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

Percentage Accurate: 76.7% → 84.3%

Time: 7.1s

Alternatives: 10

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: 76.7% 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: 84.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{+291}:\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{elif}\;t\_1 \leq -1 \cdot 10^{-147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 -1e+291)
     (- (+ x y) (* y (/ z a)))
     (if (<= t_1 -1e-147)
       t_1
       (if (<= t_1 0.0)
         (- x (/ (* y (- a z)) t))
         (- (+ x y) (/ (* z 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+291) {
		tmp = (x + y) - (y * (z / a));
	} else if (t_1 <= -1e-147) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = (x + y) - ((z * 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+291)) then
        tmp = (x + y) - (y * (z / a))
    else if (t_1 <= (-1d-147)) then
        tmp = t_1
    else if (t_1 <= 0.0d0) then
        tmp = x - ((y * (a - z)) / t)
    else
        tmp = (x + y) - ((z * 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+291) {
		tmp = (x + y) - (y * (z / a));
	} else if (t_1 <= -1e-147) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = x - ((y * (a - z)) / t);
	} else {
		tmp = (x + y) - ((z * 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+291:
		tmp = (x + y) - (y * (z / a))
	elif t_1 <= -1e-147:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = x - ((y * (a - z)) / t)
	else:
		tmp = (x + y) - ((z * 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+291)
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	elseif (t_1 <= -1e-147)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	else
		tmp = Float64(Float64(x + y) - Float64(Float64(z * 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+291)
		tmp = (x + y) - (y * (z / a));
	elseif (t_1 <= -1e-147)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = x - ((y * (a - z)) / t);
	else
		tmp = (x + y) - ((z * 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+291], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-147], t$95$1, If[LessEqual[t$95$1, 0.0], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / N[(a - t), $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))) < -9.9999999999999996e290

   1. Initial program 37.8%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 49.8

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

   5. Applied rewrites 49.8%

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

   7. Applied rewrites 63.9%

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

   if -9.9999999999999996e290 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -9.9999999999999997e-148

   1. Initial program 97.9%

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

   if -9.9999999999999997e-148 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 15.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

      5. fp-cancel-sub-sign-inv N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. fp-cancel-sub-sign-inv N/A

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac N/A

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

      15. fp-cancel-sub-sign N/A

          \[\leadsto \color{blue}{x - \frac{y \cdot z - a \cdot y}{t} \cdot -1} \]

   5. Applied rewrites 99.8%

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

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

   1. Initial program 93.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 94.6

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

   5. Applied rewrites 94.6%

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

Alternative 2: 63.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-120}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t\_1 \leq 0:\\ \;\;\;\;x\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+306}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (<= t_1 -1e-120)
     (+ x y)
     (if (<= t_1 0.0) x (if (<= t_1 5e+306) (+ x y) (/ (* z y) 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-120) {
		tmp = x + y;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 5e+306) {
		tmp = x + y;
	} else {
		tmp = (z * y) / 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-120)) then
        tmp = x + y
    else if (t_1 <= 0.0d0) then
        tmp = x
    else if (t_1 <= 5d+306) then
        tmp = x + y
    else
        tmp = (z * y) / 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-120) {
		tmp = x + y;
	} else if (t_1 <= 0.0) {
		tmp = x;
	} else if (t_1 <= 5e+306) {
		tmp = x + y;
	} else {
		tmp = (z * y) / 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-120:
		tmp = x + y
	elif t_1 <= 0.0:
		tmp = x
	elif t_1 <= 5e+306:
		tmp = x + y
	else:
		tmp = (z * y) / 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-120)
		tmp = Float64(x + y);
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 5e+306)
		tmp = Float64(x + y);
	else
		tmp = Float64(Float64(z * y) / 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-120)
		tmp = x + y;
	elseif (t_1 <= 0.0)
		tmp = x;
	elseif (t_1 <= 5e+306)
		tmp = x + y;
	else
		tmp = (z * y) / 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-120], N[(x + y), $MachinePrecision], If[LessEqual[t$95$1, 0.0], x, If[LessEqual[t$95$1, 5e+306], N[(x + y), $MachinePrecision], N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -9.99999999999999979e-121 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 4.99999999999999993e306

   1. Initial program 91.4%

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

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 N/A

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

   5. Applied rewrites 81.5%

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

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 82.0%

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

   9. Taylor expanded in a around inf

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

       1. lower-+.f64 68.7

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

   11. Applied rewrites 68.7%

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

   if -9.99999999999999979e-121 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 32.2%

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

   3. Taylor expanded in a around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 25.4

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

   5. Applied rewrites 25.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 64.2%

      \[\leadsto x - \color{blue}{0} \]
   9. Step-by-step derivation

   10. Applied rewrites 64.2%

       \[\leadsto x \]

   if 4.99999999999999993e306 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 69.1%

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

   3. Taylor expanded in a around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 60.6

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

   5. Applied rewrites 60.6%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 49.3%

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

Alternative 3: 83.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-147} \lor \neg \left(t\_1 \leq 0\right):\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (+ x y) (/ (* (- z t) y) (- a t)))))
   (if (or (<= t_1 -1e-147) (not (<= t_1 0.0)))
     (- (+ x y) (/ (* z y) (- a t)))
     (- x (/ (* y (- a z)) 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-147) || !(t_1 <= 0.0)) {
		tmp = (x + y) - ((z * y) / (a - t));
	} else {
		tmp = x - ((y * (a - 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) :: t_1
    real(8) :: tmp
    t_1 = (x + y) - (((z - t) * y) / (a - t))
    if ((t_1 <= (-1d-147)) .or. (.not. (t_1 <= 0.0d0))) then
        tmp = (x + y) - ((z * y) / (a - t))
    else
        tmp = x - ((y * (a - z)) / 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-147) || !(t_1 <= 0.0)) {
		tmp = (x + y) - ((z * y) / (a - t));
	} else {
		tmp = x - ((y * (a - z)) / 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-147) or not (t_1 <= 0.0):
		tmp = (x + y) - ((z * y) / (a - t))
	else:
		tmp = x - ((y * (a - z)) / 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-147) || !(t_1 <= 0.0))
		tmp = Float64(Float64(x + y) - Float64(Float64(z * y) / Float64(a - t)));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / 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-147) || ~((t_1 <= 0.0)))
		tmp = (x + y) - ((z * y) / (a - t));
	else
		tmp = x - ((y * (a - z)) / 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[Or[LessEqual[t$95$1, -1e-147], N[Not[LessEqual[t$95$1, 0.0]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(N[(z * y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < -9.9999999999999997e-148 or 0.0 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

   1. Initial program 89.1%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 89.6

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

   5. Applied rewrites 89.6%

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

   if -9.9999999999999997e-148 < (-.f64 (+.f64 x y) (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))) < 0.0

   1. Initial program 15.9%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

      5. fp-cancel-sub-sign-inv N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. fp-cancel-sub-sign-inv N/A

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac N/A

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

      15. fp-cancel-sub-sign N/A

          \[\leadsto \color{blue}{x - \frac{y \cdot z - a \cdot y}{t} \cdot -1} \]

   5. Applied rewrites 99.8%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq -1 \cdot 10^{-147} \lor \neg \left(\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t} \leq 0\right):\\ \;\;\;\;\left(x + y\right) - \frac{z \cdot y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+123} \lor \neg \left(t \leq 2 \cdot 10^{+155}\right):\\ \;\;\;\;\left(x + \frac{z \cdot y}{t}\right) - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1e+123) (not (<= t 2e+155)))
   (- (+ x (/ (* z y) t)) (* a (/ y t)))
   (- (+ x y) (/ (* (- z t) y) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1e+123) || !(t <= 2e+155)) {
		tmp = (x + ((z * y) / t)) - (a * (y / t));
	} 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 ((t <= (-1d+123)) .or. (.not. (t <= 2d+155))) then
        tmp = (x + ((z * y) / t)) - (a * (y / t))
    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 ((t <= -1e+123) || !(t <= 2e+155)) {
		tmp = (x + ((z * y) / t)) - (a * (y / t));
	} else {
		tmp = (x + y) - (((z - t) * y) / (a - t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -1e+123) or not (t <= 2e+155):
		tmp = (x + ((z * y) / t)) - (a * (y / t))
	else:
		tmp = (x + y) - (((z - t) * y) / (a - t))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1e+123) || !(t <= 2e+155))
		tmp = Float64(Float64(x + Float64(Float64(z * y) / t)) - Float64(a * Float64(y / t)));
	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 ((t <= -1e+123) || ~((t <= 2e+155)))
		tmp = (x + ((z * y) / t)) - (a * (y / t));
	else
		tmp = (x + y) - (((z - t) * y) / (a - t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1e+123], N[Not[LessEqual[t, 2e+155]], $MachinePrecision]], N[(N[(x + N[(N[(z * y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] - N[(a * N[(y / t), $MachinePrecision]), $MachinePrecision]), $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 t < -9.99999999999999978e122 or 2.00000000000000001e155 < t

   1. Initial program 58.6%

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

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 N/A

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

   5. Applied rewrites 61.8%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 91.5%

      \[\leadsto \left(\left(x - 0\right) + \frac{z \cdot y}{t}\right) - \color{blue}{a \cdot \frac{y}{t}} \]

   if -9.99999999999999978e122 < t < 2.00000000000000001e155

   1. Initial program 91.9%

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

4. Final simplification 91.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{+123} \lor \neg \left(t \leq 2 \cdot 10^{+155}\right):\\ \;\;\;\;\left(x + \frac{z \cdot y}{t}\right) - a \cdot \frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) - \frac{\left(z - t\right) \cdot y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-42} \lor \neg \left(a \leq 1.35 \cdot 10^{-51}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.5e-42) (not (<= a 1.35e-51)))
   (- (+ x y) (* y (/ z a)))
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.5e-42) || !(a <= 1.35e-51)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - ((y * (a - 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 <= (-8.5d-42)) .or. (.not. (a <= 1.35d-51))) then
        tmp = (x + y) - (y * (z / a))
    else
        tmp = x - ((y * (a - 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 <= -8.5e-42) || !(a <= 1.35e-51)) {
		tmp = (x + y) - (y * (z / a));
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.5e-42) or not (a <= 1.35e-51):
		tmp = (x + y) - (y * (z / a))
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.5e-42) || !(a <= 1.35e-51))
		tmp = Float64(Float64(x + y) - Float64(y * Float64(z / a)));
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.5e-42) || ~((a <= 1.35e-51)))
		tmp = (x + y) - (y * (z / a));
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.5e-42], N[Not[LessEqual[a, 1.35e-51]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] - N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.4999999999999996e-42 or 1.3499999999999999e-51 < a

   1. Initial program 87.3%

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

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

      2. *-commutative N/A

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

      3. lower-*.f64 85.9

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

   5. Applied rewrites 85.9%

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

   7. Applied rewrites 88.9%

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

   if -8.4999999999999996e-42 < a < 1.3499999999999999e-51

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

      5. fp-cancel-sub-sign-inv N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. fp-cancel-sub-sign-inv N/A

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac N/A

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

      15. fp-cancel-sub-sign N/A

          \[\leadsto \color{blue}{x - \frac{y \cdot z - a \cdot y}{t} \cdot -1} \]

   5. Applied rewrites 83.4%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.5 \cdot 10^{-42} \lor \neg \left(a \leq 1.35 \cdot 10^{-51}\right):\\ \;\;\;\;\left(x + y\right) - y \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-5} \lor \neg \left(a \leq 7.8 \cdot 10^{-42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -2.05e-5) (not (<= a 7.8e-42)))
   (+ x y)
   (- x (/ (* y (- a z)) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -2.05e-5) || !(a <= 7.8e-42)) {
		tmp = x + y;
	} else {
		tmp = x - ((y * (a - 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 <= (-2.05d-5)) .or. (.not. (a <= 7.8d-42))) then
        tmp = x + y
    else
        tmp = x - ((y * (a - 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 <= -2.05e-5) || !(a <= 7.8e-42)) {
		tmp = x + y;
	} else {
		tmp = x - ((y * (a - z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -2.05e-5) or not (a <= 7.8e-42):
		tmp = x + y
	else:
		tmp = x - ((y * (a - z)) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -2.05e-5) || !(a <= 7.8e-42))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(Float64(y * Float64(a - z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -2.05e-5) || ~((a <= 7.8e-42)))
		tmp = x + y;
	else
		tmp = x - ((y * (a - z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -2.05e-5], N[Not[LessEqual[a, 7.8e-42]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(N[(y * N[(a - z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.05000000000000002e-5 or 7.8000000000000003e-42 < a

   1. Initial program 87.1%

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

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 N/A

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 84.4%

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

   9. Taylor expanded in a around inf

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

       1. lower-+.f64 76.6

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

   11. Applied rewrites 76.6%

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

   if -2.05000000000000002e-5 < a < 7.8000000000000003e-42

   1. Initial program 79.5%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

      5. fp-cancel-sub-sign-inv N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. fp-cancel-sub-sign-inv N/A

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac N/A

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

      15. fp-cancel-sub-sign N/A

          \[\leadsto \color{blue}{x - \frac{y \cdot z - a \cdot y}{t} \cdot -1} \]

   5. Applied rewrites 80.7%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.05 \cdot 10^{-5} \lor \neg \left(a \leq 7.8 \cdot 10^{-42}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(a - z\right)}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-8} \lor \neg \left(a \leq 3.4 \cdot 10^{-97}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(-y\right) \cdot z}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.8e-8) (not (<= a 3.4e-97))) (+ x y) (- x (/ (* (- y) z) t))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.8e-8) || !(a <= 3.4e-97)) {
		tmp = x + y;
	} 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 <= (-8.8d-8)) .or. (.not. (a <= 3.4d-97))) then
        tmp = x + y
    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 <= -8.8e-8) || !(a <= 3.4e-97)) {
		tmp = x + y;
	} else {
		tmp = x - ((-y * z) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -8.8e-8) or not (a <= 3.4e-97):
		tmp = x + y
	else:
		tmp = x - ((-y * z) / t)
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.8e-8) || !(a <= 3.4e-97))
		tmp = Float64(x + y);
	else
		tmp = Float64(x - Float64(Float64(Float64(-y) * z) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -8.8e-8) || ~((a <= 3.4e-97)))
		tmp = x + y;
	else
		tmp = x - ((-y * z) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.8e-8], N[Not[LessEqual[a, 3.4e-97]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x - N[(N[((-y) * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.7999999999999994e-8 or 3.3999999999999999e-97 < a

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 N/A

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

   5. Applied rewrites 80.5%

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

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 84.7%

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

   9. Taylor expanded in a around inf

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

       1. lower-+.f64 76.4

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

   11. Applied rewrites 76.4%

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

   if -8.7999999999999994e-8 < a < 3.3999999999999999e-97

   1. Initial program 79.8%

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

   3. Taylor expanded in t around inf

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

      1. associate--l+ N/A

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

      2. distribute-lft-out-- N/A

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

      3. div-sub N/A

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

      4. *-commutative N/A

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

      5. fp-cancel-sub-sign-inv N/A

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

      6. mul-1-neg N/A

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

      7. associate-*r* N/A

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

      8. +-commutative N/A

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

      9. *-lft-identity N/A

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

      10. metadata-eval N/A

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

      11. fp-cancel-sub-sign-inv N/A

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

      12. distribute-lft-out-- N/A

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

      13. mul-1-neg N/A

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

      14. distribute-neg-frac N/A

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

      15. fp-cancel-sub-sign N/A

          \[\leadsto \color{blue}{x - \frac{y \cdot z - a \cdot y}{t} \cdot -1} \]

   5. Applied rewrites 81.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 76.1%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-8} \lor \neg \left(a \leq 3.4 \cdot 10^{-97}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\left(-y\right) \cdot z}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-8} \lor \neg \left(a \leq 3.4 \cdot 10^{-97}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -8.8e-8) (not (<= a 3.4e-97))) (+ x y) (fma y (/ z t) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -8.8e-8) || !(a <= 3.4e-97)) {
		tmp = x + y;
	} else {
		tmp = fma(y, (z / t), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -8.8e-8) || !(a <= 3.4e-97))
		tmp = Float64(x + y);
	else
		tmp = fma(y, Float64(z / t), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -8.8e-8], N[Not[LessEqual[a, 3.4e-97]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(y * N[(z / t), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.7999999999999994e-8 or 3.3999999999999999e-97 < a

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 N/A

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

   5. Applied rewrites 80.5%

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

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 84.7%

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

   9. Taylor expanded in a around inf

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

       1. lower-+.f64 76.4

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

   11. Applied rewrites 76.4%

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

   if -8.7999999999999994e-8 < a < 3.3999999999999999e-97

   1. Initial program 79.8%

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

   3. Taylor expanded in a around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 63.4

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 73.7%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{\frac{z}{t}}, x\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8.8 \cdot 10^{-8} \lor \neg \left(a \leq 3.4 \cdot 10^{-97}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{z}{t}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-29} \lor \neg \left(a \leq 3.5 \cdot 10^{-40}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -1.6e-29) (not (<= a 3.5e-40))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -1.6e-29) || !(a <= 3.5e-40)) {
		tmp = x + 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 ((a <= (-1.6d-29)) .or. (.not. (a <= 3.5d-40))) then
        tmp = x + 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 ((a <= -1.6e-29) || !(a <= 3.5e-40)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -1.6e-29) or not (a <= 3.5e-40):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -1.6e-29) || !(a <= 3.5e-40))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -1.6e-29) || ~((a <= 3.5e-40)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -1.6e-29], N[Not[LessEqual[a, 3.5e-40]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if a < -1.6e-29 or 3.5000000000000002e-40 < a

   1. Initial program 87.5%

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

   3. Taylor expanded in x around inf

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

      1. associate--l+ N/A

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

      2. +-commutative N/A

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

      3. distribute-rgt-in N/A

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

      4. *-lft-identity N/A

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

      5. lower-fma.f64 N/A

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

   5. Applied rewrites 80.8%

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

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 84.3%

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

   9. Taylor expanded in a around inf

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

       1. lower-+.f64 74.8

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

   11. Applied rewrites 74.8%

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

   if -1.6e-29 < a < 3.5000000000000002e-40

   1. Initial program 78.6%

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

   3. Taylor expanded in a around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. *-lft-identity N/A

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

      5. associate-/l* N/A

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

      6. *-commutative N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-/.f64 N/A

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

      9. lower--.f64 N/A

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

      10. +-commutative N/A

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

      11. lower-+.f64 62.7

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

   5. Applied rewrites 62.7%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 46.7%

      \[\leadsto x - \color{blue}{0} \]
   9. Step-by-step derivation

   10. Applied rewrites 46.7%

       \[\leadsto x \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{-29} \lor \neg \left(a \leq 3.5 \cdot 10^{-40}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.9% 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 83.7%

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

3. Taylor expanded in a around 0

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

   1. fp-cancel-sub-sign-inv N/A

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

   2. +-commutative N/A

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

   3. metadata-eval N/A

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

   4. *-lft-identity N/A

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

   5. associate-/l* N/A

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

   6. *-commutative N/A

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

   7. lower-fma.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. lower--.f64 N/A

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

   10. +-commutative N/A

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

   11. lower-+.f64 51.4

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

5. Applied rewrites 51.4%

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

6. Taylor expanded in z around 0

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

8. Applied rewrites 49.2%

   \[\leadsto x - \color{blue}{0} \]
9. Step-by-step derivation

10. Applied rewrites 49.2%

    \[\leadsto x \]
11. Add Preprocessing

Developer Target 1: 87.8% 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 2024364 
(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))))