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

Percentage Accurate: 73.6% → 81.9%

Time: 11.7s

Alternatives: 22

Speedup: 1.0×

• 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: 81.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i))))
          (* j (- (* c a) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* (fma (- t) a (* 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 = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma(-t, a, (z * y)) * x;
	}
	return tmp;
}

Julia

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i)))) < +inf.0

   1. Initial program 91.1%

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

   if +inf.0 < (+.f64 (-.f64 (*.f64 x (-.f64 (*.f64 y z) (*.f64 t a))) (*.f64 b (-.f64 (*.f64 c z) (*.f64 t i)))) (*.f64 j (-.f64 (*.f64 c a) (*.f64 y i))))

   1. Initial program 0.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 55.2%

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

Alternative 2: 73.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ t_2 := \mathsf{fma}\left(i \cdot t, b, \mathsf{fma}\left(\mathsf{fma}\left(-t, x, j \cdot c\right), a, t\_1\right)\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-116}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{-281}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\right)\\ \mathbf{elif}\;a \leq 2.1 \cdot 10^{-66}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- i) j (* z x)) y))
        (t_2 (fma (* i t) b (fma (fma (- t) x (* j c)) a t_1))))
   (if (<= a -2.3e-116)
     t_2
     (if (<= a -1.12e-281)
       (fma (fma (- t) a (* z y)) x (* (fma (- y) j (* b t)) i))
       (if (<= a 2.1e-66) (fma (fma (- c) z (* i t)) 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 = fma(-i, j, (z * x)) * y;
	double t_2 = fma((i * t), b, fma(fma(-t, x, (j * c)), a, t_1));
	double tmp;
	if (a <= -2.3e-116) {
		tmp = t_2;
	} else if (a <= -1.12e-281) {
		tmp = fma(fma(-t, a, (z * y)), x, (fma(-y, j, (b * t)) * i));
	} else if (a <= 2.1e-66) {
		tmp = fma(fma(-c, z, (i * t)), b, t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(fma(Float64(-i), j, Float64(z * x)) * y)
	t_2 = fma(Float64(i * t), b, fma(fma(Float64(-t), x, Float64(j * c)), a, t_1))
	tmp = 0.0
	if (a <= -2.3e-116)
		tmp = t_2;
	elseif (a <= -1.12e-281)
		tmp = fma(fma(Float64(-t), a, Float64(z * y)), x, Float64(fma(Float64(-y), j, Float64(b * t)) * i));
	elseif (a <= 2.1e-66)
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, Block[{t$95$2 = N[(N[(i * t), $MachinePrecision] * b + N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a + t$95$1), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.3e-116], t$95$2, If[LessEqual[a, -1.12e-281], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.1e-66], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + t$95$1), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.30000000000000002e-116 or 2.1e-66 < 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 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 83.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 80.2%

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

   if -2.30000000000000002e-116 < a < -1.12e-281

   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 c around 0

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

   5. Applied rewrites 85.4%

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

   if -1.12e-281 < a < 2.1e-66

   1. Initial program 80.3%

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

   3. Taylor expanded in a around 0

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

   5. Applied rewrites 78.2%

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

Alternative 3: 77.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq 1.45 \cdot 10^{+226}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \mathsf{fma}\left(\mathsf{fma}\left(-t, x, j \cdot c\right), a, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i 1.45e+226)
   (fma
    (fma (- c) z (* i t))
    b
    (fma (fma (- t) x (* j c)) a (* (fma (- i) j (* z x)) y)))
   (* (fma (- y) j (* b t)) 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 (i <= 1.45e+226) {
		tmp = fma(fma(-c, z, (i * t)), b, fma(fma(-t, x, (j * c)), a, (fma(-i, j, (z * x)) * y)));
	} else {
		tmp = fma(-y, j, (b * t)) * i;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= 1.45e+226)
		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 = Float64(fma(Float64(-y), j, Float64(b * t)) * i);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, 1.45e+226], 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[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < 1.44999999999999987e226

   1. Initial program 75.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 80.8%

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

   if 1.44999999999999987e226 < i

   1. Initial program 62.7%

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

   3. Taylor expanded in 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 95.8%

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

Alternative 4: 70.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, a, z \cdot y\right)\\ t_2 := \mathsf{fma}\left(-c, z, i \cdot t\right)\\ t_3 := \mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \mathbf{if}\;i \leq -2.3 \cdot 10^{+249}:\\ \;\;\;\;t\_2 \cdot b\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-24}:\\ \;\;\;\;\mathsf{fma}\left(t\_1, x, t\_3\right)\\ \mathbf{elif}\;i \leq 170000000000:\\ \;\;\;\;\mathsf{fma}\left(t\_1, x, \mathsf{fma}\left(-z, b, j \cdot a\right) \cdot c\right)\\ \mathbf{elif}\;i \leq 3 \cdot 10^{+208}:\\ \;\;\;\;\mathsf{fma}\left(t\_2, b, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (fma (- t) a (* z y)))
        (t_2 (fma (- c) z (* i t)))
        (t_3 (* (fma (- y) j (* b t)) i)))
   (if (<= i -2.3e+249)
     (* t_2 b)
     (if (<= i -1.1e-24)
       (fma t_1 x t_3)
       (if (<= i 170000000000.0)
         (fma t_1 x (* (fma (- z) b (* j a)) c))
         (if (<= i 3e+208) (fma t_2 b (* (fma (- i) j (* z x)) y)) t_3))))))

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));
	double t_2 = fma(-c, z, (i * t));
	double t_3 = fma(-y, j, (b * t)) * i;
	double tmp;
	if (i <= -2.3e+249) {
		tmp = t_2 * b;
	} else if (i <= -1.1e-24) {
		tmp = fma(t_1, x, t_3);
	} else if (i <= 170000000000.0) {
		tmp = fma(t_1, x, (fma(-z, b, (j * a)) * c));
	} else if (i <= 3e+208) {
		tmp = fma(t_2, b, (fma(-i, j, (z * x)) * y));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = fma(Float64(-t), a, Float64(z * y))
	t_2 = fma(Float64(-c), z, Float64(i * t))
	t_3 = Float64(fma(Float64(-y), j, Float64(b * t)) * i)
	tmp = 0.0
	if (i <= -2.3e+249)
		tmp = Float64(t_2 * b);
	elseif (i <= -1.1e-24)
		tmp = fma(t_1, x, t_3);
	elseif (i <= 170000000000.0)
		tmp = fma(t_1, x, Float64(fma(Float64(-z), b, Float64(j * a)) * c));
	elseif (i <= 3e+208)
		tmp = fma(t_2, b, Float64(fma(Float64(-i), j, Float64(z * x)) * y));
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[i, -2.3e+249], N[(t$95$2 * b), $MachinePrecision], If[LessEqual[i, -1.1e-24], N[(t$95$1 * x + t$95$3), $MachinePrecision], If[LessEqual[i, 170000000000.0], N[(t$95$1 * x + N[(N[((-z) * b + N[(j * a), $MachinePrecision]), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3e+208], N[(t$95$2 * b + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.2999999999999998e249

   1. Initial program 44.4%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 77.8%

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

   if -2.2999999999999998e249 < i < -1.10000000000000001e-24

   1. Initial program 80.5%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 82.3%

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

   if -1.10000000000000001e-24 < i < 1.7e11

   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 i around 0

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

   5. Applied rewrites 74.9%

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

   if 1.7e11 < i < 2.99999999999999995e208

   1. Initial program 67.5%

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

   3. Taylor expanded in a around 0

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

   5. Applied rewrites 77.0%

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

   if 2.99999999999999995e208 < i

   1. Initial program 64.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 86.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 65.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-156} \lor \neg \left(x \leq 4.5 \cdot 10^{-112}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) \cdot b\right) \cdot c + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -1.85e-156) (not (<= x 4.5e-112)))
   (fma (fma (- t) a (* z y)) x (* (fma (- y) j (* b t)) i))
   (+ (* (* (- z) b) c) (* 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 ((x <= -1.85e-156) || !(x <= 4.5e-112)) {
		tmp = fma(fma(-t, a, (z * y)), x, (fma(-y, j, (b * t)) * i));
	} else {
		tmp = ((-z * b) * c) + (j * ((c * a) - (y * i)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -1.85e-156) || !(x <= 4.5e-112))
		tmp = fma(fma(Float64(-t), a, Float64(z * y)), x, Float64(fma(Float64(-y), j, Float64(b * t)) * i));
	else
		tmp = Float64(Float64(Float64(Float64(-z) * b) * c) + 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[x, -1.85e-156], N[Not[LessEqual[x, 4.5e-112]], $MachinePrecision]], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision], N[(N[(N[((-z) * b), $MachinePrecision] * c), $MachinePrecision] + N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.85e-156 or 4.50000000000000012e-112 < x

   1. Initial program 77.2%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 75.3%

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

   if -1.85e-156 < x < 4.50000000000000012e-112

   1. Initial program 65.9%

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

   3. Taylor expanded in c around inf

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

   5. Applied rewrites 66.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-156} \lor \neg \left(x \leq 4.5 \cdot 10^{-112}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(-z\right) \cdot b\right) \cdot c + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-70} \lor \neg \left(a \leq 7000000\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \left(j \cdot a\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -3.1e-70) (not (<= a 7000000.0)))
   (fma (fma (- t) a (* z y)) x (* (* j a) c))
   (fma (fma (- c) z (* i t)) b (* (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 <= -3.1e-70) || !(a <= 7000000.0)) {
		tmp = fma(fma(-t, a, (z * y)), x, ((j * a) * c));
	} else {
		tmp = fma(fma(-c, z, (i * t)), b, (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 <= -3.1e-70) || !(a <= 7000000.0))
		tmp = fma(fma(Float64(-t), a, Float64(z * y)), x, Float64(Float64(j * a) * c));
	else
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, 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, -3.1e-70], N[Not[LessEqual[a, 7000000.0]], $MachinePrecision]], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.1e-70 or 7e6 < a

   1. Initial program 66.7%

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

   3. Taylor expanded in i around 0

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

   5. Applied rewrites 72.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 69.8%

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

   if -3.1e-70 < a < 7e6

   1. Initial program 82.8%

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

   3. Taylor expanded in a around 0

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

   5. Applied rewrites 75.3%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.1 \cdot 10^{-70} \lor \neg \left(a \leq 7000000\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \left(j \cdot a\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 52.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.95 \cdot 10^{+249}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot t, b, \mathsf{fma}\left(-j, i, z \cdot x\right) \cdot y\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-249}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-286}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;i \leq 250000:\\ \;\;\;\;\mathsf{fma}\left(z, y, \left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.95e+249)
   (* (fma (- c) z (* i t)) b)
   (if (<= i -2.1e-25)
     (fma (* i t) b (* (fma (- j) i (* z x)) y))
     (if (<= i -1.1e-249)
       (* (fma (- t) x (* j c)) a)
       (if (<= i 9.5e-286)
         (* (fma (- b) c (* y x)) z)
         (if (<= i 250000.0)
           (* (fma z y (* (- t) a)) x)
           (* (fma (- y) j (* b t)) 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 (i <= -1.95e+249) {
		tmp = fma(-c, z, (i * t)) * b;
	} else if (i <= -2.1e-25) {
		tmp = fma((i * t), b, (fma(-j, i, (z * x)) * y));
	} else if (i <= -1.1e-249) {
		tmp = fma(-t, x, (j * c)) * a;
	} else if (i <= 9.5e-286) {
		tmp = fma(-b, c, (y * x)) * z;
	} else if (i <= 250000.0) {
		tmp = fma(z, y, (-t * a)) * x;
	} else {
		tmp = fma(-y, j, (b * t)) * i;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.95e+249)
		tmp = Float64(fma(Float64(-c), z, Float64(i * t)) * b);
	elseif (i <= -2.1e-25)
		tmp = fma(Float64(i * t), b, Float64(fma(Float64(-j), i, Float64(z * x)) * y));
	elseif (i <= -1.1e-249)
		tmp = Float64(fma(Float64(-t), x, Float64(j * c)) * a);
	elseif (i <= 9.5e-286)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	elseif (i <= 250000.0)
		tmp = Float64(fma(z, y, Float64(Float64(-t) * a)) * x);
	else
		tmp = Float64(fma(Float64(-y), j, Float64(b * t)) * i);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.95e+249], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[i, -2.1e-25], N[(N[(i * t), $MachinePrecision] * b + N[(N[((-j) * i + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.1e-249], N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 9.5e-286], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[i, 250000.0], N[(N[(z * y + N[((-t) * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.9499999999999998e249

   1. Initial program 44.4%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 77.8%

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

   if -1.9499999999999998e249 < i < -2.10000000000000002e-25

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 75.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 77.6%

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

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{fma}\left(i \cdot t, b, y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 70.5%

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

   if -2.10000000000000002e-25 < i < -1.1e-249

   1. Initial program 74.7%

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

   3. Taylor expanded in 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 58.1%

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

   if -1.1e-249 < i < 9.5000000000000004e-286

   1. Initial program 73.3%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 73.7%

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

   if 9.5000000000000004e-286 < i < 2.5e5

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 64.8%

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

   7. Applied rewrites 64.8%

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

   if 2.5e5 < i

   1. Initial program 66.8%

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

   3. Taylor expanded in 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 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]
3. Recombined 6 regimes into one program.
4. Add Preprocessing

Alternative 8: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{if}\;a \leq -1.9 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(z, y, \left(-t\right) \cdot a\right) \cdot x\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-262}:\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{elif}\;a \leq 3.5 \cdot 10^{-169}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;a \leq 1400000:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (fma (- t) x (* j c)) a)))
   (if (<= a -1.9e+169)
     t_1
     (if (<= a -3.2e+52)
       (* (fma z y (* (- t) a)) x)
       (if (<= a -1.7e-262)
         (* (fma (- i) j (* z x)) y)
         (if (<= a 3.5e-169)
           (* (fma (- b) c (* y x)) z)
           (if (<= a 1400000.0) (* (fma (- c) z (* i t)) b) 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 tmp;
	if (a <= -1.9e+169) {
		tmp = t_1;
	} else if (a <= -3.2e+52) {
		tmp = fma(z, y, (-t * a)) * x;
	} else if (a <= -1.7e-262) {
		tmp = fma(-i, j, (z * x)) * y;
	} else if (a <= 3.5e-169) {
		tmp = fma(-b, c, (y * x)) * z;
	} else if (a <= 1400000.0) {
		tmp = fma(-c, z, (i * t)) * b;
	} 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)
	tmp = 0.0
	if (a <= -1.9e+169)
		tmp = t_1;
	elseif (a <= -3.2e+52)
		tmp = Float64(fma(z, y, Float64(Float64(-t) * a)) * x);
	elseif (a <= -1.7e-262)
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	elseif (a <= 3.5e-169)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	elseif (a <= 1400000.0)
		tmp = Float64(fma(Float64(-c), z, Float64(i * t)) * b);
	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]}, If[LessEqual[a, -1.9e+169], t$95$1, If[LessEqual[a, -3.2e+52], N[(N[(z * y + N[((-t) * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[a, -1.7e-262], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[a, 3.5e-169], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[a, 1400000.0], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.89999999999999996e169 or 1.4e6 < a

   1. Initial program 66.0%

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

   3. Taylor expanded in 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 63.6%

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

   if -1.89999999999999996e169 < a < -3.2e52

   1. Initial program 65.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 62.4%

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

   7. Applied rewrites 66.3%

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

   if -3.2e52 < a < -1.69999999999999995e-262

   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 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 60.4%

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

   if -1.69999999999999995e-262 < a < 3.5000000000000003e-169

   1. Initial program 83.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 72.6%

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

   if 3.5000000000000003e-169 < a < 1.4e6

   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 b around inf

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

   5. Applied rewrites 55.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 9: 60.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.36 \cdot 10^{-70} \lor \neg \left(a \leq 120000\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \left(j \cdot a\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(\left(-j\right) \cdot y\right) \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.36e-70) (not (<= a 120000.0)))
   (fma (fma (- t) a (* z y)) x (* (* j a) c))
   (fma (fma (- c) z (* i t)) b (* (* (- j) 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 ((a <= -1.36e-70) || !(a <= 120000.0)) {
		tmp = fma(fma(-t, a, (z * y)), x, ((j * a) * c));
	} else {
		tmp = fma(fma(-c, z, (i * t)), b, ((-j * y) * i));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.36e-70) || !(a <= 120000.0))
		tmp = fma(fma(Float64(-t), a, Float64(z * y)), x, Float64(Float64(j * a) * c));
	else
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, Float64(Float64(Float64(-j) * y) * i));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.36e-70], N[Not[LessEqual[a, 120000.0]], $MachinePrecision]], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-j) * y), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.36000000000000001e-70 or 1.2e5 < a

   1. Initial program 66.7%

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

   3. Taylor expanded in i around 0

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

   5. Applied rewrites 72.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 69.8%

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

   if -1.36000000000000001e-70 < a < 1.2e5

   1. Initial program 82.8%

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

   3. Taylor expanded in 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 72.9%

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

   6. Taylor expanded in i around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 68.7%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.36 \cdot 10^{-70} \lor \neg \left(a \leq 120000\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \left(j \cdot a\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(\left(-j\right) \cdot y\right) \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-71} \lor \neg \left(a \leq 80000\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \left(j \cdot a\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(\left(-i\right) \cdot y\right) \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -7e-71) (not (<= a 80000.0)))
   (fma (fma (- t) a (* z y)) x (* (* j a) c))
   (fma (fma (- c) z (* i t)) b (* (* (- i) y) j))))

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 <= -7e-71) || !(a <= 80000.0)) {
		tmp = fma(fma(-t, a, (z * y)), x, ((j * a) * c));
	} else {
		tmp = fma(fma(-c, z, (i * t)), b, ((-i * y) * j));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -7e-71) || !(a <= 80000.0))
		tmp = fma(fma(Float64(-t), a, Float64(z * y)), x, Float64(Float64(j * a) * c));
	else
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, Float64(Float64(Float64(-i) * y) * j));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -7e-71], N[Not[LessEqual[a, 80000.0]], $MachinePrecision]], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + N[(N[((-i) * y), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.9999999999999998e-71 or 8e4 < a

   1. Initial program 66.7%

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

   3. Taylor expanded in i around 0

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

   5. Applied rewrites 72.6%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 69.8%

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

   if -6.9999999999999998e-71 < a < 8e4

   1. Initial program 82.8%

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

   3. Taylor expanded in 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 72.9%

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

   6. Taylor expanded in i around inf

      \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, -1 \cdot \left(i \cdot \left(j \cdot y\right)\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 68.7%

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

   10. Applied rewrites 67.2%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-71} \lor \neg \left(a \leq 80000\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \left(j \cdot a\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(\left(-i\right) \cdot y\right) \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 48.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(i \cdot t, b, \left(z \cdot y\right) \cdot x\right)\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-249}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-286}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;i \leq 250000:\\ \;\;\;\;\mathsf{fma}\left(z, y, \left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -7e-25)
   (fma (* i t) b (* (* z y) x))
   (if (<= i -1.1e-249)
     (* (fma (- t) x (* j c)) a)
     (if (<= i 9.5e-286)
       (* (fma (- b) c (* y x)) z)
       (if (<= i 250000.0)
         (* (fma z y (* (- t) a)) x)
         (* (fma (- y) j (* b t)) 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 (i <= -7e-25) {
		tmp = fma((i * t), b, ((z * y) * x));
	} else if (i <= -1.1e-249) {
		tmp = fma(-t, x, (j * c)) * a;
	} else if (i <= 9.5e-286) {
		tmp = fma(-b, c, (y * x)) * z;
	} else if (i <= 250000.0) {
		tmp = fma(z, y, (-t * a)) * x;
	} else {
		tmp = fma(-y, j, (b * t)) * i;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -7e-25)
		tmp = fma(Float64(i * t), b, Float64(Float64(z * y) * x));
	elseif (i <= -1.1e-249)
		tmp = Float64(fma(Float64(-t), x, Float64(j * c)) * a);
	elseif (i <= 9.5e-286)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	elseif (i <= 250000.0)
		tmp = Float64(fma(z, y, Float64(Float64(-t) * a)) * x);
	else
		tmp = Float64(fma(Float64(-y), j, Float64(b * t)) * i);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -7e-25], N[(N[(i * t), $MachinePrecision] * b + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.1e-249], N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 9.5e-286], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[i, 250000.0], N[(N[(z * y + N[((-t) * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -7.0000000000000004e-25

   1. Initial program 75.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 71.2%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 70.0%

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

   9. Taylor expanded in z around inf

      \[\leadsto \mathsf{fma}\left(i \cdot t, b, x \cdot \left(y \cdot z\right)\right) \]
   10. Step-by-step derivation

   11. Applied rewrites 57.9%

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

   if -7.0000000000000004e-25 < i < -1.1e-249

   1. Initial program 74.7%

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

   3. Taylor expanded in 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 58.1%

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

   if -1.1e-249 < i < 9.5000000000000004e-286

   1. Initial program 73.3%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 73.7%

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

   if 9.5000000000000004e-286 < i < 2.5e5

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 64.8%

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

   7. Applied rewrites 64.8%

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

   if 2.5e5 < i

   1. Initial program 66.8%

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

   3. Taylor expanded in 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 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 12: 48.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -7 \cdot 10^{-25}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\\ \mathbf{elif}\;i \leq -1.1 \cdot 10^{-249}:\\ \;\;\;\;\mathsf{fma}\left(-t, x, j \cdot c\right) \cdot a\\ \mathbf{elif}\;i \leq 9.5 \cdot 10^{-286}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \mathbf{elif}\;i \leq 250000:\\ \;\;\;\;\mathsf{fma}\left(z, y, \left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -7e-25)
   (* (fma (- c) z (* i t)) b)
   (if (<= i -1.1e-249)
     (* (fma (- t) x (* j c)) a)
     (if (<= i 9.5e-286)
       (* (fma (- b) c (* y x)) z)
       (if (<= i 250000.0)
         (* (fma z y (* (- t) a)) x)
         (* (fma (- y) j (* b t)) 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 (i <= -7e-25) {
		tmp = fma(-c, z, (i * t)) * b;
	} else if (i <= -1.1e-249) {
		tmp = fma(-t, x, (j * c)) * a;
	} else if (i <= 9.5e-286) {
		tmp = fma(-b, c, (y * x)) * z;
	} else if (i <= 250000.0) {
		tmp = fma(z, y, (-t * a)) * x;
	} else {
		tmp = fma(-y, j, (b * t)) * i;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -7e-25)
		tmp = Float64(fma(Float64(-c), z, Float64(i * t)) * b);
	elseif (i <= -1.1e-249)
		tmp = Float64(fma(Float64(-t), x, Float64(j * c)) * a);
	elseif (i <= 9.5e-286)
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	elseif (i <= 250000.0)
		tmp = Float64(fma(z, y, Float64(Float64(-t) * a)) * x);
	else
		tmp = Float64(fma(Float64(-y), j, Float64(b * t)) * i);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -7e-25], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision], If[LessEqual[i, -1.1e-249], N[(N[((-t) * x + N[(j * c), $MachinePrecision]), $MachinePrecision] * a), $MachinePrecision], If[LessEqual[i, 9.5e-286], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision], If[LessEqual[i, 250000.0], N[(N[(z * y + N[((-t) * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[((-y) * j + N[(b * t), $MachinePrecision]), $MachinePrecision] * i), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -7.0000000000000004e-25

   1. Initial program 75.5%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 54.6%

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

   if -7.0000000000000004e-25 < i < -1.1e-249

   1. Initial program 74.7%

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

   3. Taylor expanded in 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 58.1%

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

   if -1.1e-249 < i < 9.5000000000000004e-286

   1. Initial program 73.3%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 73.7%

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

   if 9.5000000000000004e-286 < i < 2.5e5

   1. Initial program 81.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 64.8%

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

   7. Applied rewrites 64.8%

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

   if 2.5e5 < i

   1. Initial program 66.8%

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

   3. Taylor expanded in 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 70.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, j, b \cdot t\right) \cdot i} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 13: 59.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-70} \lor \neg \left(a \leq 1.9 \cdot 10^{-65}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \left(j \cdot a\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(z \cdot y\right) \cdot x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.3e-70) (not (<= a 1.9e-65)))
   (fma (fma (- t) a (* z y)) x (* (* j a) c))
   (fma (fma (- c) z (* i t)) b (* (* 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 tmp;
	if ((a <= -1.3e-70) || !(a <= 1.9e-65)) {
		tmp = fma(fma(-t, a, (z * y)), x, ((j * a) * c));
	} else {
		tmp = fma(fma(-c, z, (i * t)), b, ((z * y) * x));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.3e-70) || !(a <= 1.9e-65))
		tmp = fma(fma(Float64(-t), a, Float64(z * y)), x, Float64(Float64(j * a) * c));
	else
		tmp = fma(fma(Float64(-c), z, Float64(i * t)), b, Float64(Float64(z * y) * x));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.3e-70], N[Not[LessEqual[a, 1.9e-65]], $MachinePrecision]], N[(N[((-t) * a + N[(z * y), $MachinePrecision]), $MachinePrecision] * x + N[(N[(j * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.30000000000000001e-70 or 1.9000000000000001e-65 < a

   1. Initial program 68.7%

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

   3. Taylor expanded in i around 0

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

   5. Applied rewrites 70.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 67.7%

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

   if -1.30000000000000001e-70 < a < 1.9000000000000001e-65

   1. Initial program 82.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 69.9%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 66.2%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{-70} \lor \neg \left(a \leq 1.9 \cdot 10^{-65}\right):\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-t, a, z \cdot y\right), x, \left(j \cdot a\right) \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\mathsf{fma}\left(-c, z, i \cdot t\right), b, \left(z \cdot y\right) \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 51.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+80} \lor \neg \left(y \leq 10^{+70}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, a, i \cdot b\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -5.5e+80) (not (<= y 1e+70)))
   (* (fma (- i) j (* z x)) y)
   (* (fma (- x) a (* i b)) t)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((y <= -5.5e+80) || !(y <= 1e+70)) {
		tmp = fma(-i, j, (z * x)) * y;
	} else {
		tmp = fma(-x, a, (i * b)) * t;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -5.5e+80) || !(y <= 1e+70))
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	else
		tmp = Float64(fma(Float64(-x), a, Float64(i * b)) * t);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -5.5e+80], N[Not[LessEqual[y, 1e+70]], $MachinePrecision]], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[((-x) * a + N[(i * b), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.49999999999999967e80 or 1.00000000000000007e70 < y

   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 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 75.5%

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

   if -5.49999999999999967e80 < y < 1.00000000000000007e70

   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 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 50.4%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+80} \lor \neg \left(y \leq 10^{+70}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-x, a, i \cdot b\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+81} \lor \neg \left(y \leq 2 \cdot 10^{+50}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -1.4e+81) (not (<= y 2e+50)))
   (* (fma (- i) j (* z x)) y)
   (* (fma (- c) z (* 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 ((y <= -1.4e+81) || !(y <= 2e+50)) {
		tmp = fma(-i, j, (z * x)) * y;
	} else {
		tmp = fma(-c, z, (i * t)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -1.4e+81) || !(y <= 2e+50))
		tmp = Float64(fma(Float64(-i), j, Float64(z * x)) * y);
	else
		tmp = Float64(fma(Float64(-c), z, Float64(i * t)) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -1.4e+81], N[Not[LessEqual[y, 2e+50]], $MachinePrecision]], N[(N[((-i) * j + N[(z * x), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999997e81 or 2.0000000000000002e50 < y

   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 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 72.8%

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

   if -1.39999999999999997e81 < y < 2.0000000000000002e50

   1. Initial program 80.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 45.9%

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

4. Final simplification 56.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+81} \lor \neg \left(y \leq 2 \cdot 10^{+50}\right):\\ \;\;\;\;\mathsf{fma}\left(-i, j, z \cdot x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 49.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-111} \lor \neg \left(x \leq 4.4 \cdot 10^{+74}\right):\\ \;\;\;\;\mathsf{fma}\left(z, y, \left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -9.5e-111) (not (<= x 4.4e+74)))
   (* (fma z y (* (- t) a)) x)
   (* (fma (- c) z (* 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 ((x <= -9.5e-111) || !(x <= 4.4e+74)) {
		tmp = fma(z, y, (-t * a)) * x;
	} else {
		tmp = fma(-c, z, (i * t)) * b;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -9.5e-111) || !(x <= 4.4e+74))
		tmp = Float64(fma(z, y, Float64(Float64(-t) * a)) * x);
	else
		tmp = Float64(fma(Float64(-c), z, Float64(i * t)) * b);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -9.5e-111], N[Not[LessEqual[x, 4.4e+74]], $MachinePrecision]], N[(N[(z * y + N[((-t) * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[((-c) * z + N[(i * t), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.4999999999999995e-111 or 4.4000000000000002e74 < x

   1. Initial program 75.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 62.9%

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

   7. Applied rewrites 62.9%

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

   if -9.4999999999999995e-111 < x < 4.4000000000000002e74

   1. Initial program 72.9%

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

   3. Taylor expanded in b around inf

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

   5. Applied rewrites 45.1%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-111} \lor \neg \left(x \leq 4.4 \cdot 10^{+74}\right):\\ \;\;\;\;\mathsf{fma}\left(z, y, \left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-c, z, i \cdot t\right) \cdot b\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-18} \lor \neg \left(a \leq 3.4 \cdot 10^{-66}\right):\\ \;\;\;\;\mathsf{fma}\left(z, y, \left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -5.8e-18) (not (<= a 3.4e-66)))
   (* (fma z y (* (- t) a)) x)
   (* (fma (- b) c (* 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-18) || !(a <= 3.4e-66)) {
		tmp = fma(z, y, (-t * a)) * x;
	} else {
		tmp = fma(-b, c, (y * x)) * z;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -5.8e-18) || !(a <= 3.4e-66))
		tmp = Float64(fma(z, y, Float64(Float64(-t) * a)) * x);
	else
		tmp = Float64(fma(Float64(-b), c, Float64(y * x)) * z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -5.8e-18], N[Not[LessEqual[a, 3.4e-66]], $MachinePrecision]], N[(N[(z * y + N[((-t) * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[(N[((-b) * c + N[(y * x), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.8e-18 or 3.39999999999999997e-66 < a

   1. Initial program 68.5%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 52.1%

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

   7. Applied rewrites 51.4%

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

   if -5.8e-18 < a < 3.39999999999999997e-66

   1. Initial program 82.0%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 53.3%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.8 \cdot 10^{-18} \lor \neg \left(a \leq 3.4 \cdot 10^{-66}\right):\\ \;\;\;\;\mathsf{fma}\left(z, y, \left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-b, c, y \cdot x\right) \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 42.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-151} \lor \neg \left(x \leq 1.25 \cdot 10^{-98}\right):\\ \;\;\;\;\mathsf{fma}\left(z, y, \left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \left(c \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= x -5.6e-151) (not (<= x 1.25e-98)))
   (* (fma z y (* (- t) a)) 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 ((x <= -5.6e-151) || !(x <= 1.25e-98)) {
		tmp = fma(z, y, (-t * a)) * x;
	} else {
		tmp = -b * (c * z);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((x <= -5.6e-151) || !(x <= 1.25e-98))
		tmp = Float64(fma(z, y, Float64(Float64(-t) * a)) * x);
	else
		tmp = Float64(Float64(-b) * Float64(c * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[x, -5.6e-151], N[Not[LessEqual[x, 1.25e-98]], $MachinePrecision]], N[(N[(z * y + N[((-t) * a), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], N[((-b) * N[(c * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.6000000000000002e-151 or 1.25000000000000005e-98 < x

   1. Initial program 77.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   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 55.4%

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

   7. Applied rewrites 55.4%

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

   if -5.6000000000000002e-151 < x < 1.25000000000000005e-98

   1. Initial program 65.5%

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

   3. Taylor expanded in i around 0

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

   5. Applied rewrites 49.6%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 25.2%

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

   9. Taylor expanded in b around inf

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

   11. Applied rewrites 30.1%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-151} \lor \neg \left(x \leq 1.25 \cdot 10^{-98}\right):\\ \;\;\;\;\mathsf{fma}\left(z, y, \left(-t\right) \cdot a\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;\left(-b\right) \cdot \left(c \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.6% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+90} \lor \neg \left(y \leq 1.8 \cdot 10^{+181}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= y -1.25e+90) (not (<= y 1.8e+181))) (* (* y x) z) (* (* b t) 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 ((y <= -1.25e+90) || !(y <= 1.8e+181)) {
		tmp = (y * x) * z;
	} else {
		tmp = (b * t) * i;
	}
	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 ((y <= (-1.25d+90)) .or. (.not. (y <= 1.8d+181))) then
        tmp = (y * x) * z
    else
        tmp = (b * t) * i
    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 ((y <= -1.25e+90) || !(y <= 1.8e+181)) {
		tmp = (y * x) * z;
	} else {
		tmp = (b * t) * i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (y <= -1.25e+90) or not (y <= 1.8e+181):
		tmp = (y * x) * z
	else:
		tmp = (b * t) * i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((y <= -1.25e+90) || !(y <= 1.8e+181))
		tmp = Float64(Float64(y * x) * z);
	else
		tmp = Float64(Float64(b * t) * i);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((y <= -1.25e+90) || ~((y <= 1.8e+181)))
		tmp = (y * x) * z;
	else
		tmp = (b * t) * i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[y, -1.25e+90], N[Not[LessEqual[y, 1.8e+181]], $MachinePrecision]], N[(N[(y * x), $MachinePrecision] * z), $MachinePrecision], N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2500000000000001e90 or 1.79999999999999992e181 < y

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf

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

   5. Applied rewrites 65.4%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 61.7%

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

   if -1.2500000000000001e90 < y < 1.79999999999999992e181

   1. Initial program 78.6%

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

   3. Taylor expanded in t around 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 47.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 27.0%

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

   10. Applied rewrites 28.8%

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

4. Final simplification 37.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+90} \lor \neg \left(y \leq 1.8 \cdot 10^{+181}\right):\\ \;\;\;\;\left(y \cdot x\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.9% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+61}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+60}:\\ \;\;\;\;\left(j \cdot c\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4e+61)
   (* (* b t) i)
   (if (<= t 5e+60) (* (* j c) a) (* (* 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 (t <= -4e+61) {
		tmp = (b * t) * i;
	} else if (t <= 5e+60) {
		tmp = (j * c) * a;
	} 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 (t <= (-4d+61)) then
        tmp = (b * t) * i
    else if (t <= 5d+60) then
        tmp = (j * c) * a
    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 (t <= -4e+61) {
		tmp = (b * t) * i;
	} else if (t <= 5e+60) {
		tmp = (j * c) * a;
	} else {
		tmp = (i * t) * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4e+61:
		tmp = (b * t) * i
	elif t <= 5e+60:
		tmp = (j * c) * a
	else:
		tmp = (i * t) * b
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4e+61)
		tmp = Float64(Float64(b * t) * i);
	elseif (t <= 5e+60)
		tmp = Float64(Float64(j * c) * a);
	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 (t <= -4e+61)
		tmp = (b * t) * i;
	elseif (t <= 5e+60)
		tmp = (j * c) * a;
	else
		tmp = (i * t) * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4e+61], N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[t, 5e+60], N[(N[(j * c), $MachinePrecision] * a), $MachinePrecision], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9999999999999998e61

   1. Initial program 66.7%

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

   3. Taylor expanded in t around 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 72.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 41.9%

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

   10. Applied rewrites 48.1%

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

   if -3.9999999999999998e61 < t < 4.99999999999999975e60

   1. Initial program 80.5%

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

   3. Taylor expanded in i around 0

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

   5. Applied rewrites 70.6%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 25.7%

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

   if 4.99999999999999975e60 < t

   1. Initial program 63.0%

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

   3. Taylor expanded in t around 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 66.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 38.2%

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

Alternative 21: 29.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{+61}:\\ \;\;\;\;\left(b \cdot t\right) \cdot i\\ \mathbf{elif}\;t \leq 5 \cdot 10^{+60}:\\ \;\;\;\;\left(c \cdot a\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot t\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4e+61)
   (* (* b t) i)
   (if (<= t 5e+60) (* (* 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 (t <= -4e+61) {
		tmp = (b * t) * i;
	} else if (t <= 5e+60) {
		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 (t <= (-4d+61)) then
        tmp = (b * t) * i
    else if (t <= 5d+60) 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 (t <= -4e+61) {
		tmp = (b * t) * i;
	} else if (t <= 5e+60) {
		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 t <= -4e+61:
		tmp = (b * t) * i
	elif t <= 5e+60:
		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 (t <= -4e+61)
		tmp = Float64(Float64(b * t) * i);
	elseif (t <= 5e+60)
		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 (t <= -4e+61)
		tmp = (b * t) * i;
	elseif (t <= 5e+60)
		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[LessEqual[t, -4e+61], N[(N[(b * t), $MachinePrecision] * i), $MachinePrecision], If[LessEqual[t, 5e+60], N[(N[(c * a), $MachinePrecision] * j), $MachinePrecision], N[(N[(i * t), $MachinePrecision] * b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.9999999999999998e61

   1. Initial program 66.7%

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

   3. Taylor expanded in t around 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 72.0%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 41.9%

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

   10. Applied rewrites 48.1%

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

   if -3.9999999999999998e61 < t < 4.99999999999999975e60

   1. Initial program 80.5%

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

   3. Taylor expanded in i around 0

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

   5. Applied rewrites 70.6%

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

   6. Taylor expanded in j around inf

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

   8. Applied rewrites 25.7%

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

   10. Applied rewrites 25.2%

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

   if 4.99999999999999975e60 < t

   1. Initial program 63.0%

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

   3. Taylor expanded in t around 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 66.9%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 38.2%

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

Alternative 22: 21.9% accurate, 5.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.0%

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

3. Taylor expanded in t around 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 39.9%

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

6. Taylor expanded in x around 0

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

8. Applied rewrites 22.1%

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

10. Applied rewrites 23.0%

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

Developer Target 1: 59.6% 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 2025022 
(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)))))