	} else {
		tmp = x - (y * (z / (a - t)));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2d+126)) .or. (.not. (a <= 1.55d+73))) then
        tmp = y + x
    else
        tmp = x - (y * (z / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2e+126) || !(a <= 1.55e+73)) {
		tmp = y + x;
	} else {
		tmp = x - (y * (z / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2e+126) or not (a <= 1.55e+73):
		tmp = y + x
	else:
		tmp = x - (y * (z / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2e+126) || !(a <= 1.55e+73))
		tmp = Float64(y + x);
	else
		tmp = Float64(x - Float64(y * Float64(z / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2e+126) || ~((a <= 1.55e+73)))
		tmp = y + x;
	else
		tmp = x - (y * (z / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2e+126], N[Not[LessEqual[a, 1.55e+73]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x - N[(y * N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.99999999999999985e126 or 1.55e73 < a

   1. Initial program 79.9%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 89.1

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

   5. Applied rewrites 89.1%

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

   if -1.99999999999999985e126 < a < 1.55e73

   1. Initial program 76.6%

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

   3. Taylor expanded in z around inf

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

      1. associate-/l* N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift--.f64 80.0

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 88.6%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{+126} \lor \neg \left(a \leq 1.55 \cdot 10^{+73}\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \frac{z}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-33} \lor \neg \left(a \leq 42\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.8e-33) (not (<= a 42.0))) (+ y x) (+ x (/ (* y z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-33) || !(a <= 42.0)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-2.8d-33)) .or. (.not. (a <= 42.0d0))) then
        tmp = y + x
    else
        tmp = x + ((y * z) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.8e-33) || !(a <= 42.0)) {
		tmp = y + x;
	} else {
		tmp = x + ((y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.8e-33) or not (a <= 42.0):
		tmp = y + x
	else:
		tmp = x + ((y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.8e-33) || !(a <= 42.0))
		tmp = Float64(y + x);
	else
		tmp = Float64(x + Float64(Float64(y * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.8e-33) || ~((a <= 42.0)))
		tmp = y + x;
	else
		tmp = x + ((y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.8e-33], N[Not[LessEqual[a, 42.0]], $MachinePrecision]], N[(y + x), $MachinePrecision], N[(x + N[(N[(y * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.8e-33 or 42 < a

   1. Initial program 78.2%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 79.7

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

   5. Applied rewrites 79.7%

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

   if -2.8e-33 < a < 42

   1. Initial program 77.6%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 81.7

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

   5. Applied rewrites 81.7%

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

   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. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower-*.f64 N/A

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

      5. lower--.f64 80.1

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

   8. Applied rewrites 80.1%

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

   9. Taylor expanded in z around inf

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

       1. lift-/.f64 N/A

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

       2. lift-*.f64 76.4

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

   11. Applied rewrites 76.4%

       \[\leadsto x + \frac{y \cdot z}{t} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.8 \cdot 10^{-33} \lor \neg \left(a \leq 42\right):\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.0% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5500000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-94}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= x -5500000000000.0) x (if (<= x 7.5e-94) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -5500000000000.0) {
		tmp = x;
	} else if (x <= 7.5e-94) {
		tmp = y;
	} 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 (x <= (-5500000000000.0d0)) then
        tmp = x
    else if (x <= 7.5d-94) then
        tmp = y
    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 (x <= -5500000000000.0) {
		tmp = x;
	} else if (x <= 7.5e-94) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if x <= -5500000000000.0:
		tmp = x
	elif x <= 7.5e-94:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -5500000000000.0)
		tmp = x;
	elseif (x <= 7.5e-94)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -5500000000000.0)
		tmp = x;
	elseif (x <= 7.5e-94)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[x, -5500000000000.0], x, If[LessEqual[x, 7.5e-94], y, x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e12 or 7.5000000000000003e-94 < x

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 74.8%

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

   if -5.5e12 < x < 7.5000000000000003e-94

   1. Initial program 71.4%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 65.4

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

   5. Applied rewrites 65.4%

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

   6. Taylor expanded in a around inf

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

   8. Applied rewrites 38.4%

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

Alternative 8: 61.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.85 \cdot 10^{+200}:\\ \;\;\;\;y + x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= t 1.85e+200) (+ y x) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.85e+200) {
		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 (t <= 1.85d+200) 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 (t <= 1.85e+200) {
		tmp = y + x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= 1.85e+200:
		tmp = y + x
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.85e+200)
		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 (t <= 1.85e+200)
		tmp = y + x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.85e+200], N[(y + x), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < 1.8500000000000001e200

   1. Initial program 81.0%

      \[\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \]
   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 68.4

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

   5. Applied rewrites 68.4%

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

   if 1.8500000000000001e200 < t

   1. Initial program 39.3%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 69.2%

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

Alternative 9: 49.7% 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 77.9%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 51.1%

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

Developer Target 1: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(y + x\right) - \left(\left(z - t\right) \cdot \frac{1}{a - t}\right) \cdot y\\ t_2 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_2 < -1.3664970889390727 \cdot 10^{-7}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 < 1.4754293444577233 \cdot 10^{-239}:\\ \;\;\;\;\frac{y \cdot \left(a - z\right) - x \cdot t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ y x) (* (* (- z t) (/ 1.0 (- a t))) y)))
        (t_2 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (< t_2 -1.3664970889390727e-7)
     t_1
     (if (< t_2 1.4754293444577233e-239)
       (/ (- (* y (- a z)) (* x t)) (- a t))
       t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y + x) - (((z - t) * (1.0d0 / (a - t))) * y)
    t_2 = (x + y) - (((z - t) * y) / (a - t))
    if (t_2 < (-1.3664970889390727d-7)) then
        tmp = t_1
    else if (t_2 < 1.4754293444577233d-239) then
        tmp = ((y * (a - z)) - (x * t)) / (a - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	double t_2 = (x + y) - (((z - t) * y) / (a - t));
	double tmp;
	if (t_2 < -1.3664970889390727e-7) {
		tmp = t_1;
	} else if (t_2 < 1.4754293444577233e-239) {
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y)
	t_2 = (x + y) - (((z - t) * y) / (a - t))
	tmp = 0
	if t_2 < -1.3664970889390727e-7:
		tmp = t_1
	elif t_2 < 1.4754293444577233e-239:
		tmp = ((y * (a - z)) - (x * t)) / (a - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y + x) - Float64(Float64(Float64(z - t) * Float64(1.0 / 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 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = Float64(Float64(Float64(y * Float64(a - z)) - Float64(x * t)) / Float64(a - t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y + x) - (((z - t) * (1.0 / (a - t))) * y);
	t_2 = (x + y) - (((z - t) * y) / (a - t));
	tmp = 0.0;
	if (t_2 < -1.3664970889390727e-7)
		tmp = t_1;
	elseif (t_2 < 1.4754293444577233e-239)
		tmp = ((y * (a - z)) - (x * t)) / (a - t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y + x), $MachinePrecision] - N[(N[(N[(z - t), $MachinePrecision] * N[(1.0 / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $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[Less[t$95$2, -1.3664970889390727e-7], t$95$1, If[Less[t$95$2, 1.4754293444577233e-239], N[(N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2025064 
(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))))