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

Percentage Accurate: 91.7% → 97.2%

Time: 6.3s

Alternatives: 9

Speedup: 0.5×

• 28.6% 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: 91.7% 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: 97.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+250}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, x, \left(-t\right) \cdot \frac{z}{a}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+294}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-z\right) \cdot t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - \frac{t}{x} \cdot z}{a} \cdot x\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 -5e+250)
     (fma (/ y a) x (* (- t) (/ z a)))
     (if (<= t_1 5e+294)
       (/ (fma y x (* (- z) t)) a)
       (* (/ (- y (* (/ t x) z)) a) x)))))

C

assert(x < y && y < z && z < t && t < a);
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 <= -5e+250) {
		tmp = fma((y / a), x, (-t * (z / a)));
	} else if (t_1 <= 5e+294) {
		tmp = fma(y, x, (-z * t)) / a;
	} else {
		tmp = ((y - ((t / x) * z)) / a) * x;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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 <= -5e+250)
		tmp = fma(Float64(y / a), x, Float64(Float64(-t) * Float64(z / a)));
	elseif (t_1 <= 5e+294)
		tmp = Float64(fma(y, x, Float64(Float64(-z) * t)) / a);
	else
		tmp = Float64(Float64(Float64(y - Float64(Float64(t / x) * z)) / a) * x);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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, -5e+250], N[(N[(y / a), $MachinePrecision] * x + N[((-t) * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+294], N[(N[(y * x + N[((-z) * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision], N[(N[(N[(y - N[(N[(t / x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -5.0000000000000002e250

   1. Initial program 76.4%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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. div-sub N/A

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. associate-/l* N/A

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

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

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

      8. lift-*.f64 N/A

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

      9. associate-/l* N/A

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

      10. *-commutative N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-*.f64 N/A

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

      14. lower-neg.f64 N/A

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

      15. lower-/.f64 89.9

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

   4. Applied rewrites 89.9%

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

   if -5.0000000000000002e250 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999999e294

   1. Initial program 99.5%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 99.6

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

   4. Applied rewrites 99.6%

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

   if 4.9999999999999999e294 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 63.9%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 85.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 94.4

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

   10. Applied rewrites 94.4%

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

Alternative 2: 54.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := \frac{x \cdot y - z \cdot t}{a}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{+294}:\\ \;\;\;\;\frac{y}{a} \cdot x\\ \mathbf{elif}\;t\_1 \leq 10^{+242}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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)) a)))
   (if (<= t_1 -2e+294)
     (* (/ y a) x)
     (if (<= t_1 1e+242) (/ (* y x) a) (* (/ x a) y)))))

C

assert(x < y && y < z && z < t && t < a);
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)) / a;
	double tmp;
	if (t_1 <= -2e+294) {
		tmp = (y / a) * x;
	} else if (t_1 <= 1e+242) {
		tmp = (y * x) / a;
	} 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.
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) :: t_1
    real(8) :: tmp
    t_1 = ((x * y) - (z * t)) / a
    if (t_1 <= (-2d+294)) then
        tmp = (y / a) * x
    else if (t_1 <= 1d+242) then
        tmp = (y * x) / a
    else
        tmp = (x / a) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
assert x < y && y < z && z < t && t < a;
public static double code(double x, double y, double z, double t, double a) {
	double t_1 = ((x * y) - (z * t)) / a;
	double tmp;
	if (t_1 <= -2e+294) {
		tmp = (y / a) * x;
	} else if (t_1 <= 1e+242) {
		tmp = (y * x) / a;
	} else {
		tmp = (x / a) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	t_1 = ((x * y) - (z * t)) / a
	tmp = 0
	if t_1 <= -2e+294:
		tmp = (y / a) * x
	elif t_1 <= 1e+242:
		tmp = (y * x) / a
	else:
		tmp = (x / a) * y
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
x, y, z, t, a = sort([x, y, z, t, a])
function code(x, y, z, t, a)
	t_1 = Float64(Float64(Float64(x * y) - Float64(z * t)) / a)
	tmp = 0.0
	if (t_1 <= -2e+294)
		tmp = Float64(Float64(y / a) * x);
	elseif (t_1 <= 1e+242)
		tmp = Float64(Float64(y * x) / a);
	else
		tmp = Float64(Float64(x / a) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
function tmp_2 = code(x, y, z, t, a)
	t_1 = ((x * y) - (z * t)) / a;
	tmp = 0.0;
	if (t_1 <= -2e+294)
		tmp = (y / a) * x;
	elseif (t_1 <= 1e+242)
		tmp = (y * x) / a;
	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.
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[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]}, If[LessEqual[t$95$1, -2e+294], N[(N[(y / a), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[t$95$1, 1e+242], N[(N[(y * x), $MachinePrecision] / a), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < -2.00000000000000013e294

   1. Initial program 82.0%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 55.9

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

   5. Applied rewrites 55.9%

      \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
   6. 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. *-commutative N/A

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

      5. associate-*l/ N/A

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

      6. lift-/.f64 N/A

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

      7. lower-*.f64 55.8

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

   7. Applied rewrites 55.8%

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

   if -2.00000000000000013e294 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a) < 1.00000000000000005e242

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 53.9

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

   5. Applied rewrites 53.9%

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

   if 1.00000000000000005e242 < (/.f64 (-.f64 (*.f64 x y) (*.f64 z t)) a)

   1. Initial program 80.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 62.9

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

   5. Applied rewrites 62.9%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y - z \cdot t}{a} \leq -2 \cdot 10^{+294}:\\ \;\;\;\;\frac{y}{a} \cdot x\\ \mathbf{elif}\;\frac{x \cdot y - z \cdot t}{a} \leq 10^{+242}:\\ \;\;\;\;\frac{y \cdot x}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 96.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} t_1 := x \cdot y - z \cdot t\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+294}\right):\\ \;\;\;\;\frac{y - \frac{t}{x} \cdot z}{a} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-z\right) \cdot t\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 5e+294)))
     (* (/ (- y (* (/ t x) z)) a) x)
     (/ (fma y x (* (- z) t)) a))))

C

assert(x < y && y < z && z < t && t < a);
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 <= 5e+294)) {
		tmp = ((y - ((t / x) * z)) / a) * x;
	} else {
		tmp = fma(y, x, (-z * t)) / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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 <= 5e+294))
		tmp = Float64(Float64(Float64(y - Float64(Float64(t / x) * z)) / a) * x);
	else
		tmp = Float64(fma(y, x, Float64(Float64(-z) * t)) / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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, 5e+294]], $MachinePrecision]], N[(N[(N[(y - N[(N[(t / x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision] * x), $MachinePrecision], N[(N[(y * x + N[((-z) * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 x y) (*.f64 z t)) < -inf.0 or 4.9999999999999999e294 < (-.f64 (*.f64 x y) (*.f64 z t))

   1. Initial program 66.5%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 65.0%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 86.1%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 92.3

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

   10. Applied rewrites 92.3%

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

   if -inf.0 < (-.f64 (*.f64 x y) (*.f64 z t)) < 4.9999999999999999e294

   1. Initial program 99.6%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 99.6

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

   4. Applied rewrites 99.6%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - z \cdot t \leq -\infty \lor \neg \left(x \cdot y - z \cdot t \leq 5 \cdot 10^{+294}\right):\\ \;\;\;\;\frac{y - \frac{t}{x} \cdot z}{a} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-z\right) \cdot t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+267}\right):\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-z\right) \cdot t\right)}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= (* x y) (- INFINITY)) (not (<= (* x y) 2e+267)))
   (* (/ x a) y)
   (/ (fma y x (* (- z) t)) a)))

C

assert(x < y && y < z && z < t && t < a);
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)) || !((x * y) <= 2e+267)) {
		tmp = (x / a) * y;
	} else {
		tmp = fma(y, x, (-z * t)) / a;
	}
	return tmp;
}

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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)) || !(Float64(x * y) <= 2e+267))
		tmp = Float64(Float64(x / a) * y);
	else
		tmp = Float64(fma(y, x, Float64(Float64(-z) * t)) / a);
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(x * y), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+267]], $MachinePrecision]], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision], N[(N[(y * x + N[((-z) * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0 or 1.9999999999999999e267 < (*.f64 x y)

   1. Initial program 64.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 99.8

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

   5. Applied rewrites 99.8%

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

   if -inf.0 < (*.f64 x y) < 1.9999999999999999e267

   1. Initial program 96.1%

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

      1. lift--.f64 N/A

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

      2. lift-*.f64 N/A

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

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

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

      4. lift-*.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. lower-*.f64 N/A

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

      8. lower-neg.f64 96.2

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

   4. Applied rewrites 96.2%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+267}\right):\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, x, \left(-z\right) \cdot t\right)}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+267}\right):\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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 (<= (* x y) (- INFINITY)) (not (<= (* x y) 2e+267)))
   (* (/ x a) y)
   (/ (- (* x y) (* z t)) a)))

C

assert(x < y && y < z && z < t && t < a);
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)) || !((x * y) <= 2e+267)) {
		tmp = (x / a) * y;
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a;
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) || !((x * y) <= 2e+267)) {
		tmp = (x / a) * y;
	} else {
		tmp = ((x * y) - (z * t)) / a;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[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) or not ((x * y) <= 2e+267):
		tmp = (x / a) * y
	else:
		tmp = ((x * y) - (z * t)) / a
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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)) || !(Float64(x * y) <= 2e+267))
		tmp = Float64(Float64(x / a) * y);
	else
		tmp = Float64(Float64(Float64(x * y) - Float64(z * t)) / a);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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) || ~(((x * y) <= 2e+267)))
		tmp = (x / a) * y;
	else
		tmp = ((x * y) - (z * t)) / a;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(x * y), $MachinePrecision], (-Infinity)], N[Not[LessEqual[N[(x * y), $MachinePrecision], 2e+267]], $MachinePrecision]], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(x * y), $MachinePrecision] - N[(z * t), $MachinePrecision]), $MachinePrecision] / a), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < -inf.0 or 1.9999999999999999e267 < (*.f64 x y)

   1. Initial program 64.4%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 99.8

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

   5. Applied rewrites 99.8%

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

   if -inf.0 < (*.f64 x y) < 1.9999999999999999e267

   1. Initial program 96.1%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -\infty \lor \neg \left(x \cdot y \leq 2 \cdot 10^{+267}\right):\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y - z \cdot t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+47} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+110}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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+47) (not (<= (* z t) 2e+110)))
   (* (- z) (/ t a))
   (* (/ x a) y)))

C

assert(x < y && y < z && z < t && t < a);
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+47) || !((z * t) <= 2e+110)) {
		tmp = -z * (t / a);
	} 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.
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+47)) .or. (.not. ((z * t) <= 2d+110))) then
        tmp = -z * (t / a)
    else
        tmp = (x / a) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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+47) || !((z * t) <= 2e+110)) {
		tmp = -z * (t / a);
	} else {
		tmp = (x / a) * y;
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if ((z * t) <= -4e+47) or not ((z * t) <= 2e+110):
		tmp = -z * (t / a)
	else:
		tmp = (x / a) * y
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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+47) || !(Float64(z * t) <= 2e+110))
		tmp = Float64(Float64(-z) * Float64(t / a));
	else
		tmp = Float64(Float64(x / a) * y);
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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+47) || ~(((z * t) <= 2e+110)))
		tmp = -z * (t / a);
	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.
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+47], N[Not[LessEqual[N[(z * t), $MachinePrecision], 2e+110]], $MachinePrecision]], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z t) < -4.0000000000000002e47 or 2e110 < (*.f64 z t)

   1. Initial program 87.6%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-/.f64 85.0

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

   5. Applied rewrites 85.0%

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

   if -4.0000000000000002e47 < (*.f64 z t) < 2e110

   1. Initial program 94.1%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 72.9

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

   5. Applied rewrites 72.9%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -4 \cdot 10^{+47} \lor \neg \left(z \cdot t \leq 2 \cdot 10^{+110}\right):\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 72.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\\\ [x, y, z, t, a] = \mathsf{sort}([x, y, z, t, a])\\ \\ \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+110}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) -5e+23)
   (* (/ (- z) a) t)
   (if (<= (* z t) 2e+110) (* (/ x a) y) (* (- z) (/ t a)))))

C

assert(x < y && y < z && z < t && t < a);
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) <= -5e+23) {
		tmp = (-z / a) * t;
	} else if ((z * t) <= 2e+110) {
		tmp = (x / a) * y;
	} else {
		tmp = -z * (t / a);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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) <= (-5d+23)) then
        tmp = (-z / a) * t
    else if ((z * t) <= 2d+110) then
        tmp = (x / a) * y
    else
        tmp = -z * (t / a)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a;
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) <= -5e+23) {
		tmp = (-z / a) * t;
	} else if ((z * t) <= 2e+110) {
		tmp = (x / a) * y;
	} else {
		tmp = -z * (t / a);
	}
	return tmp;
}

Python

[x, y, z, t, a] = sort([x, y, z, t, a])
[x, y, z, t, a] = sort([x, y, z, t, a])
def code(x, y, z, t, a):
	tmp = 0
	if (z * t) <= -5e+23:
		tmp = (-z / a) * t
	elif (z * t) <= 2e+110:
		tmp = (x / a) * y
	else:
		tmp = -z * (t / a)
	return tmp

Julia

x, y, z, t, a = sort([x, y, z, t, a])
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) <= -5e+23)
		tmp = Float64(Float64(Float64(-z) / a) * t);
	elseif (Float64(z * t) <= 2e+110)
		tmp = Float64(Float64(x / a) * y);
	else
		tmp = Float64(Float64(-z) * Float64(t / a));
	end
	return tmp
end

MATLAB

x, y, z, t, a = num2cell(sort([x, y, z, t, a])){:}
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) <= -5e+23)
		tmp = (-z / a) * t;
	elseif ((z * t) <= 2e+110)
		tmp = (x / a) * y;
	else
		tmp = -z * (t / a);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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], -5e+23], N[(N[((-z) / a), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[N[(z * t), $MachinePrecision], 2e+110], N[(N[(x / a), $MachinePrecision] * y), $MachinePrecision], N[((-z) * N[(t / a), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z t) < -4.9999999999999999e23

   1. Initial program 87.7%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-/.f64 76.3

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

   5. Applied rewrites 76.3%

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

      1. lift-*.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. frac-2neg N/A

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

      4. lift-neg.f64 N/A

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

      5. associate-*r/ N/A

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

      6. associate-*l/ N/A

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

      7. lift-neg.f64 N/A

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

      8. frac-2neg N/A

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

      9. lift-/.f64 N/A

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

      10. lift-neg.f64 N/A

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

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

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

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

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

      13. lift-/.f64 N/A

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

      14. distribute-frac-neg N/A

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

      15. lift-neg.f64 N/A

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

      16. lower-*.f64 N/A

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

      17. lower-/.f64 71.8

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

   7. Applied rewrites 71.8%

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

   if -4.9999999999999999e23 < (*.f64 z t) < 2e110

   1. Initial program 94.5%

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

   3. Taylor expanded in x around inf

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

      1. associate-*l/ N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 75.6

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

   5. Applied rewrites 75.6%

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

   if 2e110 < (*.f64 z t)

   1. Initial program 87.2%

      \[\frac{x \cdot y - z \cdot t}{a} \]
   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-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-*r* N/A

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

      4. associate-*r/ N/A

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

      5. lower-*.f64 N/A

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

      6. mul-1-neg N/A

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

      7. lower-neg.f64 N/A

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

      8. lower-/.f64 93.3

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

   5. Applied rewrites 93.3%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot t \leq -5 \cdot 10^{+23}:\\ \;\;\;\;\frac{-z}{a} \cdot t\\ \mathbf{elif}\;z \cdot t \leq 2 \cdot 10^{+110}:\\ \;\;\;\;\frac{x}{a} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) \cdot \frac{t}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.3% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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[(y / a), $MachinePrecision] * x), $MachinePrecision]

Derivation

1. Initial program 91.6%

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

3. Taylor expanded in x around inf

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 52.7

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

5. Applied rewrites 52.7%

   \[\leadsto \color{blue}{\frac{x}{a} \cdot y} \]
6. 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. *-commutative N/A

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

   5. associate-*l/ N/A

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

   6. lift-/.f64 N/A

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

   7. lower-*.f64 52.8

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

7. Applied rewrites 52.8%

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

8. Final simplification 52.8%

   \[\leadsto \frac{y}{a} \cdot x \]
9. Add Preprocessing

Alternative 9: 51.7% accurate, 1.5× speedup

Math

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

FPCore

NOTE: x, y, z, t, and a should be sorted in increasing order before calling this function.
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);
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.
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;
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])
[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])
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])){:}
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.
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. Taylor expanded in x around inf

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

   1. associate-*l/ N/A

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

   2. lower-*.f64 N/A

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

   3. lower-/.f64 52.7

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

5. Applied rewrites 52.7%

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

6. Final simplification 52.7%

   \[\leadsto \frac{x}{a} \cdot y \]
7. Add Preprocessing

Developer Target 1: 91.8% 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 2025026 
(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))