Data.Colour.Matrix:inverse from colour-2.3.3, B

Percentage Accurate: 92.0% → 97.4%

Time: 3.7s

Alternatives: 7

Speedup: 0.5×

• 28.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 92.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot y - z \cdot t}{a} \end{array} \]

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, \left(-t\right) \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{+273}:\\ \;\;\;\;\frac{t\_1}{a}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y, \left(-z\right) \cdot \frac{t}{a}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (<= t_1 (- INFINITY))
     (fma (/ y a) x (* (- t) (/ z a)))
     (if (<= t_1 1e+273) (/ t_1 a) (fma (/ x a) y (* (- z) (/ t a)))))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = fma((y / a), x, (-t * (z / a)));
	} else if (t_1 <= 1e+273) {
		tmp = t_1 / a;
	} else {
		tmp = fma((x / a), y, (-z * (t / a)));
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = fma(Float64(y / a), x, Float64(Float64(-t) * Float64(z / a)));
	elseif (t_1 <= 1e+273)
		tmp = Float64(t_1 / a);
	else
		tmp = fma(Float64(x / a), y, Float64(Float64(-z) * Float64(t / a)));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(y / a), $MachinePrecision] * x + N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e+273], N[(t$95$1 / a), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y + N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0

   1. Initial program 66.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. *-commutative N/A

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

      12. associate-*l/ N/A

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

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

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

      14. *-commutative N/A

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

      15. mul-1-neg N/A

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

      16. associate-*r/ N/A

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

      17. lower-fma.f64 N/A

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

      18. lower-/.f64 N/A

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

      19. associate-*l/ N/A

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

      20. associate-*l* N/A

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

      21. *-commutative N/A

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

      22. associate-*r* N/A

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

      23. *-commutative N/A

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

   4. Applied rewrites 93.3%

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

      1. lift-neg.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. distribute-lft-neg-out N/A

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

      5. associate-*r/ N/A

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

      6. *-commutative N/A

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

      7. associate-/l* N/A

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

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

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

      9. mul-1-neg N/A

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

      10. lower-*.f64 N/A

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

      11. mul-1-neg N/A

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

      12. lift-neg.f64 N/A

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

      13. lower-/.f64 96.6

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

   6. Applied rewrites 96.6%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 9.99999999999999945e272

   1. Initial program 98.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 9.99999999999999945e272 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 73.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. associate-*l/ N/A

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

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

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r/ N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 96.8%

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

Alternative 2: 97.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 10^{+273}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y, \left(-z\right) \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* x y) (* z t))))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 1e+273)))
     (fma (/ x a) y (* (- z) (/ t a)))
     (/ t_1 a))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double t_1 = (x * y) - (z * t);
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 1e+273)) {
		tmp = fma((x / a), y, (-z * (t / a)));
	} else {
		tmp = t_1 / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(x * y) - Float64(z * t))
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 1e+273))
		tmp = fma(Float64(x / a), y, Float64(Float64(-z) * Float64(t / a)));
	else
		tmp = Float64(t_1 / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 1e+273]], $MachinePrecision]], N[(N[(x / a), $MachinePrecision] * y + N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 9.99999999999999945e272 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 70.1%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. associate-*l/ N/A

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

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

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r/ N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 95.2%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 9.99999999999999945e272

   1. Initial program 98.6%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 10^{+273}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{a}, y, \left(-z\right) \cdot \frac{t}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+186}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* x y) (- INFINITY))
   (* (/ x a) y)
   (if (<= (* x y) 2e+186) (/ (- (* x y) (* z t)) a) (* (/ y a) x))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -((double) INFINITY)) {
		tmp = (x / a) * y;
	} else if ((x * y) <= 2e+186) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (y / a) * x;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x * y) <= -Double.POSITIVE_INFINITY) {
		tmp = (x / a) * y;
	} else if ((x * y) <= 2e+186) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = (y / a) * x;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (x * y) <= -math.inf:
		tmp = (x / a) * y
	elif (x * y) <= 2e+186:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = (y / a) * x
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x * y) <= Float64(-Inf))
		tmp = Float64(Float64(x / a) * y);
	elseif (Float64(x * y) <= 2e+186)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = Float64(Float64(y / a) * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((x * y) <= -Inf)
		tmp = (x / a) * y;
	elseif ((x * y) <= 2e+186)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = (y / a) * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x * y), $MachinePrecision], (-Infinity)], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+186], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 x y) < -inf.0

   1. Initial program 58.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. associate-*l/ N/A

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

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

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r/ N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 88.8%

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

   5. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. associate-*r/ N/A

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

      3. distribute-lft-neg-out N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. associate-*l/ N/A

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

      12. lower-*.f64 N/A

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

      13. lift-/.f64 99.1

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

   7. Applied rewrites 99.1%

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

   if -inf.0 < (*.f64 x y) < 1.99999999999999996e186

   1. Initial program 96.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   if 1.99999999999999996e186 < (*.f64 x y)

   1. Initial program 68.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. associate-*l/ N/A

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

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

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r/ N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 94.4%

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

   5. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. associate-*r/ N/A

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

      3. distribute-lft-neg-out N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. associate-*l/ N/A

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

      12. lower-*.f64 N/A

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

      13. lift-/.f64 94.4

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

   7. Applied rewrites 94.4%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-/.f64 94.2

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

   9. Applied rewrites 94.2%

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

Alternative 4: 73.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+52} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (or (<= (* z t) -4e+52) (not (<= (* z t) 5e+40)))
   (* (/ (- z) a) t)
   (* (/ x a) y)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * t) <= -4e+52) || !((z * t) <= 5e+40)) {
		tmp = (-z / a) * t;
	} else {
		tmp = (x / a) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (((z * t) <= (-4d+52)) .or. (.not. ((z * t) <= 5d+40))) then
        tmp = (-z / a) * t
    else
        tmp = (x / a) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (((z * t) <= -4e+52) || !((z * t) <= 5e+40)) {
		tmp = (-z / a) * t;
	} else {
		tmp = (x / a) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((z * t) <= -4e+52) or not ((z * t) <= 5e+40):
		tmp = (-z / a) * t
	else:
		tmp = (x / a) * y
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if ((Float64(z * t) <= -4e+52) || !(Float64(z * t) <= 5e+40))
		tmp = Float64(Float64(Float64(-z) / a) * t);
	else
		tmp = Float64(Float64(x / a) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (((z * t) <= -4e+52) || ~(((z * t) <= 5e+40)))
		tmp = (-z / a) * t;
	else
		tmp = (x / a) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[N[(z * t), $MachinePrecision], -4e+52], N[Not[LessEqual[N[(z * t), $MachinePrecision], 5e+40]], $MachinePrecision]], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4e52 or 5.00000000000000003e40 < (*.f64 z t)

   1. Initial program 90.8%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. associate-*l/ N/A

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

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

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r/ N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 96.9%

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

   5. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*r/ N/A

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

      3. distribute-lft-neg-out N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

   7. Applied rewrites 87.7%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-frac-neg N/A

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

      3. lift-/.f64 N/A

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

      4. lift-neg.f64 84.8

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

   10. Applied rewrites 84.8%

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

   if -4e52 < (*.f64 z t) < 5.00000000000000003e40

   1. Initial program 92.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. associate-*l/ N/A

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

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

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r/ N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 84.4%

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

   5. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. associate-*r/ N/A

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

      3. distribute-lft-neg-out N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. associate-*l/ N/A

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

      12. lower-*.f64 N/A

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

      13. lift-/.f64 70.7

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

   7. Applied rewrites 70.7%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+52} \lor \neg \left(z \cdot t \leq 5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 73.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+52}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{elif}\;z \cdot t \leq 5 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= (* z t) -4e+52)
   (* (- z) (/ t a))
   (if (<= (* z t) 5e+40) (* (/ x a) y) (* (/ (- z) a) t))))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -4e+52) {
		tmp = -z * (t / a);
	} else if ((z * t) <= 5e+40) {
		tmp = (x / a) * y;
	} else {
		tmp = (-z / a) * t;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z * t) <= (-4d+52)) then
        tmp = -z * (t / a)
    else if ((z * t) <= 5d+40) then
        tmp = (x / a) * y
    else
        tmp = (-z / a) * t
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z * t) <= -4e+52) {
		tmp = -z * (t / a);
	} else if ((z * t) <= 5e+40) {
		tmp = (x / a) * y;
	} else {
		tmp = (-z / a) * t;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -4e+52:
		tmp = -z * (t / a)
	elif (z * t) <= 5e+40:
		tmp = (x / a) * y
	else:
		tmp = (-z / a) * t
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(z * t) <= -4e+52)
		tmp = Float64(Float64(-z) * Float64(t / a));
	elseif (Float64(z * t) <= 5e+40)
		tmp = Float64(Float64(x / a) * y);
	else
		tmp = Float64(Float64(Float64(-z) / a) * t);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z * t) <= -4e+52)
		tmp = -z * (t / a);
	elseif ((z * t) <= 5e+40)
		tmp = (x / a) * y;
	else
		tmp = (-z / a) * t;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[N[(z * t), $MachinePrecision], -4e+52], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 5e+40], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4e52

   1. Initial program 91.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

      1. associate-*l/ N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

      4. associate-*r* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. mul-1-neg N/A

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

      8. lower-neg.f64 N/A

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

      9. lower-/.f64 89.8

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

   5. Applied rewrites 89.8%

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

   if -4e52 < (*.f64 z t) < 5.00000000000000003e40

   1. Initial program 92.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. associate-*l/ N/A

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

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

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r/ N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 84.4%

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

   5. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. associate-*r/ N/A

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

      3. distribute-lft-neg-out N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. associate-*l/ N/A

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

      12. lower-*.f64 N/A

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

      13. lift-/.f64 70.7

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

   7. Applied rewrites 70.7%

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

   if 5.00000000000000003e40 < (*.f64 z t)

   1. Initial program 90.3%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. associate-*l/ N/A

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

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

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r/ N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 99.8%

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

   5. Taylor expanded in t around inf

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

      1. associate-*l/ N/A

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

      2. associate-*r/ N/A

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

      3. distribute-lft-neg-out N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. *-commutative N/A

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

      12. lower-*.f64 N/A

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

   7. Applied rewrites 91.8%

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

   8. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. distribute-frac-neg N/A

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

      3. lift-/.f64 N/A

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

      4. lift-neg.f64 88.5

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

   10. Applied rewrites 88.5%

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

Alternative 6: 52.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.38 \cdot 10^{-232}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a)
 :precision binary64
 (if (<= x -1.38e-232) (* (/ x a) y) (* (/ y a) x)))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.38e-232) {
		tmp = (x / a) * y;
	} else {
		tmp = (y / a) * x;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (x <= (-1.38d-232)) then
        tmp = (x / a) * y
    else
        tmp = (y / a) * x
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (x <= -1.38e-232) {
		tmp = (x / a) * y;
	} else {
		tmp = (y / a) * x;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if x <= -1.38e-232:
		tmp = (x / a) * y
	else:
		tmp = (y / a) * x
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	tmp = 0.0
	if (x <= -1.38e-232)
		tmp = Float64(Float64(x / a) * y);
	else
		tmp = Float64(Float64(y / a) * x);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (x <= -1.38e-232)
		tmp = (x / a) * y;
	else
		tmp = (y / a) * x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := If[LessEqual[x, -1.38e-232], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision], N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3799999999999999e-232

   1. Initial program 91.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. associate-*l/ N/A

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

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

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r/ N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 89.5%

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

   5. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. associate-*r/ N/A

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

      3. distribute-lft-neg-out N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. associate-*l/ N/A

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

      12. lower-*.f64 N/A

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

      13. lift-/.f64 59.5

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

   7. Applied rewrites 59.5%

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

   if -1.3799999999999999e-232 < x

   1. Initial program 91.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-*.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. frac-2neg N/A

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

      6. *-commutative N/A

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

      7. frac-2neg N/A

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

      8. *-commutative N/A

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

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

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

      10. div-add N/A

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

      11. associate-*l/ N/A

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

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

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

      13. *-commutative N/A

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

      14. mul-1-neg N/A

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

      15. associate-*r/ N/A

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

      16. lower-fma.f64 N/A

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

      17. lower-/.f64 N/A

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

      18. associate-*l/ N/A

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

      19. associate-*l* N/A

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

      20. *-commutative N/A

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

      21. associate-*r* N/A

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

      22. *-commutative N/A

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

      23. lower-*.f64 N/A

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

   4. Applied rewrites 89.6%

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

   5. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. associate-*r/ N/A

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

      3. distribute-lft-neg-out N/A

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

      4. *-commutative N/A

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

      5. mul-1-neg N/A

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

      6. div-add-rev N/A

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

      7. mul-1-neg N/A

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

      8. *-commutative N/A

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

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

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

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

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

      11. associate-*l/ N/A

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

      12. lower-*.f64 N/A

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

      13. lift-/.f64 44.7

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

   7. Applied rewrites 44.7%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. associate-*l/ N/A

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

      4. associate-/l* N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-/.f64 43.7

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

   9. Applied rewrites 43.7%

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

Alternative 7: 52.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \frac{x}{a} \cdot y \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
(FPCore (x y z t a) :precision binary64 (* (/ x a) y))

C

assert(x < y && y < z && z < t && t < a);
double code(double x, double y, double z, double t, double a) {
	return (x / a) * y;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 / a) * y
end function

Java

assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	return (x / a) * y;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	return (x / a) * y

Julia

x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	return Float64(Float64(x / a) * y)
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp = code(x, y, z, t, a)
	tmp = (x / a) * y;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_] := N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]

Derivation

1. Initial program 91.6%

   \[\frac{x \cdot y - z \cdot t}{a} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift--.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. lift-*.f64 N/A

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

   5. frac-2neg N/A

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

   6. *-commutative N/A

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

   7. frac-2neg N/A

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

   8. *-commutative N/A

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

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

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

   10. div-add N/A

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

   11. associate-*l/ N/A

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

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

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

   13. *-commutative N/A

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

   14. mul-1-neg N/A

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

   15. associate-*r/ N/A

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

   16. lower-fma.f64 N/A

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

   17. lower-/.f64 N/A

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

   18. associate-*l/ N/A

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

   19. associate-*l* N/A

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

   20. *-commutative N/A

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

   21. associate-*r* N/A

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

   22. *-commutative N/A

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

   23. lower-*.f64 N/A

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

4. Applied rewrites 89.5%

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

5. Taylor expanded in x around inf

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

   1. associate-*l/ N/A

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

   2. associate-*r/ N/A

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

   3. distribute-lft-neg-out N/A

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

   4. *-commutative N/A

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

   5. mul-1-neg N/A

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

   6. div-add-rev N/A

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

   7. mul-1-neg N/A

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

   8. *-commutative N/A

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

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

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

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

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

   11. associate-*l/ N/A

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

   12. lower-*.f64 N/A

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

   13. lift-/.f64 51.4

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

7. Applied rewrites 51.4%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
8. Add Preprocessing

Developer Target 1: 92.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a} \cdot x - \frac{t}{a} \cdot z\\ \mathbf{if}\;z < -2.468684968699548 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z < 6.309831121978371 \cdot 10^{-71}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- (* (/ y a) x) (* (/ t a) z))))
   (if (< z -2.468684968699548e+170)
     t_1
     (if (< z 6.309831121978371e-71) (/ (- (* x y) (* z t)) a) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a)
use fmin_fmax_functions
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y / a) * x) - ((t / a) * z)
    if (z < (-2.468684968699548d+170)) then
        tmp = t_1
    else if (z < 6.309831121978371d-71) then
        tmp = ((x * y) - (z * t)) / a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((y / a) * x) - ((t / a) * z);
	double tmp;
	if (z < -2.468684968699548e+170) {
		tmp = t_1;
	} else if (z < 6.309831121978371e-71) {
		tmp = ((x * y) - (z * t)) / a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = ((y / a) * x) - ((t / a) * z)
	tmp = 0
	if z < -2.468684968699548e+170:
		tmp = t_1
	elif z < 6.309831121978371e-71:
		tmp = ((x * y) - (z * t)) / a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(y / a) * x) - Float64(Float64(t / a) * z))
	tmp = 0.0
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = ((y / a) * x) - ((t / a) * z);
	tmp = 0.0;
	if (z < -2.468684968699548e+170)
		tmp = t_1;
	elseif (z < 6.309831121978371e-71)
		tmp = ((x * y) - (z * t)) / a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision] - N[(N[(t / a), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.468684968699548e+170], t$95$1, If[Less[z, 6.309831121978371e-71], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2025028 
(FPCore (x y z t a)
  :name "Data.Colour.Matrix:inverse from colour-2.3.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -246868496869954800000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (/ y a) x) (* (/ t a) z)) (if (< z 6309831121978371/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (/ (- (* x y) (* z t)) a) (- (* (/ y a) x) (* (/ t a) z)))))

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