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

Percentage Accurate: 73.2% → 84.5%

Time: 17.2s

Alternatives: 7

Speedup: N/A×

• 57.7% 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: 73.2% 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: 84.5% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-1 \cdot b\right) \cdot \left(i \cdot t\right)\\ t_2 := a \cdot \left(t \cdot x\right)\\ t_3 := \mathsf{fma}\left(-1 \cdot a, x, \frac{\mathsf{fma}\left(\mathsf{fma}\left(-1 \cdot i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right)}{t} - b \cdot \mathsf{fma}\left(-1, i, \frac{c \cdot z}{t}\right)\right) \cdot t\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-270}:\\ \;\;\;\;\mathsf{fma}\left(-1, t\_2, \mathsf{fma}\left(j, a \cdot c - i \cdot y, z \cdot \left(x \cdot y - b \cdot c\right)\right)\right) - t\_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(-1, t\_2, \mathsf{fma}\left(c, \mathsf{fma}\left(-1, b \cdot z, a \cdot j\right), y \cdot \mathsf{fma}\left(-1, i \cdot j, x \cdot z\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* -1.0 b) (* i t)))
        (t_2 (* a (* t x)))
        (t_3
         (*
          (fma
           (* -1.0 a)
           x
           (-
            (/ (fma (fma (* -1.0 i) y (* c a)) j (* (* z y) x)) t)
            (* b (fma -1.0 i (/ (* c z) t)))))
          t)))
   (if (<= t -2.5e+43)
     t_3
     (if (<= t 2.5e-270)
       (-
        (fma -1.0 t_2 (fma j (- (* a c) (* i y)) (* z (- (* x y) (* b c)))))
        t_1)
       (if (<= t 3e-15)
         (-
          (fma
           -1.0
           t_2
           (fma c (fma -1.0 (* b z) (* a j)) (* y (fma -1.0 (* i j) (* x z)))))
          t_1)
         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 = (-1.0 * b) * (i * t);
	double t_2 = a * (t * x);
	double t_3 = fma((-1.0 * a), x, ((fma(fma((-1.0 * i), y, (c * a)), j, ((z * y) * x)) / t) - (b * fma(-1.0, i, ((c * z) / t))))) * t;
	double tmp;
	if (t <= -2.5e+43) {
		tmp = t_3;
	} else if (t <= 2.5e-270) {
		tmp = fma(-1.0, t_2, fma(j, ((a * c) - (i * y)), (z * ((x * y) - (b * c))))) - t_1;
	} else if (t <= 3e-15) {
		tmp = fma(-1.0, t_2, fma(c, fma(-1.0, (b * z), (a * j)), (y * fma(-1.0, (i * j), (x * z))))) - t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-1.0 * b) * Float64(i * t))
	t_2 = Float64(a * Float64(t * x))
	t_3 = Float64(fma(Float64(-1.0 * a), x, Float64(Float64(fma(fma(Float64(-1.0 * i), y, Float64(c * a)), j, Float64(Float64(z * y) * x)) / t) - Float64(b * fma(-1.0, i, Float64(Float64(c * z) / t))))) * t)
	tmp = 0.0
	if (t <= -2.5e+43)
		tmp = t_3;
	elseif (t <= 2.5e-270)
		tmp = Float64(fma(-1.0, t_2, fma(j, Float64(Float64(a * c) - Float64(i * y)), Float64(z * Float64(Float64(x * y) - Float64(b * c))))) - t_1);
	elseif (t <= 3e-15)
		tmp = Float64(fma(-1.0, t_2, fma(c, fma(-1.0, Float64(b * z), Float64(a * j)), Float64(y * fma(-1.0, Float64(i * j), Float64(x * z))))) - t_1);
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(-1.0 * b), $MachinePrecision] * N[(i * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(N[(-1.0 * a), $MachinePrecision] * x + N[(N[(N[(N[(N[(-1.0 * i), $MachinePrecision] * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(b * N[(-1.0 * i + N[(N[(c * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision]}, If[LessEqual[t, -2.5e+43], t$95$3, If[LessEqual[t, 2.5e-270], N[(N[(-1.0 * t$95$2 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision] + N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[t, 3e-15], N[(N[(-1.0 * t$95$2 + N[(c * N[(-1.0 * N[(b * z), $MachinePrecision] + N[(a * j), $MachinePrecision]), $MachinePrecision] + N[(y * N[(-1.0 * N[(i * j), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.5000000000000002e43 or 3e-15 < t

   1. Initial program 71.9%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 81.9%

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

   6. Taylor expanded in b around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 86.8

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

   8. Applied rewrites 86.8%

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

   if -2.5000000000000002e43 < t < 2.4999999999999999e-270

   1. Initial program 84.3%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 87.9%

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

   6. Taylor expanded in i around 0

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

   8. Applied rewrites 87.9%

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

   9. Taylor expanded in z around 0

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

       1. lower--.f64 N/A

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

   11. Applied rewrites 90.9%

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

   if 2.4999999999999999e-270 < t < 3e-15

   1. Initial program 72.0%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 84.8%

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

   6. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

   8. Applied rewrites 88.6%

      \[\leadsto \mathsf{fma}\left(-1, a \cdot \left(t \cdot x\right), \mathsf{fma}\left(c, \mathsf{fma}\left(-1, b \cdot z, a \cdot j\right), y \cdot \mathsf{fma}\left(-1, i \cdot j, x \cdot z\right)\right)\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+43}:\\ \;\;\;\;\mathsf{fma}\left(-1 \cdot a, x, \frac{\mathsf{fma}\left(\mathsf{fma}\left(-1 \cdot i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right)}{t} - b \cdot \mathsf{fma}\left(-1, i, \frac{c \cdot z}{t}\right)\right) \cdot t\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-270}:\\ \;\;\;\;\mathsf{fma}\left(-1, a \cdot \left(t \cdot x\right), \mathsf{fma}\left(j, a \cdot c - i \cdot y, z \cdot \left(x \cdot y - b \cdot c\right)\right)\right) - \left(-1 \cdot b\right) \cdot \left(i \cdot t\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-15}:\\ \;\;\;\;\mathsf{fma}\left(-1, a \cdot \left(t \cdot x\right), \mathsf{fma}\left(c, \mathsf{fma}\left(-1, b \cdot z, a \cdot j\right), y \cdot \mathsf{fma}\left(-1, i \cdot j, x \cdot z\right)\right)\right) - \left(-1 \cdot b\right) \cdot \left(i \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1 \cdot a, x, \frac{\mathsf{fma}\left(\mathsf{fma}\left(-1 \cdot i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right)}{t} - b \cdot \mathsf{fma}\left(-1, i, \frac{c \cdot z}{t}\right)\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 80.3% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+56} \lor \neg \left(t \leq 3 \cdot 10^{-15}\right):\\ \;\;\;\;\mathsf{fma}\left(-1 \cdot a, x, \frac{\mathsf{fma}\left(\mathsf{fma}\left(-1 \cdot i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right)}{t} - b \cdot \mathsf{fma}\left(-1, i, \frac{c \cdot z}{t}\right)\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, a \cdot \left(t \cdot x\right), \mathsf{fma}\left(c, \mathsf{fma}\left(-1, b \cdot z, a \cdot j\right), y \cdot \mathsf{fma}\left(-1, i \cdot j, x \cdot z\right)\right)\right) - \left(-1 \cdot b\right) \cdot \left(i \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.25e+56) (not (<= t 3e-15)))
   (*
    (fma
     (* -1.0 a)
     x
     (-
      (/ (fma (fma (* -1.0 i) y (* c a)) j (* (* z y) x)) t)
      (* b (fma -1.0 i (/ (* c z) t)))))
    t)
   (-
    (fma
     -1.0
     (* a (* t x))
     (fma c (fma -1.0 (* b z) (* a j)) (* y (fma -1.0 (* i j) (* x z)))))
    (* (* -1.0 b) (* i 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 ((t <= -1.25e+56) || !(t <= 3e-15)) {
		tmp = fma((-1.0 * a), x, ((fma(fma((-1.0 * i), y, (c * a)), j, ((z * y) * x)) / t) - (b * fma(-1.0, i, ((c * z) / t))))) * t;
	} else {
		tmp = fma(-1.0, (a * (t * x)), fma(c, fma(-1.0, (b * z), (a * j)), (y * fma(-1.0, (i * j), (x * z))))) - ((-1.0 * b) * (i * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.25e+56) || !(t <= 3e-15))
		tmp = Float64(fma(Float64(-1.0 * a), x, Float64(Float64(fma(fma(Float64(-1.0 * i), y, Float64(c * a)), j, Float64(Float64(z * y) * x)) / t) - Float64(b * fma(-1.0, i, Float64(Float64(c * z) / t))))) * t);
	else
		tmp = Float64(fma(-1.0, Float64(a * Float64(t * x)), fma(c, fma(-1.0, Float64(b * z), Float64(a * j)), Float64(y * fma(-1.0, Float64(i * j), Float64(x * z))))) - Float64(Float64(-1.0 * b) * Float64(i * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.25e+56], N[Not[LessEqual[t, 3e-15]], $MachinePrecision]], N[(N[(N[(-1.0 * a), $MachinePrecision] * x + N[(N[(N[(N[(N[(-1.0 * i), $MachinePrecision] * y + N[(c * a), $MachinePrecision]), $MachinePrecision] * j + N[(N[(z * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] - N[(b * N[(-1.0 * i + N[(N[(c * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision], N[(N[(-1.0 * N[(a * N[(t * x), $MachinePrecision]), $MachinePrecision] + N[(c * N[(-1.0 * N[(b * z), $MachinePrecision] + N[(a * j), $MachinePrecision]), $MachinePrecision] + N[(y * N[(-1.0 * N[(i * j), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-1.0 * b), $MachinePrecision] * N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.25000000000000006e56 or 3e-15 < t

   1. Initial program 71.8%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 82.1%

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

   6. Taylor expanded in b around 0

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

      1. lower-*.f64 N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lift-*.f64 87.2

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

   8. Applied rewrites 87.2%

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

   if -1.25000000000000006e56 < t < 3e-15

   1. Initial program 79.5%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 86.4%

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

   6. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

   8. Applied rewrites 86.4%

      \[\leadsto \mathsf{fma}\left(-1, a \cdot \left(t \cdot x\right), \mathsf{fma}\left(c, \mathsf{fma}\left(-1, b \cdot z, a \cdot j\right), y \cdot \mathsf{fma}\left(-1, i \cdot j, x \cdot z\right)\right)\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+56} \lor \neg \left(t \leq 3 \cdot 10^{-15}\right):\\ \;\;\;\;\mathsf{fma}\left(-1 \cdot a, x, \frac{\mathsf{fma}\left(\mathsf{fma}\left(-1 \cdot i, y, c \cdot a\right), j, \left(z \cdot y\right) \cdot x\right)}{t} - b \cdot \mathsf{fma}\left(-1, i, \frac{c \cdot z}{t}\right)\right) \cdot t\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, a \cdot \left(t \cdot x\right), \mathsf{fma}\left(c, \mathsf{fma}\left(-1, b \cdot z, a \cdot j\right), y \cdot \mathsf{fma}\left(-1, i \cdot j, x \cdot z\right)\right)\right) - \left(-1 \cdot b\right) \cdot \left(i \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.3% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-1 \cdot b\right) \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1 \cdot a, x, b \cdot \left(i - \frac{c \cdot z}{t}\right)\right) \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* (* -1.0 b) (- (* c z) (* t i))))
          (* j (- (* c a) (* y i))))))
   (if (<= t_1 INFINITY)
     t_1
     (* (fma (* -1.0 a) x (* b (- i (/ (* c z) t)))) t))))

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))) + ((-1.0 * b) * ((c * z) - (t * i)))) + (j * ((c * a) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = fma((-1.0 * a), x, (b * (i - ((c * z) / t)))) * t;
	}
	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(Float64(-1.0 * 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(-1.0 * a), x, Float64(b * Float64(i - Float64(Float64(c * z) / t)))) * t);
	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[(N[(-1.0 * b), $MachinePrecision] * 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[(N[(-1.0 * a), $MachinePrecision] * x + N[(b * N[(i - N[(N[(c * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * t), $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 93.5%

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

   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 t around inf

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

   5. Applied rewrites 37.6%

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

   6. Taylor expanded in b around -inf

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

      1. lower-*.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lift-*.f64 54.2

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

   8. Applied rewrites 54.2%

      \[\leadsto \mathsf{fma}\left(-1 \cdot a, x, b \cdot \left(i + -1 \cdot \frac{c \cdot z}{t}\right)\right) \cdot t \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-1 \cdot b\right) \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \leq \infty:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + \left(-1 \cdot b\right) \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1 \cdot a, x, b \cdot \left(i - \frac{c \cdot z}{t}\right)\right) \cdot t\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.6% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.85 \cdot 10^{-78} \lor \neg \left(j \leq 6.6 \cdot 10^{-66}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(x, \frac{\mathsf{fma}\left(-1 \cdot a, t, z \cdot y\right)}{j}, c \cdot a\right) - \mathsf{fma}\left(i, y, \frac{b \cdot \mathsf{fma}\left(-1 \cdot i, t, c \cdot z\right)}{j}\right)\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, c \cdot j, \mathsf{fma}\left(t, \mathsf{fma}\left(-1, a \cdot x, -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{t}\right) - \left(-1 \cdot b\right) \cdot i, z \cdot \mathsf{fma}\left(-1, b \cdot c, x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.85e-78) (not (<= j 6.6e-66)))
   (*
    (-
     (fma x (/ (fma (* -1.0 a) t (* z y)) j) (* c a))
     (fma i y (/ (* b (fma (* -1.0 i) t (* c z))) j)))
    j)
   (fma
    a
    (* c j)
    (fma
     t
     (- (fma -1.0 (* a x) (* -1.0 (/ (* i (* j y)) t))) (* (* -1.0 b) i))
     (* z (fma -1.0 (* b c) (* x y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.85e-78) || !(j <= 6.6e-66)) {
		tmp = (fma(x, (fma((-1.0 * a), t, (z * y)) / j), (c * a)) - fma(i, y, ((b * fma((-1.0 * i), t, (c * z))) / j))) * j;
	} else {
		tmp = fma(a, (c * j), fma(t, (fma(-1.0, (a * x), (-1.0 * ((i * (j * y)) / t))) - ((-1.0 * b) * i)), (z * fma(-1.0, (b * c), (x * y)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.85e-78) || !(j <= 6.6e-66))
		tmp = Float64(Float64(fma(x, Float64(fma(Float64(-1.0 * a), t, Float64(z * y)) / j), Float64(c * a)) - fma(i, y, Float64(Float64(b * fma(Float64(-1.0 * i), t, Float64(c * z))) / j))) * j);
	else
		tmp = fma(a, Float64(c * j), fma(t, Float64(fma(-1.0, Float64(a * x), Float64(-1.0 * Float64(Float64(i * Float64(j * y)) / t))) - Float64(Float64(-1.0 * b) * i)), Float64(z * fma(-1.0, Float64(b * c), Float64(x * y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.85e-78], N[Not[LessEqual[j, 6.6e-66]], $MachinePrecision]], N[(N[(N[(x * N[(N[(N[(-1.0 * a), $MachinePrecision] * t + N[(z * y), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision] + N[(c * a), $MachinePrecision]), $MachinePrecision] - N[(i * y + N[(N[(b * N[(N[(-1.0 * i), $MachinePrecision] * t + N[(c * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision] + N[(t * N[(N[(-1.0 * N[(a * x), $MachinePrecision] + N[(-1.0 * N[(N[(i * N[(j * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-1.0 * b), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] + N[(z * N[(-1.0 * N[(b * c), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.85000000000000003e-78 or 6.5999999999999998e-66 < j

   1. Initial program 75.8%

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

   3. Taylor expanded in j around inf

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

   5. Applied rewrites 80.1%

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

   if -1.85000000000000003e-78 < j < 6.5999999999999998e-66

   1. Initial program 76.1%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 71.3%

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

   6. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

   8. Applied rewrites 77.1%

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

   9. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-fma.f64 N/A

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

   11. Applied rewrites 88.8%

       \[\leadsto \mathsf{fma}\left(a, c \cdot \color{blue}{j}, \mathsf{fma}\left(t, \mathsf{fma}\left(-1, a \cdot x, -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{t}\right) - -1 \cdot \left(b \cdot i\right), z \cdot \mathsf{fma}\left(-1, b \cdot c, x \cdot y\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.85 \cdot 10^{-78} \lor \neg \left(j \leq 6.6 \cdot 10^{-66}\right):\\ \;\;\;\;\left(\mathsf{fma}\left(x, \frac{\mathsf{fma}\left(-1 \cdot a, t, z \cdot y\right)}{j}, c \cdot a\right) - \mathsf{fma}\left(i, y, \frac{b \cdot \mathsf{fma}\left(-1 \cdot i, t, c \cdot z\right)}{j}\right)\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, c \cdot j, \mathsf{fma}\left(t, \mathsf{fma}\left(-1, a \cdot x, -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{t}\right) - \left(-1 \cdot b\right) \cdot i, z \cdot \mathsf{fma}\left(-1, b \cdot c, x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.5% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+98} \lor \neg \left(t \leq 510000000000\right):\\ \;\;\;\;\mathsf{fma}\left(a, c \cdot j, \mathsf{fma}\left(t, \mathsf{fma}\left(-1, a \cdot x, -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{t}\right) - \left(-1 \cdot b\right) \cdot i, z \cdot \mathsf{fma}\left(-1, b \cdot c, x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, a \cdot \left(t \cdot x\right), \mathsf{fma}\left(c, \mathsf{fma}\left(-1, b \cdot z, a \cdot j\right), y \cdot \mathsf{fma}\left(-1, i \cdot j, x \cdot z\right)\right)\right) - \left(-1 \cdot b\right) \cdot \left(i \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.2e+98) (not (<= t 510000000000.0)))
   (fma
    a
    (* c j)
    (fma
     t
     (- (fma -1.0 (* a x) (* -1.0 (/ (* i (* j y)) t))) (* (* -1.0 b) i))
     (* z (fma -1.0 (* b c) (* x y)))))
   (-
    (fma
     -1.0
     (* a (* t x))
     (fma c (fma -1.0 (* b z) (* a j)) (* y (fma -1.0 (* i j) (* x z)))))
    (* (* -1.0 b) (* i 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 ((t <= -1.2e+98) || !(t <= 510000000000.0)) {
		tmp = fma(a, (c * j), fma(t, (fma(-1.0, (a * x), (-1.0 * ((i * (j * y)) / t))) - ((-1.0 * b) * i)), (z * fma(-1.0, (b * c), (x * y)))));
	} else {
		tmp = fma(-1.0, (a * (t * x)), fma(c, fma(-1.0, (b * z), (a * j)), (y * fma(-1.0, (i * j), (x * z))))) - ((-1.0 * b) * (i * t));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.2e+98) || !(t <= 510000000000.0))
		tmp = fma(a, Float64(c * j), fma(t, Float64(fma(-1.0, Float64(a * x), Float64(-1.0 * Float64(Float64(i * Float64(j * y)) / t))) - Float64(Float64(-1.0 * b) * i)), Float64(z * fma(-1.0, Float64(b * c), Float64(x * y)))));
	else
		tmp = Float64(fma(-1.0, Float64(a * Float64(t * x)), fma(c, fma(-1.0, Float64(b * z), Float64(a * j)), Float64(y * fma(-1.0, Float64(i * j), Float64(x * z))))) - Float64(Float64(-1.0 * b) * Float64(i * t)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.2e+98], N[Not[LessEqual[t, 510000000000.0]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision] + N[(t * N[(N[(-1.0 * N[(a * x), $MachinePrecision] + N[(-1.0 * N[(N[(i * N[(j * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-1.0 * b), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] + N[(z * N[(-1.0 * N[(b * c), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-1.0 * N[(a * N[(t * x), $MachinePrecision]), $MachinePrecision] + N[(c * N[(-1.0 * N[(b * z), $MachinePrecision] + N[(a * j), $MachinePrecision]), $MachinePrecision] + N[(y * N[(-1.0 * N[(i * j), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-1.0 * b), $MachinePrecision] * N[(i * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.1999999999999999e98 or 5.1e11 < t

   1. Initial program 66.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 80.1%

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

   6. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

   8. Applied rewrites 77.8%

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

   9. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-fma.f64 N/A

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

   11. Applied rewrites 79.1%

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

   if -1.1999999999999999e98 < t < 5.1e11

   1. Initial program 81.6%

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

   3. Taylor expanded in c around 0

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

   5. Applied rewrites 84.6%

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

   6. Taylor expanded in y around 0

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

      1. lower--.f64 N/A

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

   8. Applied rewrites 85.3%

      \[\leadsto \mathsf{fma}\left(-1, a \cdot \left(t \cdot x\right), \mathsf{fma}\left(c, \mathsf{fma}\left(-1, b \cdot z, a \cdot j\right), y \cdot \mathsf{fma}\left(-1, i \cdot j, x \cdot z\right)\right)\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+98} \lor \neg \left(t \leq 510000000000\right):\\ \;\;\;\;\mathsf{fma}\left(a, c \cdot j, \mathsf{fma}\left(t, \mathsf{fma}\left(-1, a \cdot x, -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{t}\right) - \left(-1 \cdot b\right) \cdot i, z \cdot \mathsf{fma}\left(-1, b \cdot c, x \cdot y\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-1, a \cdot \left(t \cdot x\right), \mathsf{fma}\left(c, \mathsf{fma}\left(-1, b \cdot z, a \cdot j\right), y \cdot \mathsf{fma}\left(-1, i \cdot j, x \cdot z\right)\right)\right) - \left(-1 \cdot b\right) \cdot \left(i \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.5% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{i \cdot \left(j \cdot y\right)}{t}\\ t_2 := \left(-1 \cdot b\right) \cdot i\\ \mathbf{if}\;c \leq -2.65 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(c, t \cdot \left(\frac{a \cdot j}{t} - \frac{b \cdot z}{t}\right), t \cdot \left(\mathsf{fma}\left(-1, a \cdot x, \mathsf{fma}\left(-1, t\_1, \frac{x \cdot \left(y \cdot z\right)}{t}\right)\right) - t\_2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, c \cdot j, \mathsf{fma}\left(t, \mathsf{fma}\left(-1, a \cdot x, -1 \cdot t\_1\right) - t\_2, z \cdot \mathsf{fma}\left(-1, b \cdot c, x \cdot y\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (/ (* i (* j y)) t)) (t_2 (* (* -1.0 b) i)))
   (if (<= c -2.65e+98)
     (fma
      c
      (* t (- (/ (* a j) t) (/ (* b z) t)))
      (* t (- (fma -1.0 (* a x) (fma -1.0 t_1 (/ (* x (* y z)) t))) t_2)))
     (fma
      a
      (* c j)
      (fma
       t
       (- (fma -1.0 (* a x) (* -1.0 t_1)) t_2)
       (* z (fma -1.0 (* b c) (* x y))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (i * (j * y)) / t;
	double t_2 = (-1.0 * b) * i;
	double tmp;
	if (c <= -2.65e+98) {
		tmp = fma(c, (t * (((a * j) / t) - ((b * z) / t))), (t * (fma(-1.0, (a * x), fma(-1.0, t_1, ((x * (y * z)) / t))) - t_2)));
	} else {
		tmp = fma(a, (c * j), fma(t, (fma(-1.0, (a * x), (-1.0 * t_1)) - t_2), (z * fma(-1.0, (b * c), (x * y)))));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * Float64(j * y)) / t)
	t_2 = Float64(Float64(-1.0 * b) * i)
	tmp = 0.0
	if (c <= -2.65e+98)
		tmp = fma(c, Float64(t * Float64(Float64(Float64(a * j) / t) - Float64(Float64(b * z) / t))), Float64(t * Float64(fma(-1.0, Float64(a * x), fma(-1.0, t_1, Float64(Float64(x * Float64(y * z)) / t))) - t_2)));
	else
		tmp = fma(a, Float64(c * j), fma(t, Float64(fma(-1.0, Float64(a * x), Float64(-1.0 * t_1)) - t_2), Float64(z * fma(-1.0, Float64(b * c), Float64(x * y)))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * N[(j * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(-1.0 * b), $MachinePrecision] * i), $MachinePrecision]}, If[LessEqual[c, -2.65e+98], N[(c * N[(t * N[(N[(N[(a * j), $MachinePrecision] / t), $MachinePrecision] - N[(N[(b * z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(-1.0 * N[(a * x), $MachinePrecision] + N[(-1.0 * t$95$1 + N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision] + N[(t * N[(N[(-1.0 * N[(a * x), $MachinePrecision] + N[(-1.0 * t$95$1), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision] + N[(z * N[(-1.0 * N[(b * c), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if c < -2.64999999999999999e98

   1. Initial program 56.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 56.2%

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

   6. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

   8. Applied rewrites 76.6%

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

   if -2.64999999999999999e98 < c

   1. Initial program 79.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 71.5%

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

   6. Taylor expanded in c around 0

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

      1. lower-fma.f64 N/A

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

      2. lower-*.f64 N/A

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

      3. lower--.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-*.f64 N/A

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

   8. Applied rewrites 61.6%

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

   9. Taylor expanded in z around 0

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

       1. lower-fma.f64 N/A

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

       2. lower-*.f64 N/A

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

       3. lower-fma.f64 N/A

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

   11. Applied rewrites 75.8%

       \[\leadsto \mathsf{fma}\left(a, c \cdot \color{blue}{j}, \mathsf{fma}\left(t, \mathsf{fma}\left(-1, a \cdot x, -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{t}\right) - -1 \cdot \left(b \cdot i\right), z \cdot \mathsf{fma}\left(-1, b \cdot c, x \cdot y\right)\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.65 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(c, t \cdot \left(\frac{a \cdot j}{t} - \frac{b \cdot z}{t}\right), t \cdot \left(\mathsf{fma}\left(-1, a \cdot x, \mathsf{fma}\left(-1, \frac{i \cdot \left(j \cdot y\right)}{t}, \frac{x \cdot \left(y \cdot z\right)}{t}\right)\right) - \left(-1 \cdot b\right) \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, c \cdot j, \mathsf{fma}\left(t, \mathsf{fma}\left(-1, a \cdot x, -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{t}\right) - \left(-1 \cdot b\right) \cdot i, z \cdot \mathsf{fma}\left(-1, b \cdot c, x \cdot y\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.4% accurate, N/A× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(a, c \cdot j, \mathsf{fma}\left(t, \mathsf{fma}\left(-1, a \cdot x, -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{t}\right) - \left(-1 \cdot b\right) \cdot i, z \cdot \mathsf{fma}\left(-1, b \cdot c, x \cdot y\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (fma
  a
  (* c j)
  (fma
   t
   (- (fma -1.0 (* a x) (* -1.0 (/ (* i (* j y)) t))) (* (* -1.0 b) i))
   (* z (fma -1.0 (* b c) (* x y))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return fma(a, (c * j), fma(t, (fma(-1.0, (a * x), (-1.0 * ((i * (j * y)) / t))) - ((-1.0 * b) * i)), (z * fma(-1.0, (b * c), (x * y)))));
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	return fma(a, Float64(c * j), fma(t, Float64(fma(-1.0, Float64(a * x), Float64(-1.0 * Float64(Float64(i * Float64(j * y)) / t))) - Float64(Float64(-1.0 * b) * i)), Float64(z * fma(-1.0, Float64(b * c), Float64(x * y)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision] + N[(t * N[(N[(-1.0 * N[(a * x), $MachinePrecision] + N[(-1.0 * N[(N[(i * N[(j * y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(-1.0 * b), $MachinePrecision] * i), $MachinePrecision]), $MachinePrecision] + N[(z * N[(-1.0 * N[(b * c), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.0%

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

3. Taylor expanded in t around inf

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

5. Applied rewrites 69.3%

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

6. Taylor expanded in c around 0

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

   1. lower-fma.f64 N/A

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

   2. lower-*.f64 N/A

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

   3. lower--.f64 N/A

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

   4. lower-/.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-*.f64 N/A

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

8. Applied rewrites 63.8%

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

9. Taylor expanded in z around 0

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

    1. lower-fma.f64 N/A

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

    2. lower-*.f64 N/A

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

    3. lower-fma.f64 N/A

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

11. Applied rewrites 74.3%

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

12. Final simplification 74.3%

    \[\leadsto \mathsf{fma}\left(a, c \cdot j, \mathsf{fma}\left(t, \mathsf{fma}\left(-1, a \cdot x, -1 \cdot \frac{i \cdot \left(j \cdot y\right)}{t}\right) - \left(-1 \cdot b\right) \cdot i, z \cdot \mathsf{fma}\left(-1, b \cdot c, x \cdot y\right)\right)\right) \]
13. Add Preprocessing

Reproduce

herbie shell --seed 2025065 
(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)))))