Data.Colour.Matrix:determinant from colour-2.3.3, A

Percentage Accurate: 73.6% → 80.2%

Time: 12.3s

Alternatives: 25

Speedup: 0.9×

• 58.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.6% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (+
  (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
  (* j (- (* c a) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)))

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(t * i)))) + Float64(j * Float64(Float64(c * a) - Float64(y * i))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 80.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+83} \lor \neg \left(j \leq 3.8 \cdot 10^{+60}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \mathsf{fma}\left(\mathsf{fma}\left(-x, a, i \cdot b\right), t, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-t, x, j \cdot c\right), a, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -2.9e+83) (not (<= j 3.8e+60)))
   (fma
    (fma (- i) y (* c a))
    j
    (fma (fma (- x) a (* i b)) t (* (fma (- b) c (* y x)) z)))
   (fma
    (fma (- c) z (* i t))
    b
    (fma (fma (- t) x (* j c)) a (* (fma (- i) j (* z x)) y)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -2.9e+83) || !(j <= 3.8e+60)) {
		tmp = fma(fma(-i, y, (c * a)), j, fma(fma(-x, a, (i * b)), t, (fma(-b, c, (y * x)) * z)));
	} else {
		tmp = fma(fma(-c, z, (i * t)), b, fma(fma(-t, x, (j * c)), a, (fma(-i, j, (z * x)) * y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -2.9e+83) || !(j <= 3.8e+60))
		tmp = fma(fma(Float64(-i), y, Float64(c * a)), j, fma(fma(Float64(-x), a, Float64(i * b)), t, Float64(fma(Float64(-b), c, Float64(y * x)) * z)));
	else
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, fma(fma(Float64(-t), x, Float64(j * c)), a, Float64(fma(Float64(-i), j, Float64(z * x)) * y)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -2.9e+83], N[Not[LessEqual[j, 3.8e+60]], $MachinePrecision]], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j + N[(N[((-x) * a + N[(i * b), $MachinePrecision]), $MachinePrecision] * t + N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2.89999999999999999e83 or 3.80000000000000009e60 < j

   1. Initial program 79.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 88.4%

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

   if -2.89999999999999999e83 < j < 3.80000000000000009e60

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 85.8%

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

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.9 \cdot 10^{+83} \lor \neg \left(j \leq 3.8 \cdot 10^{+60}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \mathsf{fma}\left(\mathsf{fma}\left(-x, a, i \cdot b\right), t, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-t, x, j \cdot c\right), a, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, y, c \cdot a\right)\\ \mathbf{if}\;j \leq -3.9 \cdot 10^{+197}:\\ \;\;\;\;t\_1 \cdot j\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+230}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-t, x, j \cdot c\right), a, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, j, \left(z \cdot y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- i) y (* c a))))
   (if (<= j -3.9e+197)
     (* t_1 j)
     (if (<= j 6e+230)
       (fma
        (fma (- c) z (* i t))
        b
        (fma (fma (- t) x (* j c)) a (* (fma (- i) j (* z x)) y)))
       (fma t_1 j (* (* z y) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-i, y, (c * a));
	double tmp;
	if (j <= -3.9e+197) {
		tmp = t_1 * j;
	} else if (j <= 6e+230) {
		tmp = fma(fma(-c, z, (i * t)), b, fma(fma(-t, x, (j * c)), a, (fma(-i, j, (z * x)) * y)));
	} else {
		tmp = fma(t_1, j, ((z * y) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-i), y, Float64(c * a))
	tmp = 0.0
	if (j <= -3.9e+197)
		tmp = Float64(t_1 * j);
	elseif (j <= 6e+230)
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, fma(fma(Float64(-t), x, Float64(j * c)), a, Float64(fma(Float64(-i), j, Float64(z * x)) * y)));
	else
		tmp = fma(t_1, j, Float64(Float64(z * y) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.9e+197], N[(t$95$1 * j), $MachinePrecision], If[LessEqual[j, 6e+230], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 * j + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.9e197

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 83.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j} \]

   if -3.9e197 < j < 6.00000000000000017e230

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 84.8%

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

   if 6.00000000000000017e230 < j

   1. Initial program 70.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 80.0%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 100.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.9 \cdot 10^{+197}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+230}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-t, x, j \cdot c\right), a, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{if}\;x \leq -3.9 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-195}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b + t\_1\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+161}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(y, \frac{z}{t}, -a\right) \cdot t\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i)))))
   (if (<= x -3.9e+85)
     (* (fma (- t) a (* z y)) x)
     (if (<= x -5.5e-195)
       (fma (fma (- c) z (* i t)) b (* (* j c) a))
       (if (<= x 3.8e-75)
         (+ (* (* i t) b) t_1)
         (if (<= x 6e+161)
           (+ (* (* z x) y) t_1)
           (* (* (fma y (/ z t) (- a)) t) x)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double tmp;
	if (x <= -3.9e+85) {
		tmp = fma(-t, a, (z * y)) * x;
	} else if (x <= -5.5e-195) {
		tmp = fma(fma(-c, z, (i * t)), b, ((j * c) * a));
	} else if (x <= 3.8e-75) {
		tmp = ((i * t) * b) + t_1;
	} else if (x <= 6e+161) {
		tmp = ((z * x) * y) + t_1;
	} else {
		tmp = (fma(y, (z / t), -a) * t) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	tmp = 0.0
	if (x <= -3.9e+85)
		tmp = Float64(fma(Float64(-t), a, Float64(z * y)) * x);
	elseif (x <= -5.5e-195)
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, Float64(Float64(j * c) * a));
	elseif (x <= 3.8e-75)
		tmp = Float64(Float64(Float64(i * t) * b) + t_1);
	elseif (x <= 6e+161)
		tmp = Float64(Float64(Float64(z * x) * y) + t_1);
	else
		tmp = Float64(Float64(fma(y, Float64(z / t), Float64(-a)) * t) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.9e+85], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -5.5e-195], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e-75], N[(N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[x, 6e+161], N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(y * N[(z / t), $MachinePrecision] + (-a)), $MachinePrecision] * t), $MachinePrecision] * x), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.90000000000000033e85

   1. Initial program 62.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 72.0%

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

   if -3.90000000000000033e85 < x < -5.5000000000000003e-195

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 80.1%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, a \cdot \left(c \cdot j\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 63.4%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right) \]

   if -5.5000000000000003e-195 < x < 3.79999999999999994e-75

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

   5. Applied rewrites 66.6%

      \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if 3.79999999999999994e-75 < x < 6.00000000000000023e161

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 63.7%

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

   if 6.00000000000000023e161 < x

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 89.7%

      \[\leadsto \left(\mathsf{fma}\left(y, \frac{z}{t}, -a\right) \cdot t\right) \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-195}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+161}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(y, \frac{z}{t}, -a\right) \cdot t\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ t_2 := \mathsf{fma}\left(-b, c, y \cdot x\right)\\ \mathbf{if}\;a \leq -4.3 \cdot 10^{+162}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-72}:\\ \;\;\;\;\mathsf{fma}\left(\left(-j\right) \cdot y, i, \mathsf{fma}\left(t\_2, z, \left(i \cdot t\right) \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, t\_2 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) x (* j c)) a)) (t_2 (fma (- b) c (* y x))))
   (if (<= a -4.3e+162)
     t_1
     (if (<= a 1.9e-72)
       (fma (* (- j) y) i (fma t_2 z (* (* i t) b)))
       (if (<= a 3.9e+77) (fma (fma (- i) y (* c a)) j (* t_2 z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-t, x, (j * c)) * a;
	double t_2 = fma(-b, c, (y * x));
	double tmp;
	if (a <= -4.3e+162) {
		tmp = t_1;
	} else if (a <= 1.9e-72) {
		tmp = fma((-j * y), i, fma(t_2, z, ((i * t) * b)));
	} else if (a <= 3.9e+77) {
		tmp = fma(fma(-i, y, (c * a)), j, (t_2 * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), x, Float64(j * c)) * a)
	t_2 = fma(Float64(-b), c, Float64(y * x))
	tmp = 0.0
	if (a <= -4.3e+162)
		tmp = t_1;
	elseif (a <= 1.9e-72)
		tmp = fma(Float64(Float64(-j) * y), i, fma(t_2, z, Float64(Float64(i * t) * b)));
	elseif (a <= 3.9e+77)
		tmp = fma(fma(Float64(-i), y, Float64(c * a)), j, Float64(t_2 * z));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision]}, Block[{t$95$2 = N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.3e+162], t$95$1, If[LessEqual[a, 1.9e-72], N[(N[((-j) * y), $MachinePrecision] * i + N[(t$95$2 * z + N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.9e+77], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j + N[(t$95$2 * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.3000000000000002e162 or 3.8999999999999998e77 < a

   1. Initial program 55.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 79.3%

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

   if -4.3000000000000002e162 < a < 1.90000000000000001e-72

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in a around 0

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

   8. Applied rewrites 71.5%

      \[\leadsto \mathsf{fma}\left(\left(-j\right) \cdot y, \color{blue}{i}, \mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \left(i \cdot t\right) \cdot b\right)\right) \]

   if 1.90000000000000001e-72 < a < 3.8999999999999998e77

   1. Initial program 93.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   5. Applied rewrites 78.1%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.3 \cdot 10^{+162}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-72}:\\ \;\;\;\;\mathsf{fma}\left(\left(-j\right) \cdot y, i, \mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \left(i \cdot t\right) \cdot b\right)\right)\\ \mathbf{elif}\;a \leq 3.9 \cdot 10^{+77}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-195}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(y, \frac{z}{t}, -a\right) \cdot t\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -3.9e+85)
   (* (fma (- t) a (* z y)) x)
   (if (<= x -5.5e-195)
     (fma (fma (- c) z (* i t)) b (* (* j c) a))
     (if (<= x 3.8e-75)
       (+ (* (* i t) b) (* j (- (* c a) (* y i))))
       (if (<= x 2.15e+160)
         (fma (fma (- i) y (* c a)) j (* (* z y) x))
         (* (* (fma y (/ z t) (- a)) t) x))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3.9e+85) {
		tmp = fma(-t, a, (z * y)) * x;
	} else if (x <= -5.5e-195) {
		tmp = fma(fma(-c, z, (i * t)), b, ((j * c) * a));
	} else if (x <= 3.8e-75) {
		tmp = ((i * t) * b) + (j * ((c * a) - (y * i)));
	} else if (x <= 2.15e+160) {
		tmp = fma(fma(-i, y, (c * a)), j, ((z * y) * x));
	} else {
		tmp = (fma(y, (z / t), -a) * t) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -3.9e+85)
		tmp = Float64(fma(Float64(-t), a, Float64(z * y)) * x);
	elseif (x <= -5.5e-195)
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, Float64(Float64(j * c) * a));
	elseif (x <= 3.8e-75)
		tmp = Float64(Float64(Float64(i * t) * b) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	elseif (x <= 2.15e+160)
		tmp = fma(fma(Float64(-i), y, Float64(c * a)), j, Float64(Float64(z * y) * x));
	else
		tmp = Float64(Float64(fma(y, Float64(z / t), Float64(-a)) * t) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -3.9e+85], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -5.5e-195], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.8e-75], N[(N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e+160], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(z / t), $MachinePrecision] + (-a)), $MachinePrecision] * t), $MachinePrecision] * x), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -3.90000000000000033e85

   1. Initial program 62.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 72.0%

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

   if -3.90000000000000033e85 < x < -5.5000000000000003e-195

   1. Initial program 78.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 80.1%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, a \cdot \left(c \cdot j\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 63.4%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right) \]

   if -5.5000000000000003e-195 < x < 3.79999999999999994e-75

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

   5. Applied rewrites 66.6%

      \[\leadsto \color{blue}{\left(i \cdot t\right) \cdot b} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   if 3.79999999999999994e-75 < x < 2.14999999999999994e160

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 62.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right) \]

   if 2.14999999999999994e160 < x

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 89.7%

      \[\leadsto \left(\mathsf{fma}\left(y, \frac{z}{t}, -a\right) \cdot t\right) \cdot x \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-195}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-75}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(y, \frac{z}{t}, -a\right) \cdot t\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-b, c, y \cdot x\right)\\ \mathbf{if}\;t \leq -6.6 \cdot 10^{-42} \lor \neg \left(t \leq 0.37\right):\\ \;\;\;\;\mathsf{fma}\left(t\_1, z, \mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, t\_1 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- b) c (* y x))))
   (if (or (<= t -6.6e-42) (not (<= t 0.37)))
     (fma t_1 z (* (fma (- a) x (* i b)) t))
     (fma (fma (- i) y (* c a)) j (* t_1 z)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-b, c, (y * x));
	double tmp;
	if ((t <= -6.6e-42) || !(t <= 0.37)) {
		tmp = fma(t_1, z, (fma(-a, x, (i * b)) * t));
	} else {
		tmp = fma(fma(-i, y, (c * a)), j, (t_1 * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-b), c, Float64(y * x))
	tmp = 0.0
	if ((t <= -6.6e-42) || !(t <= 0.37))
		tmp = fma(t_1, z, Float64(fma(Float64(-a), x, Float64(i * b)) * t));
	else
		tmp = fma(fma(Float64(-i), y, Float64(c * a)), j, Float64(t_1 * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -6.6e-42], N[Not[LessEqual[t, 0.37]], $MachinePrecision]], N[(t$95$1 * z + N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j + N[(t$95$1 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6000000000000005e-42 or 0.37 < t

   1. Initial program 67.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 77.4%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 69.8%

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

   if -6.6000000000000005e-42 < t < 0.37

   1. Initial program 81.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   5. Applied rewrites 72.7%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-42} \lor \neg \left(t \leq 0.37\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{-19} \lor \neg \left(t \leq 0.37\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -9.6e-19) (not (<= t 0.37)))
   (fma (fma (- b) c (* y x)) z (* (fma (- a) x (* i b)) t))
   (+ (* (* z x) y) (* j (- (* c a) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -9.6e-19) || !(t <= 0.37)) {
		tmp = fma(fma(-b, c, (y * x)), z, (fma(-a, x, (i * b)) * t));
	} else {
		tmp = ((z * x) * y) + (j * ((c * a) - (y * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -9.6e-19) || !(t <= 0.37))
		tmp = fma(fma(Float64(-b), c, Float64(y * x)), z, Float64(fma(Float64(-a), x, Float64(i * b)) * t));
	else
		tmp = Float64(Float64(Float64(z * x) * y) + Float64(j * Float64(Float64(c * a) - Float64(y * i))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -9.6e-19], N[Not[LessEqual[t, 0.37]], $MachinePrecision]], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z + N[(N[((-a) * x + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * x), $MachinePrecision] * y), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.60000000000000092e-19 or 0.37 < t

   1. Initial program 65.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 78.9%

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

   6. Taylor expanded in j around 0

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

   8. Applied rewrites 71.5%

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

   if -9.60000000000000092e-19 < t < 0.37

   1. Initial program 81.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 67.2%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.6 \cdot 10^{-19} \lor \neg \left(t \leq 0.37\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-b, c, y \cdot x\right), z, \mathsf{fma}\left(-a, x, i \cdot b\right) \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z \cdot x\right) \cdot y + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 48.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(t \cdot x\right)\\ t_2 := \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-171}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-274}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-y\right) \cdot j\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* t x))) (t_2 (* (fma (- b) c (* y x)) z)))
   (if (<= z -1.7e+48)
     t_2
     (if (<= z -3.45e-28)
       t_1
       (if (<= z -4.6e-171)
         (* (fma (- i) j (* z x)) y)
         (if (<= z -9.5e-274)
           t_1
           (if (<= z 5.6e-27) (* (fma t b (* (- y) j)) i) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double t_2 = fma(-b, c, (y * x)) * z;
	double tmp;
	if (z <= -1.7e+48) {
		tmp = t_2;
	} else if (z <= -3.45e-28) {
		tmp = t_1;
	} else if (z <= -4.6e-171) {
		tmp = fma(-i, j, (z * x)) * y;
	} else if (z <= -9.5e-274) {
		tmp = t_1;
	} else if (z <= 5.6e-27) {
		tmp = fma(t, b, (-y * j)) * i;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * Float64(t * x))
	t_2 = Float64(fma(Float64(-b), c, Float64(y * x)) * z)
	tmp = 0.0
	if (z <= -1.7e+48)
		tmp = t_2;
	elseif (z <= -3.45e-28)
		tmp = t_1;
	elseif (z <= -4.6e-171)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	elseif (z <= -9.5e-274)
		tmp = t_1;
	elseif (z <= 5.6e-27)
		tmp = Float64(fma(t, b, Float64(Float64(-y) * j)) * i);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.7e+48], t$95$2, If[LessEqual[z, -3.45e-28], t$95$1, If[LessEqual[z, -4.6e-171], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, -9.5e-274], t$95$1, If[LessEqual[z, 5.6e-27], N[(N[(t * b + N[((-y) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7000000000000002e48 or 5.5999999999999999e-27 < z

   1. Initial program 68.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

   5. Applied rewrites 62.3%

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

   if -1.7000000000000002e48 < z < -3.45000000000000001e-28 or -4.59999999999999956e-171 < z < -9.5000000000000009e-274

   1. Initial program 64.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 59.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 61.9%

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

   if -3.45000000000000001e-28 < z < -4.59999999999999956e-171

   1. Initial program 86.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 54.8%

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

   if -9.5000000000000009e-274 < z < 5.5999999999999999e-27

   1. Initial program 81.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 48.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]
   6. Step-by-step derivation

   7. Applied rewrites 48.8%

      \[\leadsto \mathsf{fma}\left(t, b, \left(-y\right) \cdot j\right) \cdot i \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-28}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-171}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-274}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-y\right) \cdot j\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-75}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(y, \frac{z}{t}, -a\right) \cdot t\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -3.9e+85)
   (* (fma (- t) a (* z y)) x)
   (if (<= x 3.5e-75)
     (fma (fma (- c) z (* i t)) b (* (* j c) a))
     (if (<= x 2.15e+160)
       (fma (fma (- i) y (* c a)) j (* (* z y) x))
       (* (* (fma y (/ z t) (- a)) t) x)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3.9e+85) {
		tmp = fma(-t, a, (z * y)) * x;
	} else if (x <= 3.5e-75) {
		tmp = fma(fma(-c, z, (i * t)), b, ((j * c) * a));
	} else if (x <= 2.15e+160) {
		tmp = fma(fma(-i, y, (c * a)), j, ((z * y) * x));
	} else {
		tmp = (fma(y, (z / t), -a) * t) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -3.9e+85)
		tmp = Float64(fma(Float64(-t), a, Float64(z * y)) * x);
	elseif (x <= 3.5e-75)
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, Float64(Float64(j * c) * a));
	elseif (x <= 2.15e+160)
		tmp = fma(fma(Float64(-i), y, Float64(c * a)), j, Float64(Float64(z * y) * x));
	else
		tmp = Float64(Float64(fma(y, Float64(z / t), Float64(-a)) * t) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -3.9e+85], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 3.5e-75], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.15e+160], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(z / t), $MachinePrecision] + (-a)), $MachinePrecision] * t), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.90000000000000033e85

   1. Initial program 62.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 72.0%

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

   if -3.90000000000000033e85 < x < 3.49999999999999985e-75

   1. Initial program 74.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 84.5%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, a \cdot \left(c \cdot j\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 61.6%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right) \]

   if 3.49999999999999985e-75 < x < 2.14999999999999994e160

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0

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

   5. Applied rewrites 79.2%

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

   6. Taylor expanded in y around inf

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

   8. Applied rewrites 62.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right) \]

   if 2.14999999999999994e160 < x

   1. Initial program 77.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 86.9%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 89.7%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-75}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{+160}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(y, \frac{z}{t}, -a\right) \cdot t\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{if}\;a \leq -2.95 \cdot 10^{+246}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-291}:\\ \;\;\;\;\left(i \cdot b\right) \cdot t\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+256}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* t x))))
   (if (<= a -2.95e+246)
     (* (* c a) j)
     (if (<= a -4.3e-16)
       t_1
       (if (<= a 1.06e-291)
         (* (* i b) t)
         (if (<= a 2.1e+103)
           (* (* z y) x)
           (if (<= a 3.3e+256) t_1 (* (* j a) c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double tmp;
	if (a <= -2.95e+246) {
		tmp = (c * a) * j;
	} else if (a <= -4.3e-16) {
		tmp = t_1;
	} else if (a <= 1.06e-291) {
		tmp = (i * b) * t;
	} else if (a <= 2.1e+103) {
		tmp = (z * y) * x;
	} else if (a <= 3.3e+256) {
		tmp = t_1;
	} else {
		tmp = (j * a) * c;
	}
	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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * (t * x)
    if (a <= (-2.95d+246)) then
        tmp = (c * a) * j
    else if (a <= (-4.3d-16)) then
        tmp = t_1
    else if (a <= 1.06d-291) then
        tmp = (i * b) * t
    else if (a <= 2.1d+103) then
        tmp = (z * y) * x
    else if (a <= 3.3d+256) then
        tmp = t_1
    else
        tmp = (j * a) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double tmp;
	if (a <= -2.95e+246) {
		tmp = (c * a) * j;
	} else if (a <= -4.3e-16) {
		tmp = t_1;
	} else if (a <= 1.06e-291) {
		tmp = (i * b) * t;
	} else if (a <= 2.1e+103) {
		tmp = (z * y) * x;
	} else if (a <= 3.3e+256) {
		tmp = t_1;
	} else {
		tmp = (j * a) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (t * x)
	tmp = 0
	if a <= -2.95e+246:
		tmp = (c * a) * j
	elif a <= -4.3e-16:
		tmp = t_1
	elif a <= 1.06e-291:
		tmp = (i * b) * t
	elif a <= 2.1e+103:
		tmp = (z * y) * x
	elif a <= 3.3e+256:
		tmp = t_1
	else:
		tmp = (j * a) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * Float64(t * x))
	tmp = 0.0
	if (a <= -2.95e+246)
		tmp = Float64(Float64(c * a) * j);
	elseif (a <= -4.3e-16)
		tmp = t_1;
	elseif (a <= 1.06e-291)
		tmp = Float64(Float64(i * b) * t);
	elseif (a <= 2.1e+103)
		tmp = Float64(Float64(z * y) * x);
	elseif (a <= 3.3e+256)
		tmp = t_1;
	else
		tmp = Float64(Float64(j * a) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -a * (t * x);
	tmp = 0.0;
	if (a <= -2.95e+246)
		tmp = (c * a) * j;
	elseif (a <= -4.3e-16)
		tmp = t_1;
	elseif (a <= 1.06e-291)
		tmp = (i * b) * t;
	elseif (a <= 2.1e+103)
		tmp = (z * y) * x;
	elseif (a <= 3.3e+256)
		tmp = t_1;
	else
		tmp = (j * a) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.95e+246], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[a, -4.3e-16], t$95$1, If[LessEqual[a, 1.06e-291], N[(N[(i * b), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[a, 2.1e+103], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 3.3e+256], t$95$1, N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.94999999999999988e246

   1. Initial program 60.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 61.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 61.1%

      \[\leadsto \left(j \cdot c\right) \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 65.9%

       \[\leadsto \left(c \cdot a\right) \cdot j \]

   if -2.94999999999999988e246 < a < -4.2999999999999999e-16 or 2.1000000000000002e103 < a < 3.2999999999999999e256

   1. Initial program 59.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 60.1%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 45.4%

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

   if -4.2999999999999999e-16 < a < 1.05999999999999992e-291

   1. Initial program 86.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 40.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(b \cdot i\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 33.2%

      \[\leadsto \left(i \cdot b\right) \cdot t \]

   if 1.05999999999999992e-291 < a < 2.1000000000000002e103

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 34.5%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 28.3%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if 3.2999999999999999e256 < a

   1. Initial program 69.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot j\right) \cdot c \]
   7. Step-by-step derivation

   8. Applied rewrites 77.6%

      \[\leadsto \left(j \cdot a\right) \cdot c \]
3. Recombined 5 regimes into one program.

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.95 \cdot 10^{+246}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;a \leq -4.3 \cdot 10^{-16}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{-291}:\\ \;\;\;\;\left(i \cdot b\right) \cdot t\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+256}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 49.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-28}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-148}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- b) c (* y x)) z)))
   (if (<= z -1.7e+48)
     t_1
     (if (<= z -3.45e-28)
       (* (- a) (* t x))
       (if (<= z -8.6e-148)
         (* (fma (- i) j (* z x)) y)
         (if (<= z 5.6e-27) (* (fma (- i) y (* c a)) j) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-b, c, (y * x)) * z;
	double tmp;
	if (z <= -1.7e+48) {
		tmp = t_1;
	} else if (z <= -3.45e-28) {
		tmp = -a * (t * x);
	} else if (z <= -8.6e-148) {
		tmp = fma(-i, j, (z * x)) * y;
	} else if (z <= 5.6e-27) {
		tmp = fma(-i, y, (c * a)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-b), c, Float64(y * x)) * z)
	tmp = 0.0
	if (z <= -1.7e+48)
		tmp = t_1;
	elseif (z <= -3.45e-28)
		tmp = Float64(Float64(-a) * Float64(t * x));
	elseif (z <= -8.6e-148)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	elseif (z <= 5.6e-27)
		tmp = Float64(fma(Float64(-i), y, Float64(c * a)) * j);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -1.7e+48], t$95$1, If[LessEqual[z, -3.45e-28], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.6e-148], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[z, 5.6e-27], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7000000000000002e48 or 5.5999999999999999e-27 < z

   1. Initial program 68.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

   5. Applied rewrites 62.3%

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

   if -1.7000000000000002e48 < z < -3.45000000000000001e-28

   1. Initial program 64.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 64.9%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 65.0%

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

   if -3.45000000000000001e-28 < z < -8.5999999999999997e-148

   1. Initial program 84.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 57.2%

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

   if -8.5999999999999997e-148 < z < 5.5999999999999999e-27

   1. Initial program 78.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 52.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-28}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-148}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 58.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(y, \frac{z}{t}, -a\right) \cdot t\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= x -3.9e+85)
   (* (fma (- t) a (* z y)) x)
   (if (<= x 2.3e-60)
     (fma (fma (- c) z (* i t)) b (* (* j c) a))
     (* (* (fma y (/ z t) (- a)) t) x))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (x <= -3.9e+85) {
		tmp = fma(-t, a, (z * y)) * x;
	} else if (x <= 2.3e-60) {
		tmp = fma(fma(-c, z, (i * t)), b, ((j * c) * a));
	} else {
		tmp = (fma(y, (z / t), -a) * t) * x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (x <= -3.9e+85)
		tmp = Float64(fma(Float64(-t), a, Float64(z * y)) * x);
	elseif (x <= 2.3e-60)
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, Float64(Float64(j * c) * a));
	else
		tmp = Float64(Float64(fma(y, Float64(z / t), Float64(-a)) * t) * x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[x, -3.9e+85], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, 2.3e-60], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision], N[(N[(N[(y * N[(z / t), $MachinePrecision] + (-a)), $MachinePrecision] * t), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.90000000000000033e85

   1. Initial program 62.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 72.0%

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

   if -3.90000000000000033e85 < x < 2.3000000000000001e-60

   1. Initial program 74.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 84.8%

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

   6. Taylor expanded in c around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, a \cdot \left(c \cdot j\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 61.0%

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right) \]

   if 2.3000000000000001e-60 < x

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 68.2%

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

   6. Taylor expanded in t around inf

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

   8. Applied rewrites 69.3%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{+85}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-60}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(j \cdot c\right) \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\mathsf{fma}\left(y, \frac{z}{t}, -a\right) \cdot t\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 43.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{+248}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+163}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-y\right) \cdot j\right) \cdot i\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+256}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -7.4e+248)
   (* (* c a) j)
   (if (<= a -2.7e+163)
     (* (* (- a) t) x)
     (if (<= a 3.1e+104)
       (* (fma t b (* (- y) j)) i)
       (if (<= a 3.3e+256) (* (- a) (* t x)) (* (* j a) c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -7.4e+248) {
		tmp = (c * a) * j;
	} else if (a <= -2.7e+163) {
		tmp = (-a * t) * x;
	} else if (a <= 3.1e+104) {
		tmp = fma(t, b, (-y * j)) * i;
	} else if (a <= 3.3e+256) {
		tmp = -a * (t * x);
	} else {
		tmp = (j * a) * c;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -7.4e+248)
		tmp = Float64(Float64(c * a) * j);
	elseif (a <= -2.7e+163)
		tmp = Float64(Float64(Float64(-a) * t) * x);
	elseif (a <= 3.1e+104)
		tmp = Float64(fma(t, b, Float64(Float64(-y) * j)) * i);
	elseif (a <= 3.3e+256)
		tmp = Float64(Float64(-a) * Float64(t * x));
	else
		tmp = Float64(Float64(j * a) * c);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -7.4e+248], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[a, -2.7e+163], N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, 3.1e+104], N[(N[(t * b + N[((-y) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[a, 3.3e+256], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.39999999999999961e248

   1. Initial program 63.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 64.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 63.9%

      \[\leadsto \left(j \cdot c\right) \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 69.0%

       \[\leadsto \left(c \cdot a\right) \cdot j \]

   if -7.39999999999999961e248 < a < -2.69999999999999999e163

   1. Initial program 40.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 74.4%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(-1 \cdot \left(a \cdot t\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 61.0%

      \[\leadsto \left(\left(-a\right) \cdot t\right) \cdot x \]

   if -2.69999999999999999e163 < a < 3.10000000000000017e104

   1. Initial program 82.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 41.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]
   6. Step-by-step derivation

   7. Applied rewrites 41.7%

      \[\leadsto \mathsf{fma}\left(t, b, \left(-y\right) \cdot j\right) \cdot i \]

   if 3.10000000000000017e104 < a < 3.2999999999999999e256

   1. Initial program 47.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 66.5%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 59.7%

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

   if 3.2999999999999999e256 < a

   1. Initial program 69.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 77.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot j\right) \cdot c \]
   7. Step-by-step derivation

   8. Applied rewrites 77.6%

      \[\leadsto \left(j \cdot a\right) \cdot c \]
3. Recombined 5 regimes into one program.

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.4 \cdot 10^{+248}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{+163}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+104}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-y\right) \cdot j\right) \cdot i\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+256}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 30.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-80}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) \cdot b\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* t x))))
   (if (<= z -3.1e+53)
     (* (* z y) x)
     (if (<= z 2.2e-262)
       t_1
       (if (<= z 2.35e-80)
         (* (* (- j) y) i)
         (if (<= z 7800000000.0) t_1 (* (* (- z) b) c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double tmp;
	if (z <= -3.1e+53) {
		tmp = (z * y) * x;
	} else if (z <= 2.2e-262) {
		tmp = t_1;
	} else if (z <= 2.35e-80) {
		tmp = (-j * y) * i;
	} else if (z <= 7800000000.0) {
		tmp = t_1;
	} else {
		tmp = (-z * b) * c;
	}
	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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * (t * x)
    if (z <= (-3.1d+53)) then
        tmp = (z * y) * x
    else if (z <= 2.2d-262) then
        tmp = t_1
    else if (z <= 2.35d-80) then
        tmp = (-j * y) * i
    else if (z <= 7800000000.0d0) then
        tmp = t_1
    else
        tmp = (-z * b) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double tmp;
	if (z <= -3.1e+53) {
		tmp = (z * y) * x;
	} else if (z <= 2.2e-262) {
		tmp = t_1;
	} else if (z <= 2.35e-80) {
		tmp = (-j * y) * i;
	} else if (z <= 7800000000.0) {
		tmp = t_1;
	} else {
		tmp = (-z * b) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (t * x)
	tmp = 0
	if z <= -3.1e+53:
		tmp = (z * y) * x
	elif z <= 2.2e-262:
		tmp = t_1
	elif z <= 2.35e-80:
		tmp = (-j * y) * i
	elif z <= 7800000000.0:
		tmp = t_1
	else:
		tmp = (-z * b) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * Float64(t * x))
	tmp = 0.0
	if (z <= -3.1e+53)
		tmp = Float64(Float64(z * y) * x);
	elseif (z <= 2.2e-262)
		tmp = t_1;
	elseif (z <= 2.35e-80)
		tmp = Float64(Float64(Float64(-j) * y) * i);
	elseif (z <= 7800000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(-z) * b) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -a * (t * x);
	tmp = 0.0;
	if (z <= -3.1e+53)
		tmp = (z * y) * x;
	elseif (z <= 2.2e-262)
		tmp = t_1;
	elseif (z <= 2.35e-80)
		tmp = (-j * y) * i;
	elseif (z <= 7800000000.0)
		tmp = t_1;
	else
		tmp = (-z * b) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+53], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 2.2e-262], t$95$1, If[LessEqual[z, 2.35e-80], N[(N[((-j) * y), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[z, 7800000000.0], t$95$1, N[(N[((-z) * b), $MachinePrecision] * c), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.10000000000000019e53

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 52.7%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if -3.10000000000000019e53 < z < 2.19999999999999989e-262 or 2.34999999999999986e-80 < z < 7.8e9

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 50.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 39.1%

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

   if 2.19999999999999989e-262 < z < 2.34999999999999986e-80

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i \]
   7. Step-by-step derivation

   8. Applied rewrites 38.5%

      \[\leadsto \left(\left(-j\right) \cdot y\right) \cdot i \]

   if 7.8e9 < z

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 54.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around inf

      \[\leadsto \left(-1 \cdot \left(b \cdot z\right)\right) \cdot c \]
   7. Step-by-step derivation

   8. Applied rewrites 45.5%

      \[\leadsto \left(\left(-z\right) \cdot b\right) \cdot c \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-262}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-80}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) \cdot b\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-262}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-80}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \left(c \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* t x))))
   (if (<= z -3.1e+53)
     (* (* z y) x)
     (if (<= z 2.2e-262)
       t_1
       (if (<= z 2.35e-80)
         (* (* (- j) y) i)
         (if (<= z 7800000000.0) t_1 (* (- b) (* c z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double tmp;
	if (z <= -3.1e+53) {
		tmp = (z * y) * x;
	} else if (z <= 2.2e-262) {
		tmp = t_1;
	} else if (z <= 2.35e-80) {
		tmp = (-j * y) * i;
	} else if (z <= 7800000000.0) {
		tmp = t_1;
	} else {
		tmp = -b * (c * z);
	}
	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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * (t * x)
    if (z <= (-3.1d+53)) then
        tmp = (z * y) * x
    else if (z <= 2.2d-262) then
        tmp = t_1
    else if (z <= 2.35d-80) then
        tmp = (-j * y) * i
    else if (z <= 7800000000.0d0) then
        tmp = t_1
    else
        tmp = -b * (c * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double tmp;
	if (z <= -3.1e+53) {
		tmp = (z * y) * x;
	} else if (z <= 2.2e-262) {
		tmp = t_1;
	} else if (z <= 2.35e-80) {
		tmp = (-j * y) * i;
	} else if (z <= 7800000000.0) {
		tmp = t_1;
	} else {
		tmp = -b * (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (t * x)
	tmp = 0
	if z <= -3.1e+53:
		tmp = (z * y) * x
	elif z <= 2.2e-262:
		tmp = t_1
	elif z <= 2.35e-80:
		tmp = (-j * y) * i
	elif z <= 7800000000.0:
		tmp = t_1
	else:
		tmp = -b * (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * Float64(t * x))
	tmp = 0.0
	if (z <= -3.1e+53)
		tmp = Float64(Float64(z * y) * x);
	elseif (z <= 2.2e-262)
		tmp = t_1;
	elseif (z <= 2.35e-80)
		tmp = Float64(Float64(Float64(-j) * y) * i);
	elseif (z <= 7800000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(-b) * Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -a * (t * x);
	tmp = 0.0;
	if (z <= -3.1e+53)
		tmp = (z * y) * x;
	elseif (z <= 2.2e-262)
		tmp = t_1;
	elseif (z <= 2.35e-80)
		tmp = (-j * y) * i;
	elseif (z <= 7800000000.0)
		tmp = t_1;
	else
		tmp = -b * (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+53], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 2.2e-262], t$95$1, If[LessEqual[z, 2.35e-80], N[(N[((-j) * y), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[z, 7800000000.0], t$95$1, N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.10000000000000019e53

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 52.7%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if -3.10000000000000019e53 < z < 2.19999999999999989e-262 or 2.34999999999999986e-80 < z < 7.8e9

   1. Initial program 76.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 50.6%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 39.1%

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

   if 2.19999999999999989e-262 < z < 2.34999999999999986e-80

   1. Initial program 81.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 53.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]

   6. Taylor expanded in y around inf

      \[\leadsto \left(-1 \cdot \left(j \cdot y\right)\right) \cdot i \]
   7. Step-by-step derivation

   8. Applied rewrites 38.5%

      \[\leadsto \left(\left(-j\right) \cdot y\right) \cdot i \]

   if 7.8e9 < z

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 54.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 43.7%

      \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-262}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-80}:\\ \;\;\;\;\left(\left(-j\right) \cdot y\right) \cdot i\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \left(c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-243}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-85}:\\ \;\;\;\;\left(i \cdot b\right) \cdot t\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \left(c \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= z -3.1e+53)
   (* (* z y) x)
   (if (<= z -3.6e-243)
     (* (* (- a) t) x)
     (if (<= z 1.7e-85)
       (* (* i b) t)
       (if (<= z 7800000000.0) (* (- a) (* t x)) (* (- b) (* c z)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.1e+53) {
		tmp = (z * y) * x;
	} else if (z <= -3.6e-243) {
		tmp = (-a * t) * x;
	} else if (z <= 1.7e-85) {
		tmp = (i * b) * t;
	} else if (z <= 7800000000.0) {
		tmp = -a * (t * x);
	} else {
		tmp = -b * (c * z);
	}
	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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (z <= (-3.1d+53)) then
        tmp = (z * y) * x
    else if (z <= (-3.6d-243)) then
        tmp = (-a * t) * x
    else if (z <= 1.7d-85) then
        tmp = (i * b) * t
    else if (z <= 7800000000.0d0) then
        tmp = -a * (t * x)
    else
        tmp = -b * (c * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (z <= -3.1e+53) {
		tmp = (z * y) * x;
	} else if (z <= -3.6e-243) {
		tmp = (-a * t) * x;
	} else if (z <= 1.7e-85) {
		tmp = (i * b) * t;
	} else if (z <= 7800000000.0) {
		tmp = -a * (t * x);
	} else {
		tmp = -b * (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if z <= -3.1e+53:
		tmp = (z * y) * x
	elif z <= -3.6e-243:
		tmp = (-a * t) * x
	elif z <= 1.7e-85:
		tmp = (i * b) * t
	elif z <= 7800000000.0:
		tmp = -a * (t * x)
	else:
		tmp = -b * (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (z <= -3.1e+53)
		tmp = Float64(Float64(z * y) * x);
	elseif (z <= -3.6e-243)
		tmp = Float64(Float64(Float64(-a) * t) * x);
	elseif (z <= 1.7e-85)
		tmp = Float64(Float64(i * b) * t);
	elseif (z <= 7800000000.0)
		tmp = Float64(Float64(-a) * Float64(t * x));
	else
		tmp = Float64(Float64(-b) * Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (z <= -3.1e+53)
		tmp = (z * y) * x;
	elseif (z <= -3.6e-243)
		tmp = (-a * t) * x;
	elseif (z <= 1.7e-85)
		tmp = (i * b) * t;
	elseif (z <= 7800000000.0)
		tmp = -a * (t * x);
	else
		tmp = -b * (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[z, -3.1e+53], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, -3.6e-243], N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 1.7e-85], N[(N[(i * b), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 7800000000.0], N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision], N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.10000000000000019e53

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 52.7%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if -3.10000000000000019e53 < z < -3.6000000000000001e-243

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 55.9%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(-1 \cdot \left(a \cdot t\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 43.8%

      \[\leadsto \left(\left(-a\right) \cdot t\right) \cdot x \]

   if -3.6000000000000001e-243 < z < 1.7e-85

   1. Initial program 81.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 44.3%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(b \cdot i\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 31.7%

      \[\leadsto \left(i \cdot b\right) \cdot t \]

   if 1.7e-85 < z < 7.8e9

   1. Initial program 81.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 57.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 38.1%

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

   if 7.8e9 < z

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 54.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 43.7%

      \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-243}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-85}:\\ \;\;\;\;\left(i \cdot b\right) \cdot t\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \left(c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-297}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-85}:\\ \;\;\;\;\left(i \cdot b\right) \cdot t\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \left(c \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- a) (* t x))))
   (if (<= z -3.1e+53)
     (* (* z y) x)
     (if (<= z -6e-297)
       t_1
       (if (<= z 1.7e-85)
         (* (* i b) t)
         (if (<= z 7800000000.0) t_1 (* (- b) (* c z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double tmp;
	if (z <= -3.1e+53) {
		tmp = (z * y) * x;
	} else if (z <= -6e-297) {
		tmp = t_1;
	} else if (z <= 1.7e-85) {
		tmp = (i * b) * t;
	} else if (z <= 7800000000.0) {
		tmp = t_1;
	} else {
		tmp = -b * (c * z);
	}
	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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = -a * (t * x)
    if (z <= (-3.1d+53)) then
        tmp = (z * y) * x
    else if (z <= (-6d-297)) then
        tmp = t_1
    else if (z <= 1.7d-85) then
        tmp = (i * b) * t
    else if (z <= 7800000000.0d0) then
        tmp = t_1
    else
        tmp = -b * (c * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = -a * (t * x);
	double tmp;
	if (z <= -3.1e+53) {
		tmp = (z * y) * x;
	} else if (z <= -6e-297) {
		tmp = t_1;
	} else if (z <= 1.7e-85) {
		tmp = (i * b) * t;
	} else if (z <= 7800000000.0) {
		tmp = t_1;
	} else {
		tmp = -b * (c * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -a * (t * x)
	tmp = 0
	if z <= -3.1e+53:
		tmp = (z * y) * x
	elif z <= -6e-297:
		tmp = t_1
	elif z <= 1.7e-85:
		tmp = (i * b) * t
	elif z <= 7800000000.0:
		tmp = t_1
	else:
		tmp = -b * (c * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-a) * Float64(t * x))
	tmp = 0.0
	if (z <= -3.1e+53)
		tmp = Float64(Float64(z * y) * x);
	elseif (z <= -6e-297)
		tmp = t_1;
	elseif (z <= 1.7e-85)
		tmp = Float64(Float64(i * b) * t);
	elseif (z <= 7800000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(-b) * Float64(c * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -a * (t * x);
	tmp = 0.0;
	if (z <= -3.1e+53)
		tmp = (z * y) * x;
	elseif (z <= -6e-297)
		tmp = t_1;
	elseif (z <= 1.7e-85)
		tmp = (i * b) * t;
	elseif (z <= 7800000000.0)
		tmp = t_1;
	else
		tmp = -b * (c * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-a) * N[(t * x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+53], N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, -6e-297], t$95$1, If[LessEqual[z, 1.7e-85], N[(N[(i * b), $MachinePrecision] * t), $MachinePrecision], If[LessEqual[z, 7800000000.0], t$95$1, N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.10000000000000019e53

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 57.0%

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

   6. Taylor expanded in y around inf

      \[\leadsto \left(y \cdot z\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 52.7%

      \[\leadsto \left(z \cdot y\right) \cdot x \]

   if -3.10000000000000019e53 < z < -5.9999999999999999e-297 or 1.7e-85 < z < 7.8e9

   1. Initial program 74.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 52.7%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 39.6%

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

   if -5.9999999999999999e-297 < z < 1.7e-85

   1. Initial program 83.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 45.5%

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

   6. Taylor expanded in x around 0

      \[\leadsto \left(b \cdot i\right) \cdot t \]
   7. Step-by-step derivation

   8. Applied rewrites 33.6%

      \[\leadsto \left(i \cdot b\right) \cdot t \]

   if 7.8e9 < z

   1. Initial program 66.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 54.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around inf

      \[\leadsto -1 \cdot \color{blue}{\left(b \cdot \left(c \cdot z\right)\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 43.7%

      \[\leadsto \left(-b\right) \cdot \color{blue}{\left(c \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+53}:\\ \;\;\;\;\left(z \cdot y\right) \cdot x\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-297}:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-85}:\\ \;\;\;\;\left(i \cdot b\right) \cdot t\\ \mathbf{elif}\;z \leq 7800000000:\\ \;\;\;\;\left(-a\right) \cdot \left(t \cdot x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \left(c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{if}\;x \leq -6.6 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-200}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-56}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) a (* z y)) x)))
   (if (<= x -6.6e+79)
     t_1
     (if (<= x -1.18e-200)
       (* (fma (- c) z (* i t)) b)
       (if (<= x 1.8e-56) (* (fma (- i) y (* c a)) j) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-t, a, (z * y)) * x;
	double tmp;
	if (x <= -6.6e+79) {
		tmp = t_1;
	} else if (x <= -1.18e-200) {
		tmp = fma(-c, z, (i * t)) * b;
	} else if (x <= 1.8e-56) {
		tmp = fma(-i, y, (c * a)) * j;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-t), a, Float64(z * y)) * x)
	tmp = 0.0
	if (x <= -6.6e+79)
		tmp = t_1;
	elseif (x <= -1.18e-200)
		tmp = Float64(fma(Float64(-c), z, Float64(i * t)) * b);
	elseif (x <= 1.8e-56)
		tmp = Float64(fma(Float64(-i), y, Float64(c * a)) * j);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -6.6e+79], t$95$1, If[LessEqual[x, -1.18e-200], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[x, 1.8e-56], N[(N[((-i) * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.6000000000000003e79 or 1.79999999999999989e-56 < x

   1. Initial program 73.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 69.9%

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

   if -6.6000000000000003e79 < x < -1.17999999999999996e-200

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 51.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b} \]

   if -1.17999999999999996e-200 < x < 1.79999999999999989e-56

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 52.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+79}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \mathbf{elif}\;x \leq -1.18 \cdot 10^{-200}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-56}:\\ \;\;\;\;\mathsf{fma}\left(-i, y, c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-t, a, z \cdot y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 47.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-242}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-y\right) \cdot j\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- b) c (* y x)) z)))
   (if (<= z -4.2e+48)
     t_1
     (if (<= z -1.6e-242)
       (* (* (- a) t) x)
       (if (<= z 5.6e-27) (* (fma t b (* (- y) j)) i) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = fma(-b, c, (y * x)) * z;
	double tmp;
	if (z <= -4.2e+48) {
		tmp = t_1;
	} else if (z <= -1.6e-242) {
		tmp = (-a * t) * x;
	} else if (z <= 5.6e-27) {
		tmp = fma(t, b, (-y * j)) * i;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-b), c, Float64(y * x)) * z)
	tmp = 0.0
	if (z <= -4.2e+48)
		tmp = t_1;
	elseif (z <= -1.6e-242)
		tmp = Float64(Float64(Float64(-a) * t) * x);
	elseif (z <= 5.6e-27)
		tmp = Float64(fma(t, b, Float64(Float64(-y) * j)) * i);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]}, If[LessEqual[z, -4.2e+48], t$95$1, If[LessEqual[z, -1.6e-242], N[(N[((-a) * t), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[z, 5.6e-27], N[(N[(t * b + N[((-y) * j), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.1999999999999997e48 or 5.5999999999999999e-27 < z

   1. Initial program 68.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

   5. Applied rewrites 62.3%

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

   if -4.1999999999999997e48 < z < -1.59999999999999999e-242

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 56.8%

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

   6. Taylor expanded in y around 0

      \[\leadsto \left(-1 \cdot \left(a \cdot t\right)\right) \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 44.2%

      \[\leadsto \left(\left(-a\right) \cdot t\right) \cdot x \]

   if -1.59999999999999999e-242 < z < 5.5999999999999999e-27

   1. Initial program 80.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 48.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]
   6. Step-by-step derivation

   7. Applied rewrites 48.3%

      \[\leadsto \mathsf{fma}\left(t, b, \left(-y\right) \cdot j\right) \cdot i \]
3. Recombined 3 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+48}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-242}:\\ \;\;\;\;\left(\left(-a\right) \cdot t\right) \cdot x\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-27}:\\ \;\;\;\;\mathsf{fma}\left(t, b, \left(-y\right) \cdot j\right) \cdot i\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 51.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+140} \lor \neg \left(a \leq 1.1 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -8e+140) (not (<= a 1.1e+69)))
   (* (fma (- t) x (* j c)) a)
   (* (fma (- i) j (* z x)) y)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -8e+140) || !(a <= 1.1e+69)) {
		tmp = fma(-t, x, (j * c)) * a;
	} else {
		tmp = fma(-i, j, (z * x)) * y;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -8e+140) || !(a <= 1.1e+69))
		tmp = Float64(fma(Float64(-t), x, Float64(j * c)) * a);
	else
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -8e+140], N[Not[LessEqual[a, 1.1e+69]], $MachinePrecision]], N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -8.00000000000000047e140 or 1.1000000000000001e69 < a

   1. Initial program 55.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf

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

   5. Applied rewrites 77.9%

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

   if -8.00000000000000047e140 < a < 1.1000000000000001e69

   1. Initial program 83.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

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

   5. Applied rewrites 50.8%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -8 \cdot 10^{+140} \lor \neg \left(a \leq 1.1 \cdot 10^{+69}\right):\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 28.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+80} \lor \neg \left(a \leq 2 \cdot 10^{+226}\right):\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -5.8e+80) (not (<= a 2e+226))) (* (* c a) j) (* (* y x) z)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -5.8e+80) || !(a <= 2e+226)) {
		tmp = (c * a) * j;
	} else {
		tmp = (y * x) * z;
	}
	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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-5.8d+80)) .or. (.not. (a <= 2d+226))) then
        tmp = (c * a) * j
    else
        tmp = (y * x) * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -5.8e+80) || !(a <= 2e+226)) {
		tmp = (c * a) * j;
	} else {
		tmp = (y * x) * z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -5.8e+80) or not (a <= 2e+226):
		tmp = (c * a) * j
	else:
		tmp = (y * x) * z
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -5.8e+80) || !(a <= 2e+226))
		tmp = Float64(Float64(c * a) * j);
	else
		tmp = Float64(Float64(y * x) * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -5.8e+80) || ~((a <= 2e+226)))
		tmp = (c * a) * j;
	else
		tmp = (y * x) * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -5.8e+80], N[Not[LessEqual[a, 2e+226]], $MachinePrecision]], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.79999999999999971e80 or 1.99999999999999992e226 < a

   1. Initial program 59.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 54.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 47.1%

      \[\leadsto \left(j \cdot c\right) \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 49.8%

       \[\leadsto \left(c \cdot a\right) \cdot j \]

   if -5.79999999999999971e80 < a < 1.99999999999999992e226

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

   5. Applied rewrites 41.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 27.2%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+80} \lor \neg \left(a \leq 2 \cdot 10^{+226}\right):\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.3% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+23} \lor \neg \left(a \leq 4.5 \cdot 10^{+128}\right):\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -4.8e+23) (not (<= a 4.5e+128))) (* (* c a) j) (* (* i t) b)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -4.8e+23) || !(a <= 4.5e+128)) {
		tmp = (c * a) * j;
	} else {
		tmp = (i * t) * b;
	}
	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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-4.8d+23)) .or. (.not. (a <= 4.5d+128))) then
        tmp = (c * a) * j
    else
        tmp = (i * t) * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -4.8e+23) || !(a <= 4.5e+128)) {
		tmp = (c * a) * j;
	} else {
		tmp = (i * t) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -4.8e+23) or not (a <= 4.5e+128):
		tmp = (c * a) * j
	else:
		tmp = (i * t) * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -4.8e+23) || !(a <= 4.5e+128))
		tmp = Float64(Float64(c * a) * j);
	else
		tmp = Float64(Float64(i * t) * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -4.8e+23) || ~((a <= 4.5e+128)))
		tmp = (c * a) * j;
	else
		tmp = (i * t) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -4.8e+23], N[Not[LessEqual[a, 4.5e+128]], $MachinePrecision]], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8e23 or 4.5000000000000001e128 < a

   1. Initial program 57.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 45.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.5%

      \[\leadsto \left(j \cdot c\right) \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 39.4%

       \[\leadsto \left(c \cdot a\right) \cdot j \]

   if -4.8e23 < a < 4.5000000000000001e128

   1. Initial program 84.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 24.5%

      \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+23} \lor \neg \left(a \leq 4.5 \cdot 10^{+128}\right):\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.4% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+80}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+226}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -5.8e+80)
   (* (* c a) j)
   (if (<= a 2e+226) (* (* y x) z) (* (* j a) c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5.8e+80) {
		tmp = (c * a) * j;
	} else if (a <= 2e+226) {
		tmp = (y * x) * z;
	} else {
		tmp = (j * a) * c;
	}
	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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-5.8d+80)) then
        tmp = (c * a) * j
    else if (a <= 2d+226) then
        tmp = (y * x) * z
    else
        tmp = (j * a) * c
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5.8e+80) {
		tmp = (c * a) * j;
	} else if (a <= 2e+226) {
		tmp = (y * x) * z;
	} else {
		tmp = (j * a) * c;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -5.8e+80:
		tmp = (c * a) * j
	elif a <= 2e+226:
		tmp = (y * x) * z
	else:
		tmp = (j * a) * c
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -5.8e+80)
		tmp = Float64(Float64(c * a) * j);
	elseif (a <= 2e+226)
		tmp = Float64(Float64(y * x) * z);
	else
		tmp = Float64(Float64(j * a) * c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -5.8e+80)
		tmp = (c * a) * j;
	elseif (a <= 2e+226)
		tmp = (y * x) * z;
	else
		tmp = (j * a) * c;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -5.8e+80], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[a, 2e+226], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.79999999999999971e80

   1. Initial program 58.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 50.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 42.0%

      \[\leadsto \left(j \cdot c\right) \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 46.0%

       \[\leadsto \left(c \cdot a\right) \cdot j \]

   if -5.79999999999999971e80 < a < 1.99999999999999992e226

   1. Initial program 79.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

   5. Applied rewrites 41.6%

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

   6. Taylor expanded in x around inf

      \[\leadsto \left(x \cdot y\right) \cdot z \]
   7. Step-by-step derivation

   8. Applied rewrites 27.2%

      \[\leadsto \left(y \cdot x\right) \cdot z \]

   if 1.99999999999999992e226 < a

   1. Initial program 62.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 62.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto \left(a \cdot j\right) \cdot c \]
   7. Step-by-step derivation

   8. Applied rewrites 63.1%

      \[\leadsto \left(j \cdot a\right) \cdot c \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{+80}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+226}:\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot a\right) \cdot c\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.2% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+128}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot c\right) \cdot a\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -4.8e+23)
   (* (* c a) j)
   (if (<= a 4.5e+128) (* (* i t) b) (* (* j c) a))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -4.8e+23) {
		tmp = (c * a) * j;
	} else if (a <= 4.5e+128) {
		tmp = (i * t) * b;
	} else {
		tmp = (j * c) * a;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

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

real(8) function code(x, y, z, t, a, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-4.8d+23)) then
        tmp = (c * a) * j
    else if (a <= 4.5d+128) then
        tmp = (i * t) * b
    else
        tmp = (j * c) * a
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -4.8e+23) {
		tmp = (c * a) * j;
	} else if (a <= 4.5e+128) {
		tmp = (i * t) * b;
	} else {
		tmp = (j * c) * a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -4.8e+23:
		tmp = (c * a) * j
	elif a <= 4.5e+128:
		tmp = (i * t) * b
	else:
		tmp = (j * c) * a
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -4.8e+23)
		tmp = Float64(Float64(c * a) * j);
	elseif (a <= 4.5e+128)
		tmp = Float64(Float64(i * t) * b);
	else
		tmp = Float64(Float64(j * c) * a);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -4.8e+23)
		tmp = (c * a) * j;
	elseif (a <= 4.5e+128)
		tmp = (i * t) * b;
	else
		tmp = (j * c) * a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -4.8e+23], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], If[LessEqual[a, 4.5e+128], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision], N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -4.8e23

   1. Initial program 61.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 48.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 35.4%

      \[\leadsto \left(j \cdot c\right) \cdot \color{blue}{a} \]
   9. Step-by-step derivation

   10. Applied rewrites 38.6%

       \[\leadsto \left(c \cdot a\right) \cdot j \]

   if -4.8e23 < a < 4.5000000000000001e128

   1. Initial program 84.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

   5. Applied rewrites 42.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]

   6. Taylor expanded in y around 0

      \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 24.5%

      \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]

   if 4.5000000000000001e128 < a

   1. Initial program 51.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around inf

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   5. Applied rewrites 40.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c} \]

   6. Taylor expanded in z around 0

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
   7. Step-by-step derivation

   8. Applied rewrites 40.6%

      \[\leadsto \left(j \cdot c\right) \cdot \color{blue}{a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+23}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+128}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;\left(j \cdot c\right) \cdot a\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.2% accurate, 5.5× speedup

Math

\[\begin{array}{l} \\ \left(i \cdot t\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* (* i t) b))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (i * t) * b;
}

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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = (i * t) * b
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return (i * t) * b;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return (i * t) * b

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(Float64(i * t) * b)
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = (i * t) * b;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]

Derivation

1. Initial program 73.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in i around inf

   \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
4. Step-by-step derivation

5. Applied rewrites 34.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]

6. Taylor expanded in y around 0

   \[\leadsto b \cdot \color{blue}{\left(i \cdot t\right)} \]
7. Step-by-step derivation

8. Applied rewrites 18.5%

   \[\leadsto \left(i \cdot t\right) \cdot \color{blue}{b} \]

9. Final simplification 18.5%

   \[\leadsto \left(i \cdot t\right) \cdot b \]
10. Add Preprocessing

Developer Target 1: 59.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	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, b, c, i, j)
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), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2025018 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -293938859355541/2000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 32113527362226803/10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))