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

Percentage Accurate: 72.9% → 81.7%

Time: 47.2s

Alternatives: 28

Speedup: 0.5×

• 58.5% 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

real(8) function code(x, y, z, t, a, b, c, i, j)
    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: 72.9% 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

real(8) function code(x, y, z, t, a, b, c, i, j)
    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: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

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 * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

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 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = c * ((a * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = c * ((a * j) - (z * b))
	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(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * ((a * j) - (z * b));
	end
	tmp_2 = 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[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $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 91.2%

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

   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. Step-by-step derivation

      1. associate-+l- 0.0%

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

      2. *-commutative 0.0%

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

      3. sub-neg 0.0%

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

      4. sub-neg 0.0%

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

      5. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in c around inf 55.6%

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

4. Final simplification 82.9%

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

Alternative 2: 58.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t_1 + t \cdot \left(b \cdot i\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_5 := t_1 - z \cdot \left(b \cdot c\right)\\ \mathbf{if}\;j \leq -7 \cdot 10^{+124}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{+21}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-281}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-71}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{+65}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;j \leq 1.98 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{+138}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* t (* b i))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (+ (* a (* c j)) (* b (- (* t i) (* z c)))))
        (t_5 (- t_1 (* z (* b c)))))
   (if (<= j -7e+124)
     t_3
     (if (<= j -1.35e+21)
       (* c (- (* a j) (* z b)))
       (if (<= j -7.8e-178)
         t_2
         (if (<= j -1.1e-281)
           t_4
           (if (<= j 6.6e-176)
             t_2
             (if (<= j 1.3e-71)
               t_4
               (if (<= j 7.8e+65)
                 t_5
                 (if (<= j 1.98e+118)
                   (- (* i (- (* t b) (* y j))) (* b (* z c)))
                   (if (<= j 2.65e+138) t_5 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 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (t * (b * i));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double t_5 = t_1 - (z * (b * c));
	double tmp;
	if (j <= -7e+124) {
		tmp = t_3;
	} else if (j <= -1.35e+21) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -7.8e-178) {
		tmp = t_2;
	} else if (j <= -1.1e-281) {
		tmp = t_4;
	} else if (j <= 6.6e-176) {
		tmp = t_2;
	} else if (j <= 1.3e-71) {
		tmp = t_4;
	} else if (j <= 7.8e+65) {
		tmp = t_5;
	} else if (j <= 1.98e+118) {
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	} else if (j <= 2.65e+138) {
		tmp = t_5;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (t * (b * i))
    t_3 = j * ((a * c) - (y * i))
    t_4 = (a * (c * j)) + (b * ((t * i) - (z * c)))
    t_5 = t_1 - (z * (b * c))
    if (j <= (-7d+124)) then
        tmp = t_3
    else if (j <= (-1.35d+21)) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= (-7.8d-178)) then
        tmp = t_2
    else if (j <= (-1.1d-281)) then
        tmp = t_4
    else if (j <= 6.6d-176) then
        tmp = t_2
    else if (j <= 1.3d-71) then
        tmp = t_4
    else if (j <= 7.8d+65) then
        tmp = t_5
    else if (j <= 1.98d+118) then
        tmp = (i * ((t * b) - (y * j))) - (b * (z * c))
    else if (j <= 2.65d+138) then
        tmp = t_5
    else
        tmp = t_3
    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 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (t * (b * i));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	double t_5 = t_1 - (z * (b * c));
	double tmp;
	if (j <= -7e+124) {
		tmp = t_3;
	} else if (j <= -1.35e+21) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -7.8e-178) {
		tmp = t_2;
	} else if (j <= -1.1e-281) {
		tmp = t_4;
	} else if (j <= 6.6e-176) {
		tmp = t_2;
	} else if (j <= 1.3e-71) {
		tmp = t_4;
	} else if (j <= 7.8e+65) {
		tmp = t_5;
	} else if (j <= 1.98e+118) {
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	} else if (j <= 2.65e+138) {
		tmp = t_5;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 + (t * (b * i))
	t_3 = j * ((a * c) - (y * i))
	t_4 = (a * (c * j)) + (b * ((t * i) - (z * c)))
	t_5 = t_1 - (z * (b * c))
	tmp = 0
	if j <= -7e+124:
		tmp = t_3
	elif j <= -1.35e+21:
		tmp = c * ((a * j) - (z * b))
	elif j <= -7.8e-178:
		tmp = t_2
	elif j <= -1.1e-281:
		tmp = t_4
	elif j <= 6.6e-176:
		tmp = t_2
	elif j <= 1.3e-71:
		tmp = t_4
	elif j <= 7.8e+65:
		tmp = t_5
	elif j <= 1.98e+118:
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c))
	elif j <= 2.65e+138:
		tmp = t_5
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 + Float64(t * Float64(b * i)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_5 = Float64(t_1 - Float64(z * Float64(b * c)))
	tmp = 0.0
	if (j <= -7e+124)
		tmp = t_3;
	elseif (j <= -1.35e+21)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= -7.8e-178)
		tmp = t_2;
	elseif (j <= -1.1e-281)
		tmp = t_4;
	elseif (j <= 6.6e-176)
		tmp = t_2;
	elseif (j <= 1.3e-71)
		tmp = t_4;
	elseif (j <= 7.8e+65)
		tmp = t_5;
	elseif (j <= 1.98e+118)
		tmp = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) - Float64(b * Float64(z * c)));
	elseif (j <= 2.65e+138)
		tmp = t_5;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 + (t * (b * i));
	t_3 = j * ((a * c) - (y * i));
	t_4 = (a * (c * j)) + (b * ((t * i) - (z * c)));
	t_5 = t_1 - (z * (b * c));
	tmp = 0.0;
	if (j <= -7e+124)
		tmp = t_3;
	elseif (j <= -1.35e+21)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= -7.8e-178)
		tmp = t_2;
	elseif (j <= -1.1e-281)
		tmp = t_4;
	elseif (j <= 6.6e-176)
		tmp = t_2;
	elseif (j <= 1.3e-71)
		tmp = t_4;
	elseif (j <= 7.8e+65)
		tmp = t_5;
	elseif (j <= 1.98e+118)
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	elseif (j <= 2.65e+138)
		tmp = t_5;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$5 = N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7e+124], t$95$3, If[LessEqual[j, -1.35e+21], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -7.8e-178], t$95$2, If[LessEqual[j, -1.1e-281], t$95$4, If[LessEqual[j, 6.6e-176], t$95$2, If[LessEqual[j, 1.3e-71], t$95$4, If[LessEqual[j, 7.8e+65], t$95$5, If[LessEqual[j, 1.98e+118], N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.65e+138], t$95$5, t$95$3]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -7.0000000000000002e124 or 2.64999999999999992e138 < j

   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. Step-by-step derivation

      1. associate-+l- 66.4%

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

      2. *-commutative 66.4%

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

      3. sub-neg 66.4%

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

      4. sub-neg 66.4%

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

      5. *-commutative 66.4%

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

   3. Simplified 66.4%

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

   4. Taylor expanded in z around 0 70.6%

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

      1. mul-1-neg 70.6%

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

      2. *-commutative 70.6%

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

      3. associate-*l* 74.4%

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

      4. *-commutative 74.4%

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

   6. Simplified 74.4%

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

   7. Taylor expanded in j around inf 76.0%

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

   if -7.0000000000000002e124 < j < -1.35e21

   1. Initial program 58.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 58.6%

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

      2. *-commutative 58.6%

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

      3. sub-neg 58.6%

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

      4. sub-neg 58.6%

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

      5. *-commutative 58.6%

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

   3. Simplified 58.6%

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

   4. Taylor expanded in c around inf 66.2%

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

   if -1.35e21 < j < -7.8000000000000005e-178 or -1.10000000000000002e-281 < j < 6.60000000000000025e-176

   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. Step-by-step derivation

      1. associate-+l- 79.1%

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

      2. *-commutative 79.1%

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

      3. sub-neg 79.1%

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

      4. sub-neg 79.1%

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

      5. *-commutative 79.1%

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

   3. Simplified 79.1%

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

   4. Taylor expanded in j around 0 83.3%

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

      1. *-commutative 83.3%

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

      2. *-commutative 83.3%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in c around 0 75.7%

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

      1. mul-1-neg 75.7%

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

      2. associate-*r* 79.1%

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

   9. Simplified 79.1%

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

   if -7.8000000000000005e-178 < j < -1.10000000000000002e-281 or 6.60000000000000025e-176 < j < 1.2999999999999999e-71

   1. Initial program 55.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 55.7%

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

      2. *-commutative 55.7%

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

      3. sub-neg 55.7%

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

      4. sub-neg 55.7%

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

      5. *-commutative 55.7%

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

   3. Simplified 55.7%

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

   4. Taylor expanded in x around 0 56.1%

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

      1. *-commutative 56.1%

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

   6. Simplified 56.1%

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

   7. Taylor expanded in y around 0 72.0%

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

   if 1.2999999999999999e-71 < j < 7.7999999999999996e65 or 1.9800000000000001e118 < j < 2.64999999999999992e138

   1. Initial program 82.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 82.7%

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

      2. *-commutative 82.7%

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

      3. sub-neg 82.7%

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

      4. sub-neg 82.7%

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

      5. *-commutative 82.7%

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

   3. Simplified 82.7%

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

   4. Taylor expanded in j around 0 85.5%

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

      1. *-commutative 85.5%

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

      2. *-commutative 85.5%

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

   6. Simplified 85.5%

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

   7. Taylor expanded in c around inf 82.1%

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

      1. *-commutative 82.1%

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

      2. *-commutative 82.1%

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

      3. associate-*l* 82.0%

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

      4. *-commutative 82.0%

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

   9. Simplified 82.0%

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

   if 7.7999999999999996e65 < j < 1.9800000000000001e118

   1. Initial program 85.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 85.7%

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

      2. *-commutative 85.7%

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

      3. sub-neg 85.7%

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

      4. sub-neg 85.7%

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

      5. *-commutative 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in x around 0 100.0%

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

      1. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in a around 0 100.0%

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

   9. Simplified 100.0%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right) - b \cdot \left(c \cdot z\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.35 \cdot 10^{+21}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -7.8 \cdot 10^{-178}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq -1.1 \cdot 10^{-281}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6.6 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 1.3 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.8 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.98 \cdot 10^{+118}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 3: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+49}:\\ \;\;\;\;t_3 + t_1\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-48}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 0.068 \lor \neg \left(x \leq 1.9 \cdot 10^{+40}\right):\\ \;\;\;\;t_3 + t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (* b (- (* t i) (* z c)))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= x -2.3e+49)
     (+ t_3 t_1)
     (if (<= x 8e-175)
       t_2
       (if (<= x 1.35e-48)
         (- (* i (- (* t b) (* y j))) (* b (* z c)))
         (if (<= x 2e-30)
           (* c (- (* a j) (* z b)))
           (if (or (<= x 0.068) (not (<= x 1.9e+40)))
             (+ t_3 (* t (* b i)))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.3e+49) {
		tmp = t_3 + t_1;
	} else if (x <= 8e-175) {
		tmp = t_2;
	} else if (x <= 1.35e-48) {
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	} else if (x <= 2e-30) {
		tmp = c * ((a * j) - (z * b));
	} else if ((x <= 0.068) || !(x <= 1.9e+40)) {
		tmp = t_3 + (t * (b * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t_1 + (b * ((t * i) - (z * c)))
    t_3 = x * ((y * z) - (t * a))
    if (x <= (-2.3d+49)) then
        tmp = t_3 + t_1
    else if (x <= 8d-175) then
        tmp = t_2
    else if (x <= 1.35d-48) then
        tmp = (i * ((t * b) - (y * j))) - (b * (z * c))
    else if (x <= 2d-30) then
        tmp = c * ((a * j) - (z * b))
    else if ((x <= 0.068d0) .or. (.not. (x <= 1.9d+40))) then
        tmp = t_3 + (t * (b * i))
    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 * ((a * c) - (y * i));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.3e+49) {
		tmp = t_3 + t_1;
	} else if (x <= 8e-175) {
		tmp = t_2;
	} else if (x <= 1.35e-48) {
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	} else if (x <= 2e-30) {
		tmp = c * ((a * j) - (z * b));
	} else if ((x <= 0.068) || !(x <= 1.9e+40)) {
		tmp = t_3 + (t * (b * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + (b * ((t * i) - (z * c)))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2.3e+49:
		tmp = t_3 + t_1
	elif x <= 8e-175:
		tmp = t_2
	elif x <= 1.35e-48:
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c))
	elif x <= 2e-30:
		tmp = c * ((a * j) - (z * b))
	elif (x <= 0.068) or not (x <= 1.9e+40):
		tmp = t_3 + (t * (b * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2.3e+49)
		tmp = Float64(t_3 + t_1);
	elseif (x <= 8e-175)
		tmp = t_2;
	elseif (x <= 1.35e-48)
		tmp = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) - Float64(b * Float64(z * c)));
	elseif (x <= 2e-30)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif ((x <= 0.068) || !(x <= 1.9e+40))
		tmp = Float64(t_3 + Float64(t * Float64(b * i)));
	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 * ((a * c) - (y * i));
	t_2 = t_1 + (b * ((t * i) - (z * c)));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.3e+49)
		tmp = t_3 + t_1;
	elseif (x <= 8e-175)
		tmp = t_2;
	elseif (x <= 1.35e-48)
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	elseif (x <= 2e-30)
		tmp = c * ((a * j) - (z * b));
	elseif ((x <= 0.068) || ~((x <= 1.9e+40)))
		tmp = t_3 + (t * (b * i));
	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[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.3e+49], N[(t$95$3 + t$95$1), $MachinePrecision], If[LessEqual[x, 8e-175], t$95$2, If[LessEqual[x, 1.35e-48], N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2e-30], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 0.068], N[Not[LessEqual[x, 1.9e+40]], $MachinePrecision]], N[(t$95$3 + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.30000000000000002e49

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 75.7%

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

      2. *-commutative 75.7%

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

      3. sub-neg 75.7%

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

      4. sub-neg 75.7%

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

      5. *-commutative 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in b around 0 70.6%

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

   if -2.30000000000000002e49 < x < 8e-175 or 0.068000000000000005 < x < 1.90000000000000002e40

   1. Initial program 71.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.6%

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

      2. *-commutative 71.6%

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

      3. sub-neg 71.6%

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

      4. sub-neg 71.6%

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

      5. *-commutative 71.6%

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

   3. Simplified 71.6%

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

   4. Taylor expanded in x around 0 71.9%

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

      1. *-commutative 71.9%

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

   6. Simplified 71.9%

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

   if 8e-175 < x < 1.35000000000000006e-48

   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. Step-by-step derivation

      1. associate-+l- 64.3%

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

      2. *-commutative 64.3%

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

      3. sub-neg 64.3%

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

      4. sub-neg 64.3%

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

      5. *-commutative 64.3%

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

   3. Simplified 64.3%

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

   4. Taylor expanded in x around 0 60.5%

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

      1. *-commutative 60.5%

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

   6. Simplified 60.5%

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

   7. Taylor expanded in a around 0 65.0%

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

   9. Simplified 76.7%

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

   if 1.35000000000000006e-48 < x < 2e-30

   1. Initial program 27.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 27.2%

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

      2. *-commutative 27.2%

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

      3. sub-neg 27.2%

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

      4. sub-neg 27.2%

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

      5. *-commutative 27.2%

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

   3. Simplified 27.2%

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

   4. Taylor expanded in c around inf 100.0%

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

   if 2e-30 < x < 0.068000000000000005 or 1.90000000000000002e40 < x

   1. Initial program 66.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 66.6%

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

      2. *-commutative 66.6%

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

      3. sub-neg 66.6%

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

      4. sub-neg 66.6%

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

      5. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in j around 0 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

   6. Simplified 66.6%

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

   7. Taylor expanded in c around 0 73.2%

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

      1. mul-1-neg 73.2%

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

      2. associate-*r* 77.7%

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

   9. Simplified 77.7%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-175}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-48}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-30}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 0.068 \lor \neg \left(x \leq 1.9 \cdot 10^{+40}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 4: 57.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -2.8 \cdot 10^{+122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -1.55 \cdot 10^{+75}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{-39}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{-268}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+54}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x (- (* y z) (* t a))) (* z (* b c))))
        (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -2.8e+122)
     t_2
     (if (<= i -1.55e+75)
       (* c (- (* a j) (* z b)))
       (if (<= i -4.2e+51)
         (* z (- (* x y) (* b c)))
         (if (<= i -2.9e-39)
           (+ (* a (* c j)) (* b (- (* t i) (* z c))))
           (if (<= i -9e-69)
             t_1
             (if (<= i -4.3e-268)
               (* a (- (* c j) (* x t)))
               (if (<= i 1.35e+54) t_1 (- t_2 (* b (* z c))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) - (z * (b * c));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.8e+122) {
		tmp = t_2;
	} else if (i <= -1.55e+75) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= -4.2e+51) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= -2.9e-39) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (i <= -9e-69) {
		tmp = t_1;
	} else if (i <= -4.3e-268) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.35e+54) {
		tmp = t_1;
	} else {
		tmp = t_2 - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 = (x * ((y * z) - (t * a))) - (z * (b * c))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-2.8d+122)) then
        tmp = t_2
    else if (i <= (-1.55d+75)) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= (-4.2d+51)) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= (-2.9d-39)) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else if (i <= (-9d-69)) then
        tmp = t_1
    else if (i <= (-4.3d-268)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 1.35d+54) then
        tmp = t_1
    else
        tmp = t_2 - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * ((y * z) - (t * a))) - (z * (b * c));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -2.8e+122) {
		tmp = t_2;
	} else if (i <= -1.55e+75) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= -4.2e+51) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= -2.9e-39) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (i <= -9e-69) {
		tmp = t_1;
	} else if (i <= -4.3e-268) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.35e+54) {
		tmp = t_1;
	} else {
		tmp = t_2 - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) - (z * (b * c))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -2.8e+122:
		tmp = t_2
	elif i <= -1.55e+75:
		tmp = c * ((a * j) - (z * b))
	elif i <= -4.2e+51:
		tmp = z * ((x * y) - (b * c))
	elif i <= -2.9e-39:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	elif i <= -9e-69:
		tmp = t_1
	elif i <= -4.3e-268:
		tmp = a * ((c * j) - (x * t))
	elif i <= 1.35e+54:
		tmp = t_1
	else:
		tmp = t_2 - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(z * Float64(b * c)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -2.8e+122)
		tmp = t_2;
	elseif (i <= -1.55e+75)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= -4.2e+51)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= -2.9e-39)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (i <= -9e-69)
		tmp = t_1;
	elseif (i <= -4.3e-268)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 1.35e+54)
		tmp = t_1;
	else
		tmp = Float64(t_2 - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * ((y * z) - (t * a))) - (z * (b * c));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -2.8e+122)
		tmp = t_2;
	elseif (i <= -1.55e+75)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= -4.2e+51)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= -2.9e-39)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	elseif (i <= -9e-69)
		tmp = t_1;
	elseif (i <= -4.3e-268)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 1.35e+54)
		tmp = t_1;
	else
		tmp = t_2 - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.8e+122], t$95$2, If[LessEqual[i, -1.55e+75], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.2e+51], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.9e-39], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -9e-69], t$95$1, If[LessEqual[i, -4.3e-268], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.35e+54], t$95$1, N[(t$95$2 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -2.8e122

   1. Initial program 49.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 49.4%

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

      2. *-commutative 49.4%

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

      3. sub-neg 49.4%

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

      4. sub-neg 49.4%

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

      5. *-commutative 49.4%

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

   3. Simplified 49.4%

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

   4. Taylor expanded in i around inf 77.5%

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

      1. associate-*r* 77.5%

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

      2. neg-mul-1 77.5%

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

      3. cancel-sign-sub 77.5%

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

      4. +-commutative 77.5%

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

      5. mul-1-neg 77.5%

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

      6. unsub-neg 77.5%

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

      7. *-commutative 77.5%

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

   6. Simplified 77.5%

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

   if -2.8e122 < i < -1.5500000000000001e75

   1. Initial program 45.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 45.4%

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

      2. *-commutative 45.4%

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

      3. sub-neg 45.4%

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

      4. sub-neg 45.4%

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

      5. *-commutative 45.4%

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

   3. Simplified 45.4%

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

   4. Taylor expanded in c around inf 78.7%

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

   if -1.5500000000000001e75 < i < -4.2000000000000002e51

   1. Initial program 50.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 50.1%

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

      2. *-commutative 50.1%

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

      3. sub-neg 50.1%

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

      4. sub-neg 50.1%

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

      5. *-commutative 50.1%

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

   3. Simplified 50.1%

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

   4. Taylor expanded in z around inf 63.2%

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

   if -4.2000000000000002e51 < i < -2.89999999999999988e-39

   1. Initial program 70.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 70.1%

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

      2. *-commutative 70.1%

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

      3. sub-neg 70.1%

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

      4. sub-neg 70.1%

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

      5. *-commutative 70.1%

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

   3. Simplified 70.1%

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

   4. Taylor expanded in x around 0 78.7%

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

      1. *-commutative 78.7%

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

   6. Simplified 78.7%

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

   7. Taylor expanded in y around 0 73.9%

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

   if -2.89999999999999988e-39 < i < -9.00000000000000019e-69 or -4.3e-268 < i < 1.35000000000000005e54

   1. Initial program 79.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.9%

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

      2. *-commutative 79.9%

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

      3. sub-neg 79.9%

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

      4. sub-neg 79.9%

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

      5. *-commutative 79.9%

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

   3. Simplified 79.9%

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

   4. Taylor expanded in j around 0 75.4%

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

      1. *-commutative 75.4%

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

      2. *-commutative 75.4%

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

   6. Simplified 75.4%

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

   7. Taylor expanded in c around inf 67.4%

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

      1. *-commutative 67.4%

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

      2. *-commutative 67.4%

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

      3. associate-*l* 70.6%

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

      4. *-commutative 70.6%

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

   9. Simplified 70.6%

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

   if -9.00000000000000019e-69 < i < -4.3e-268

   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. Step-by-step derivation

      1. associate-+l- 77.7%

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

      2. *-commutative 77.7%

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

      3. sub-neg 77.7%

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

      4. sub-neg 77.7%

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

      5. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   4. Taylor expanded in a around inf 68.9%

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

      1. +-commutative 68.9%

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

      2. mul-1-neg 68.9%

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

      3. unsub-neg 68.9%

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

   6. Simplified 68.9%

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

   if 1.35000000000000005e54 < i

   1. Initial program 65.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 65.4%

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

      2. *-commutative 65.4%

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

      3. sub-neg 65.4%

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

      4. sub-neg 65.4%

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

      5. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in x around 0 69.3%

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

      1. *-commutative 69.3%

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

   6. Simplified 69.3%

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

   7. Taylor expanded in a around 0 63.9%

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

   9. Simplified 73.9%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right) - b \cdot \left(c \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.8 \cdot 10^{+122}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.55 \cdot 10^{+75}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{+51}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{-39}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;i \leq -4.3 \cdot 10^{-268}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]

Alternative 5: 68.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := z \cdot \left(x \cdot y\right) + \left(i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right)\\ \mathbf{if}\;j \leq -7.4 \cdot 10^{-63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c)))))
        (t_2 (+ (* z (* x y)) (+ (* i (* t b)) (* j (- (* a c) (* y i)))))))
   (if (<= j -7.4e-63)
     t_2
     (if (<= j 2.35e-104)
       t_1
       (if (<= j 2.7e-91)
         (* c (- (* a j) (* z b)))
         (if (<= j 2.7e+134) 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 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_2 = (z * (x * y)) + ((i * (t * b)) + (j * ((a * c) - (y * i))));
	double tmp;
	if (j <= -7.4e-63) {
		tmp = t_2;
	} else if (j <= 2.35e-104) {
		tmp = t_1;
	} else if (j <= 2.7e-91) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 2.7e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    t_2 = (z * (x * y)) + ((i * (t * b)) + (j * ((a * c) - (y * i))))
    if (j <= (-7.4d-63)) then
        tmp = t_2
    else if (j <= 2.35d-104) then
        tmp = t_1
    else if (j <= 2.7d-91) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= 2.7d+134) then
        tmp = 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 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	double t_2 = (z * (x * y)) + ((i * (t * b)) + (j * ((a * c) - (y * i))));
	double tmp;
	if (j <= -7.4e-63) {
		tmp = t_2;
	} else if (j <= 2.35e-104) {
		tmp = t_1;
	} else if (j <= 2.7e-91) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 2.7e+134) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	t_2 = (z * (x * y)) + ((i * (t * b)) + (j * ((a * c) - (y * i))))
	tmp = 0
	if j <= -7.4e-63:
		tmp = t_2
	elif j <= 2.35e-104:
		tmp = t_1
	elif j <= 2.7e-91:
		tmp = c * ((a * j) - (z * b))
	elif j <= 2.7e+134:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	t_2 = Float64(Float64(z * Float64(x * y)) + Float64(Float64(i * Float64(t * b)) + Float64(j * Float64(Float64(a * c) - Float64(y * i)))))
	tmp = 0.0
	if (j <= -7.4e-63)
		tmp = t_2;
	elseif (j <= 2.35e-104)
		tmp = t_1;
	elseif (j <= 2.7e-91)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= 2.7e+134)
		tmp = 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 = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	t_2 = (z * (x * y)) + ((i * (t * b)) + (j * ((a * c) - (y * i))));
	tmp = 0.0;
	if (j <= -7.4e-63)
		tmp = t_2;
	elseif (j <= 2.35e-104)
		tmp = t_1;
	elseif (j <= 2.7e-91)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= 2.7e+134)
		tmp = 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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.4e-63], t$95$2, If[LessEqual[j, 2.35e-104], t$95$1, If[LessEqual[j, 2.7e-91], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.7e+134], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -7.40000000000000025e-63 or 2.7e134 < j

   1. Initial program 65.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 65.4%

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

      2. *-commutative 65.4%

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

      3. sub-neg 65.4%

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

      4. sub-neg 65.4%

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

      5. *-commutative 65.4%

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

   3. Simplified 65.4%

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

   4. Taylor expanded in z around 0 68.8%

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

      1. mul-1-neg 68.8%

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

      2. *-commutative 68.8%

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

      3. associate-*l* 73.5%

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

      4. *-commutative 73.5%

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

   6. Simplified 73.5%

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

   7. Taylor expanded in y around inf 74.4%

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

      1. associate-*r* 73.0%

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

      2. *-commutative 73.0%

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

   9. Simplified 73.0%

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

   if -7.40000000000000025e-63 < j < 2.35e-104 or 2.6999999999999997e-91 < j < 2.7e134

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.6%

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

      2. *-commutative 76.6%

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

      3. sub-neg 76.6%

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

      4. sub-neg 76.6%

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

      5. *-commutative 76.6%

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

   3. Simplified 76.6%

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

   4. Taylor expanded in j around 0 80.9%

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

      1. *-commutative 80.9%

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

      2. *-commutative 80.9%

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

   6. Simplified 80.9%

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

   if 2.35e-104 < j < 2.6999999999999997e-91

   1. Initial program 34.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.9%

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

      2. *-commutative 34.9%

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

      3. sub-neg 34.9%

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

      4. sub-neg 34.9%

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

      5. *-commutative 34.9%

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

   3. Simplified 34.9%

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

   4. Taylor expanded in c around inf 78.5%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.4 \cdot 10^{-63}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + \left(i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + \left(i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right)\\ \end{array} \]

Alternative 6: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -1.35 \cdot 10^{-84}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;j \leq 6.9 \cdot 10^{-106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+134}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* i (* t b)) (* j (- (* a c) (* y i)))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_2 (* b (- (* t i) (* z c))))))
   (if (<= j -1.35e-84)
     (+ t_2 t_1)
     (if (<= j 6.9e-106)
       t_3
       (if (<= j 2.7e-91)
         (* c (- (* a j) (* z b)))
         (if (<= j 1.9e+134) t_3 (+ (* z (* x y)) 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 = (i * (t * b)) + (j * ((a * c) - (y * i)));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -1.35e-84) {
		tmp = t_2 + t_1;
	} else if (j <= 6.9e-106) {
		tmp = t_3;
	} else if (j <= 2.7e-91) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 1.9e+134) {
		tmp = t_3;
	} else {
		tmp = (z * (x * y)) + t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_3
    real(8) :: tmp
    t_1 = (i * (t * b)) + (j * ((a * c) - (y * i)))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 + (b * ((t * i) - (z * c)))
    if (j <= (-1.35d-84)) then
        tmp = t_2 + t_1
    else if (j <= 6.9d-106) then
        tmp = t_3
    else if (j <= 2.7d-91) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= 1.9d+134) then
        tmp = t_3
    else
        tmp = (z * (x * y)) + t_1
    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 = (i * (t * b)) + (j * ((a * c) - (y * i)));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -1.35e-84) {
		tmp = t_2 + t_1;
	} else if (j <= 6.9e-106) {
		tmp = t_3;
	} else if (j <= 2.7e-91) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 1.9e+134) {
		tmp = t_3;
	} else {
		tmp = (z * (x * y)) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (i * (t * b)) + (j * ((a * c) - (y * i)))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 + (b * ((t * i) - (z * c)))
	tmp = 0
	if j <= -1.35e-84:
		tmp = t_2 + t_1
	elif j <= 6.9e-106:
		tmp = t_3
	elif j <= 2.7e-91:
		tmp = c * ((a * j) - (z * b))
	elif j <= 1.9e+134:
		tmp = t_3
	else:
		tmp = (z * (x * y)) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(i * Float64(t * b)) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -1.35e-84)
		tmp = Float64(t_2 + t_1);
	elseif (j <= 6.9e-106)
		tmp = t_3;
	elseif (j <= 2.7e-91)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= 1.9e+134)
		tmp = t_3;
	else
		tmp = Float64(Float64(z * Float64(x * y)) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (i * (t * b)) + (j * ((a * c) - (y * i)));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (j <= -1.35e-84)
		tmp = t_2 + t_1;
	elseif (j <= 6.9e-106)
		tmp = t_3;
	elseif (j <= 2.7e-91)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= 1.9e+134)
		tmp = t_3;
	else
		tmp = (z * (x * y)) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.35e-84], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[j, 6.9e-106], t$95$3, If[LessEqual[j, 2.7e-91], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.9e+134], t$95$3, N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.35e-84

   1. Initial program 68.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 68.3%

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

      2. *-commutative 68.3%

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

      3. sub-neg 68.3%

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

      4. sub-neg 68.3%

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

      5. *-commutative 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in z around 0 70.5%

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

      1. mul-1-neg 70.5%

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

      2. *-commutative 70.5%

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

      3. associate-*l* 74.9%

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

      4. *-commutative 74.9%

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

   6. Simplified 74.9%

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

   if -1.35e-84 < j < 6.9000000000000003e-106 or 2.6999999999999997e-91 < j < 1.89999999999999999e134

   1. Initial program 76.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.7%

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

      2. *-commutative 76.7%

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

      3. sub-neg 76.7%

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

      4. sub-neg 76.7%

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

      5. *-commutative 76.7%

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

   3. Simplified 76.7%

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

   4. Taylor expanded in j around 0 81.3%

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

      1. *-commutative 81.3%

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

      2. *-commutative 81.3%

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

   6. Simplified 81.3%

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

   if 6.9000000000000003e-106 < j < 2.6999999999999997e-91

   1. Initial program 34.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.9%

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

      2. *-commutative 34.9%

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

      3. sub-neg 34.9%

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

      4. sub-neg 34.9%

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

      5. *-commutative 34.9%

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

   3. Simplified 34.9%

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

   4. Taylor expanded in c around inf 78.5%

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

   if 1.89999999999999999e134 < j

   1. Initial program 61.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 61.2%

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

      2. *-commutative 61.2%

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

      3. sub-neg 61.2%

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

      4. sub-neg 61.2%

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

      5. *-commutative 61.2%

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

   3. Simplified 61.2%

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

   4. Taylor expanded in z around 0 66.2%

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

      1. mul-1-neg 66.2%

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

      2. *-commutative 66.2%

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

      3. associate-*l* 73.3%

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

      4. *-commutative 73.3%

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

   6. Simplified 73.3%

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

   7. Taylor expanded in y around inf 83.2%

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

      1. associate-*r* 78.5%

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

      2. *-commutative 78.5%

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

   9. Simplified 78.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.35 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + \left(i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right)\\ \mathbf{elif}\;j \leq 6.9 \cdot 10^{-106}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{+134}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + \left(i \cdot \left(t \cdot b\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right)\\ \end{array} \]

Alternative 7: 68.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_2 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -3.1 \cdot 10^{+43}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+138}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_2 (* b (- (* t i) (* z c))))))
   (if (<= j -3.1e+43)
     (+ t_2 t_1)
     (if (<= j 2.35e-104)
       t_3
       (if (<= j 2.7e-91)
         (* c (- (* a j) (* z b)))
         (if (<= j 2.8e+138) t_3 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 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -3.1e+43) {
		tmp = t_2 + t_1;
	} else if (j <= 2.35e-104) {
		tmp = t_3;
	} else if (j <= 2.7e-91) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 2.8e+138) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 + (b * ((t * i) - (z * c)))
    if (j <= (-3.1d+43)) then
        tmp = t_2 + t_1
    else if (j <= 2.35d-104) then
        tmp = t_3
    else if (j <= 2.7d-91) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= 2.8d+138) then
        tmp = t_3
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (b * ((t * i) - (z * c)));
	double tmp;
	if (j <= -3.1e+43) {
		tmp = t_2 + t_1;
	} else if (j <= 2.35e-104) {
		tmp = t_3;
	} else if (j <= 2.7e-91) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= 2.8e+138) {
		tmp = t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 + (b * ((t * i) - (z * c)))
	tmp = 0
	if j <= -3.1e+43:
		tmp = t_2 + t_1
	elif j <= 2.35e-104:
		tmp = t_3
	elif j <= 2.7e-91:
		tmp = c * ((a * j) - (z * b))
	elif j <= 2.8e+138:
		tmp = t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (j <= -3.1e+43)
		tmp = Float64(t_2 + t_1);
	elseif (j <= 2.35e-104)
		tmp = t_3;
	elseif (j <= 2.7e-91)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= 2.8e+138)
		tmp = t_3;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (j <= -3.1e+43)
		tmp = t_2 + t_1;
	elseif (j <= 2.35e-104)
		tmp = t_3;
	elseif (j <= 2.7e-91)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= 2.8e+138)
		tmp = t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.1e+43], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[j, 2.35e-104], t$95$3, If[LessEqual[j, 2.7e-91], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.8e+138], t$95$3, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.1000000000000002e43

   1. Initial program 67.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.9%

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

      2. *-commutative 67.9%

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

      3. sub-neg 67.9%

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

      4. sub-neg 67.9%

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

      5. *-commutative 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in b around 0 71.3%

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

   if -3.1000000000000002e43 < j < 2.35e-104 or 2.6999999999999997e-91 < j < 2.8000000000000001e138

   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. Step-by-step derivation

      1. associate-+l- 75.2%

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

      2. *-commutative 75.2%

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

      3. sub-neg 75.2%

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

      4. sub-neg 75.2%

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

      5. *-commutative 75.2%

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

   3. Simplified 75.2%

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

   4. Taylor expanded in j around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. *-commutative 78.9%

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

   6. Simplified 78.9%

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

   if 2.35e-104 < j < 2.6999999999999997e-91

   1. Initial program 34.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 34.9%

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

      2. *-commutative 34.9%

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

      3. sub-neg 34.9%

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

      4. sub-neg 34.9%

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

      5. *-commutative 34.9%

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

   3. Simplified 34.9%

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

   4. Taylor expanded in c around inf 78.5%

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

   if 2.8000000000000001e138 < j

   1. Initial program 60.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 60.3%

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

      2. *-commutative 60.3%

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

      3. sub-neg 60.3%

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

      4. sub-neg 60.3%

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

      5. *-commutative 60.3%

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

   3. Simplified 60.3%

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

   4. Taylor expanded in z around 0 65.4%

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

      1. mul-1-neg 65.4%

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

      2. *-commutative 65.4%

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

      3. associate-*l* 72.6%

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

      4. *-commutative 72.6%

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

   6. Simplified 72.6%

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

   7. Taylor expanded in j around inf 75.7%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.1 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.7 \cdot 10^{-91}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+138}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 8: 52.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.7 \cdot 10^{+88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -1.08 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -1.7e+88)
     t_3
     (if (<= c -5.8e+42)
       t_2
       (if (<= c -6.8e+39)
         (* a (* x (- t)))
         (if (<= c -1.08e+26)
           (* z (- (* x y) (* b c)))
           (if (<= c -5.6e-141)
             t_2
             (if (<= c -1.12e-250)
               t_1
               (if (<= c 2e-294)
                 (* x (- (* y z) (* t a)))
                 (if (<= c 3.3e+43) 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 = t * ((b * i) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.7e+88) {
		tmp = t_3;
	} else if (c <= -5.8e+42) {
		tmp = t_2;
	} else if (c <= -6.8e+39) {
		tmp = a * (x * -t);
	} else if (c <= -1.08e+26) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -5.6e-141) {
		tmp = t_2;
	} else if (c <= -1.12e-250) {
		tmp = t_1;
	} else if (c <= 2e-294) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3.3e+43) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_3
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-1.7d+88)) then
        tmp = t_3
    else if (c <= (-5.8d+42)) then
        tmp = t_2
    else if (c <= (-6.8d+39)) then
        tmp = a * (x * -t)
    else if (c <= (-1.08d+26)) then
        tmp = z * ((x * y) - (b * c))
    else if (c <= (-5.6d-141)) then
        tmp = t_2
    else if (c <= (-1.12d-250)) then
        tmp = t_1
    else if (c <= 2d-294) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 3.3d+43) then
        tmp = t_1
    else
        tmp = t_3
    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 = t * ((b * i) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.7e+88) {
		tmp = t_3;
	} else if (c <= -5.8e+42) {
		tmp = t_2;
	} else if (c <= -6.8e+39) {
		tmp = a * (x * -t);
	} else if (c <= -1.08e+26) {
		tmp = z * ((x * y) - (b * c));
	} else if (c <= -5.6e-141) {
		tmp = t_2;
	} else if (c <= -1.12e-250) {
		tmp = t_1;
	} else if (c <= 2e-294) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3.3e+43) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.7e+88:
		tmp = t_3
	elif c <= -5.8e+42:
		tmp = t_2
	elif c <= -6.8e+39:
		tmp = a * (x * -t)
	elif c <= -1.08e+26:
		tmp = z * ((x * y) - (b * c))
	elif c <= -5.6e-141:
		tmp = t_2
	elif c <= -1.12e-250:
		tmp = t_1
	elif c <= 2e-294:
		tmp = x * ((y * z) - (t * a))
	elif c <= 3.3e+43:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.7e+88)
		tmp = t_3;
	elseif (c <= -5.8e+42)
		tmp = t_2;
	elseif (c <= -6.8e+39)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (c <= -1.08e+26)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (c <= -5.6e-141)
		tmp = t_2;
	elseif (c <= -1.12e-250)
		tmp = t_1;
	elseif (c <= 2e-294)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 3.3e+43)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.7e+88)
		tmp = t_3;
	elseif (c <= -5.8e+42)
		tmp = t_2;
	elseif (c <= -6.8e+39)
		tmp = a * (x * -t);
	elseif (c <= -1.08e+26)
		tmp = z * ((x * y) - (b * c));
	elseif (c <= -5.6e-141)
		tmp = t_2;
	elseif (c <= -1.12e-250)
		tmp = t_1;
	elseif (c <= 2e-294)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 3.3e+43)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.7e+88], t$95$3, If[LessEqual[c, -5.8e+42], t$95$2, If[LessEqual[c, -6.8e+39], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.08e+26], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.6e-141], t$95$2, If[LessEqual[c, -1.12e-250], t$95$1, If[LessEqual[c, 2e-294], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.3e+43], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -1.70000000000000002e88 or 3.3000000000000001e43 < c

   1. Initial program 61.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 61.1%

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

      2. *-commutative 61.1%

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

      3. sub-neg 61.1%

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

      4. sub-neg 61.1%

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

      5. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in c around inf 68.4%

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

   if -1.70000000000000002e88 < c < -5.79999999999999961e42 or -1.08e26 < c < -5.60000000000000023e-141

   1. Initial program 72.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 72.3%

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

      2. *-commutative 72.3%

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

      3. sub-neg 72.3%

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

      4. sub-neg 72.3%

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

      5. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in y around inf 70.0%

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

      1. +-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

      4. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   if -5.79999999999999961e42 < c < -6.7999999999999998e39

   1. Initial program 33.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

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

      2. *-commutative 33.3%

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

      3. sub-neg 33.3%

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

      4. sub-neg 33.3%

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

      5. *-commutative 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in c around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -6.7999999999999998e39 < c < -1.08e26

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 99.0%

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

   if -5.60000000000000023e-141 < c < -1.11999999999999996e-250 or 2.00000000000000003e-294 < c < 3.3000000000000001e43

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 78.1%

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

      2. *-commutative 78.1%

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

      3. sub-neg 78.1%

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

      4. sub-neg 78.1%

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

      5. *-commutative 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in t around inf 60.8%

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

      1. associate-*r* 60.8%

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

      2. neg-mul-1 60.8%

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

      3. cancel-sign-sub 60.8%

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

      4. +-commutative 60.8%

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

      5. mul-1-neg 60.8%

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

      6. unsub-neg 60.8%

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

      7. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   if -1.11999999999999996e-250 < c < 2.00000000000000003e-294

   1. Initial program 90.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. sub-neg 90.0%

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

      4. sub-neg 90.0%

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

      5. *-commutative 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in z around 0 90.0%

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

      1. mul-1-neg 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*l* 100.0%

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

      4. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 80.6%

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

      1. sub-neg 80.6%

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

      2. *-commutative 80.6%

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

      3. sub-neg 80.6%

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

   9. Simplified 80.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.7 \cdot 10^{+88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.8 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -6.8 \cdot 10^{+39}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -1.08 \cdot 10^{+26}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3.3 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 9: 52.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -5.2 \cdot 10^{+88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.32 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* y (- (* x z) (* i j))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -5.2e+88)
     t_3
     (if (<= c -3.6e+42)
       t_2
       (if (<= c -1.3e+40)
         (* a (* x (- t)))
         (if (<= c -1.1e+27)
           (- (* x (* y z)) (* b (* z c)))
           (if (<= c -5.6e-141)
             t_2
             (if (<= c -1.32e-250)
               t_1
               (if (<= c 1.6e-294)
                 (* x (- (* y z) (* t a)))
                 (if (<= c 7.8e+45) 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 = t * ((b * i) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5.2e+88) {
		tmp = t_3;
	} else if (c <= -3.6e+42) {
		tmp = t_2;
	} else if (c <= -1.3e+40) {
		tmp = a * (x * -t);
	} else if (c <= -1.1e+27) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (c <= -5.6e-141) {
		tmp = t_2;
	} else if (c <= -1.32e-250) {
		tmp = t_1;
	} else if (c <= 1.6e-294) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 7.8e+45) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_3
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = y * ((x * z) - (i * j))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-5.2d+88)) then
        tmp = t_3
    else if (c <= (-3.6d+42)) then
        tmp = t_2
    else if (c <= (-1.3d+40)) then
        tmp = a * (x * -t)
    else if (c <= (-1.1d+27)) then
        tmp = (x * (y * z)) - (b * (z * c))
    else if (c <= (-5.6d-141)) then
        tmp = t_2
    else if (c <= (-1.32d-250)) then
        tmp = t_1
    else if (c <= 1.6d-294) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 7.8d+45) then
        tmp = t_1
    else
        tmp = t_3
    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 = t * ((b * i) - (x * a));
	double t_2 = y * ((x * z) - (i * j));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -5.2e+88) {
		tmp = t_3;
	} else if (c <= -3.6e+42) {
		tmp = t_2;
	} else if (c <= -1.3e+40) {
		tmp = a * (x * -t);
	} else if (c <= -1.1e+27) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (c <= -5.6e-141) {
		tmp = t_2;
	} else if (c <= -1.32e-250) {
		tmp = t_1;
	} else if (c <= 1.6e-294) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 7.8e+45) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = y * ((x * z) - (i * j))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -5.2e+88:
		tmp = t_3
	elif c <= -3.6e+42:
		tmp = t_2
	elif c <= -1.3e+40:
		tmp = a * (x * -t)
	elif c <= -1.1e+27:
		tmp = (x * (y * z)) - (b * (z * c))
	elif c <= -5.6e-141:
		tmp = t_2
	elif c <= -1.32e-250:
		tmp = t_1
	elif c <= 1.6e-294:
		tmp = x * ((y * z) - (t * a))
	elif c <= 7.8e+45:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -5.2e+88)
		tmp = t_3;
	elseif (c <= -3.6e+42)
		tmp = t_2;
	elseif (c <= -1.3e+40)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (c <= -1.1e+27)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(z * c)));
	elseif (c <= -5.6e-141)
		tmp = t_2;
	elseif (c <= -1.32e-250)
		tmp = t_1;
	elseif (c <= 1.6e-294)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 7.8e+45)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = y * ((x * z) - (i * j));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -5.2e+88)
		tmp = t_3;
	elseif (c <= -3.6e+42)
		tmp = t_2;
	elseif (c <= -1.3e+40)
		tmp = a * (x * -t);
	elseif (c <= -1.1e+27)
		tmp = (x * (y * z)) - (b * (z * c));
	elseif (c <= -5.6e-141)
		tmp = t_2;
	elseif (c <= -1.32e-250)
		tmp = t_1;
	elseif (c <= 1.6e-294)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 7.8e+45)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -5.2e+88], t$95$3, If[LessEqual[c, -3.6e+42], t$95$2, If[LessEqual[c, -1.3e+40], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.1e+27], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -5.6e-141], t$95$2, If[LessEqual[c, -1.32e-250], t$95$1, If[LessEqual[c, 1.6e-294], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.8e+45], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if c < -5.2000000000000001e88 or 7.7999999999999999e45 < c

   1. Initial program 61.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 61.1%

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

      2. *-commutative 61.1%

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

      3. sub-neg 61.1%

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

      4. sub-neg 61.1%

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

      5. *-commutative 61.1%

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

   3. Simplified 61.1%

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

   4. Taylor expanded in c around inf 68.4%

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

   if -5.2000000000000001e88 < c < -3.6000000000000001e42 or -1.0999999999999999e27 < c < -5.60000000000000023e-141

   1. Initial program 72.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 72.3%

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

      2. *-commutative 72.3%

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

      3. sub-neg 72.3%

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

      4. sub-neg 72.3%

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

      5. *-commutative 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in y around inf 70.0%

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

      1. +-commutative 70.0%

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

      2. mul-1-neg 70.0%

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

      3. unsub-neg 70.0%

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

      4. *-commutative 70.0%

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

   6. Simplified 70.0%

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

   if -3.6000000000000001e42 < c < -1.3e40

   1. Initial program 33.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 33.3%

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

      2. *-commutative 33.3%

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

      3. sub-neg 33.3%

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

      4. sub-neg 33.3%

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

      5. *-commutative 33.3%

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

   3. Simplified 33.3%

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

   4. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in c around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-lft-neg-out 100.0%

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

      3. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -1.3e40 < c < -1.0999999999999999e27

   1. Initial program 100.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

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

      2. *-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in z around inf 99.0%

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

   5. Taylor expanded in x around 0 100.0%

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

      1. mul-1-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. sub-neg 100.0%

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

      4. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -5.60000000000000023e-141 < c < -1.32e-250 or 1.6000000000000001e-294 < c < 7.7999999999999999e45

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 78.1%

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

      2. *-commutative 78.1%

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

      3. sub-neg 78.1%

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

      4. sub-neg 78.1%

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

      5. *-commutative 78.1%

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

   3. Simplified 78.1%

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

   4. Taylor expanded in t around inf 60.8%

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

      1. associate-*r* 60.8%

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

      2. neg-mul-1 60.8%

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

      3. cancel-sign-sub 60.8%

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

      4. +-commutative 60.8%

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

      5. mul-1-neg 60.8%

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

      6. unsub-neg 60.8%

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

      7. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   if -1.32e-250 < c < 1.6000000000000001e-294

   1. Initial program 90.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 90.0%

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

      2. *-commutative 90.0%

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

      3. sub-neg 90.0%

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

      4. sub-neg 90.0%

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

      5. *-commutative 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in z around 0 90.0%

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

      1. mul-1-neg 90.0%

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

      2. *-commutative 90.0%

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

      3. associate-*l* 100.0%

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

      4. *-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around inf 80.6%

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

      1. sub-neg 80.6%

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

      2. *-commutative 80.6%

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

      3. sub-neg 80.6%

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

   9. Simplified 80.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -5.2 \cdot 10^{+88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{+42}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{+40}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -1.1 \cdot 10^{+27}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.32 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 7.8 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 10: 59.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+123}:\\ \;\;\;\;t_1 - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + \left(i \cdot \left(t \cdot b\right) + c \cdot \left(a \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-295}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2e+123)
     (- t_1 (* z (* b c)))
     (if (<= x -4e-81)
       (+ (* z (* x y)) (+ (* i (* t b)) (* c (* a j))))
       (if (<= x -3e-295)
         (* j (- (* a c) (* y i)))
         (if (<= x 1.2e-178)
           (+ (* a (* c j)) (* b (- (* t i) (* z c))))
           (if (<= x 5.8e+45)
             (- (* i (- (* t b) (* y j))) (* b (* z c)))
             (+ t_1 (* t (* b i))))))))))

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));
	double tmp;
	if (x <= -2e+123) {
		tmp = t_1 - (z * (b * c));
	} else if (x <= -4e-81) {
		tmp = (z * (x * y)) + ((i * (t * b)) + (c * (a * j)));
	} else if (x <= -3e-295) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 1.2e-178) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 5.8e+45) {
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	} else {
		tmp = t_1 + (t * (b * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-2d+123)) then
        tmp = t_1 - (z * (b * c))
    else if (x <= (-4d-81)) then
        tmp = (z * (x * y)) + ((i * (t * b)) + (c * (a * j)))
    else if (x <= (-3d-295)) then
        tmp = j * ((a * c) - (y * i))
    else if (x <= 1.2d-178) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else if (x <= 5.8d+45) then
        tmp = (i * ((t * b) - (y * j))) - (b * (z * c))
    else
        tmp = t_1 + (t * (b * 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 t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2e+123) {
		tmp = t_1 - (z * (b * c));
	} else if (x <= -4e-81) {
		tmp = (z * (x * y)) + ((i * (t * b)) + (c * (a * j)));
	} else if (x <= -3e-295) {
		tmp = j * ((a * c) - (y * i));
	} else if (x <= 1.2e-178) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 5.8e+45) {
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	} else {
		tmp = t_1 + (t * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -2e+123:
		tmp = t_1 - (z * (b * c))
	elif x <= -4e-81:
		tmp = (z * (x * y)) + ((i * (t * b)) + (c * (a * j)))
	elif x <= -3e-295:
		tmp = j * ((a * c) - (y * i))
	elif x <= 1.2e-178:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	elif x <= 5.8e+45:
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c))
	else:
		tmp = t_1 + (t * (b * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -2e+123)
		tmp = Float64(t_1 - Float64(z * Float64(b * c)));
	elseif (x <= -4e-81)
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(Float64(i * Float64(t * b)) + Float64(c * Float64(a * j))));
	elseif (x <= -3e-295)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (x <= 1.2e-178)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (x <= 5.8e+45)
		tmp = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) - Float64(b * Float64(z * c)));
	else
		tmp = Float64(t_1 + Float64(t * Float64(b * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2e+123)
		tmp = t_1 - (z * (b * c));
	elseif (x <= -4e-81)
		tmp = (z * (x * y)) + ((i * (t * b)) + (c * (a * j)));
	elseif (x <= -3e-295)
		tmp = j * ((a * c) - (y * i));
	elseif (x <= 1.2e-178)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	elseif (x <= 5.8e+45)
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	else
		tmp = t_1 + (t * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2e+123], N[(t$95$1 - N[(z * N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4e-81], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3e-295], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.2e-178], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+45], N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -1.99999999999999996e123

   1. Initial program 74.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 74.1%

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

      2. *-commutative 74.1%

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

      3. sub-neg 74.1%

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

      4. sub-neg 74.1%

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

      5. *-commutative 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in j around 0 78.0%

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

      1. *-commutative 78.0%

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

      2. *-commutative 78.0%

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

   6. Simplified 78.0%

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

   7. Taylor expanded in c around inf 75.0%

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

      1. *-commutative 75.0%

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

      2. *-commutative 75.0%

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

      3. associate-*l* 75.0%

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

      4. *-commutative 75.0%

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

   9. Simplified 75.0%

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

   if -1.99999999999999996e123 < x < -3.9999999999999998e-81

   1. Initial program 77.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 77.8%

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

      2. *-commutative 77.8%

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

      3. sub-neg 77.8%

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

      4. sub-neg 77.8%

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

      5. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   4. Taylor expanded in z around 0 70.0%

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

      1. mul-1-neg 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*l* 69.9%

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

      4. *-commutative 69.9%

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

   6. Simplified 69.9%

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

   7. Taylor expanded in y around inf 68.5%

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

      1. associate-*r* 70.1%

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

      2. *-commutative 70.1%

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

   9. Simplified 70.1%

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

   10. Taylor expanded in a around inf 70.0%

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

       1. associate-*r* 63.7%

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

       2. *-commutative 63.7%

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

       3. associate-*l* 68.4%

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

   12. Simplified 68.4%

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

   if -3.9999999999999998e-81 < x < -2.99999999999999996e-295

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 64.2%

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

      2. *-commutative 64.2%

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

      3. sub-neg 64.2%

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

      4. sub-neg 64.2%

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

      5. *-commutative 64.2%

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

   3. Simplified 64.2%

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

   4. Taylor expanded in z around 0 58.0%

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

      1. mul-1-neg 58.0%

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

      2. *-commutative 58.0%

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

      3. associate-*l* 60.8%

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

      4. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   7. Taylor expanded in j around inf 67.1%

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

   if -2.99999999999999996e-295 < x < 1.20000000000000002e-178

   1. Initial program 63.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 63.2%

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

      2. *-commutative 63.2%

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

      3. sub-neg 63.2%

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

      4. sub-neg 63.2%

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

      5. *-commutative 63.2%

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

   3. Simplified 63.2%

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

   4. Taylor expanded in x around 0 67.2%

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

      1. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in y around 0 69.9%

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

   if 1.20000000000000002e-178 < x < 5.7999999999999994e45

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.7%

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

      2. *-commutative 67.7%

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

      3. sub-neg 67.7%

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

      4. sub-neg 67.7%

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

      5. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in x around 0 59.5%

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

      1. *-commutative 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in a around 0 61.8%

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

   9. Simplified 69.3%

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

   if 5.7999999999999994e45 < x

   1. Initial program 67.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.2%

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

      2. *-commutative 67.2%

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

      3. sub-neg 67.2%

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

      4. sub-neg 67.2%

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

      5. *-commutative 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in j around 0 68.8%

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

      1. *-commutative 68.8%

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

      2. *-commutative 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in c around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. associate-*r* 78.0%

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

   9. Simplified 78.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - \left(-\left(b \cdot i\right) \cdot t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - z \cdot \left(b \cdot c\right)\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-81}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + \left(i \cdot \left(t \cdot b\right) + c \cdot \left(a \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-295}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+45}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 11: 59.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+54}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + \left(i \cdot \left(t \cdot b\right) + c \cdot \left(a \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-296}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* x (- (* y z) (* t a)))))
   (if (<= x -6.2e+54)
     (+ t_2 t_1)
     (if (<= x -6.2e-86)
       (+ (* z (* x y)) (+ (* i (* t b)) (* c (* a j))))
       (if (<= x -5.2e-296)
         t_1
         (if (<= x 4.8e-178)
           (+ (* a (* c j)) (* b (- (* t i) (* z c))))
           (if (<= x 3.2e+44)
             (- (* i (- (* t b) (* y j))) (* b (* z c)))
             (+ t_2 (* t (* b i))))))))))

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 * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.2e+54) {
		tmp = t_2 + t_1;
	} else if (x <= -6.2e-86) {
		tmp = (z * (x * y)) + ((i * (t * b)) + (c * (a * j)));
	} else if (x <= -5.2e-296) {
		tmp = t_1;
	} else if (x <= 4.8e-178) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 3.2e+44) {
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	} else {
		tmp = t_2 + (t * (b * i));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    if (x <= (-6.2d+54)) then
        tmp = t_2 + t_1
    else if (x <= (-6.2d-86)) then
        tmp = (z * (x * y)) + ((i * (t * b)) + (c * (a * j)))
    else if (x <= (-5.2d-296)) then
        tmp = t_1
    else if (x <= 4.8d-178) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else if (x <= 3.2d+44) then
        tmp = (i * ((t * b) - (y * j))) - (b * (z * c))
    else
        tmp = t_2 + (t * (b * 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 t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -6.2e+54) {
		tmp = t_2 + t_1;
	} else if (x <= -6.2e-86) {
		tmp = (z * (x * y)) + ((i * (t * b)) + (c * (a * j)));
	} else if (x <= -5.2e-296) {
		tmp = t_1;
	} else if (x <= 4.8e-178) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 3.2e+44) {
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	} else {
		tmp = t_2 + (t * (b * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -6.2e+54:
		tmp = t_2 + t_1
	elif x <= -6.2e-86:
		tmp = (z * (x * y)) + ((i * (t * b)) + (c * (a * j)))
	elif x <= -5.2e-296:
		tmp = t_1
	elif x <= 4.8e-178:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	elif x <= 3.2e+44:
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c))
	else:
		tmp = t_2 + (t * (b * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -6.2e+54)
		tmp = Float64(t_2 + t_1);
	elseif (x <= -6.2e-86)
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(Float64(i * Float64(t * b)) + Float64(c * Float64(a * j))));
	elseif (x <= -5.2e-296)
		tmp = t_1;
	elseif (x <= 4.8e-178)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (x <= 3.2e+44)
		tmp = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) - Float64(b * Float64(z * c)));
	else
		tmp = Float64(t_2 + Float64(t * Float64(b * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -6.2e+54)
		tmp = t_2 + t_1;
	elseif (x <= -6.2e-86)
		tmp = (z * (x * y)) + ((i * (t * b)) + (c * (a * j)));
	elseif (x <= -5.2e-296)
		tmp = t_1;
	elseif (x <= 4.8e-178)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	elseif (x <= 3.2e+44)
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	else
		tmp = t_2 + (t * (b * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.2e+54], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[x, -6.2e-86], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] + N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.2e-296], t$95$1, If[LessEqual[x, 4.8e-178], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+44], N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -6.1999999999999999e54

   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. Step-by-step derivation

      1. associate-+l- 79.5%

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

      2. *-commutative 79.5%

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

      3. sub-neg 79.5%

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

      4. sub-neg 79.5%

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

      5. *-commutative 79.5%

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

   3. Simplified 79.5%

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

   4. Taylor expanded in b around 0 74.1%

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

   if -6.1999999999999999e54 < x < -6.19999999999999977e-86

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 72.5%

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

      2. *-commutative 72.5%

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

      3. sub-neg 72.5%

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

      4. sub-neg 72.5%

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

      5. *-commutative 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in z around 0 62.7%

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

      1. mul-1-neg 62.7%

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

      2. *-commutative 62.7%

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

      3. associate-*l* 65.2%

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

      4. *-commutative 65.2%

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

   6. Simplified 65.2%

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

   7. Taylor expanded in y around inf 62.9%

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

      1. associate-*r* 65.5%

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

      2. *-commutative 65.5%

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

   9. Simplified 65.5%

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

   10. Taylor expanded in a around inf 72.6%

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

       1. associate-*r* 62.6%

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

       2. *-commutative 62.6%

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

       3. associate-*l* 70.0%

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

   12. Simplified 70.0%

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

   if -6.19999999999999977e-86 < x < -5.2000000000000001e-296

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 64.2%

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

      2. *-commutative 64.2%

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

      3. sub-neg 64.2%

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

      4. sub-neg 64.2%

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

      5. *-commutative 64.2%

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

   3. Simplified 64.2%

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

   4. Taylor expanded in z around 0 58.0%

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

      1. mul-1-neg 58.0%

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

      2. *-commutative 58.0%

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

      3. associate-*l* 60.8%

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

      4. *-commutative 60.8%

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

   6. Simplified 60.8%

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

   7. Taylor expanded in j around inf 67.1%

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

   if -5.2000000000000001e-296 < x < 4.8000000000000001e-178

   1. Initial program 63.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 63.2%

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

      2. *-commutative 63.2%

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

      3. sub-neg 63.2%

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

      4. sub-neg 63.2%

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

      5. *-commutative 63.2%

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

   3. Simplified 63.2%

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

   4. Taylor expanded in x around 0 67.2%

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

      1. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   7. Taylor expanded in y around 0 69.9%

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

   if 4.8000000000000001e-178 < x < 3.20000000000000004e44

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.7%

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

      2. *-commutative 67.7%

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

      3. sub-neg 67.7%

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

      4. sub-neg 67.7%

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

      5. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in x around 0 59.5%

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

      1. *-commutative 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in a around 0 61.8%

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

   9. Simplified 69.3%

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

   if 3.20000000000000004e44 < x

   1. Initial program 67.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.2%

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

      2. *-commutative 67.2%

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

      3. sub-neg 67.2%

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

      4. sub-neg 67.2%

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

      5. *-commutative 67.2%

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

   3. Simplified 67.2%

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

   4. Taylor expanded in j around 0 68.8%

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

      1. *-commutative 68.8%

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

      2. *-commutative 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in c around 0 76.4%

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

      1. mul-1-neg 76.4%

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

      2. associate-*r* 78.0%

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

   9. Simplified 78.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - \left(-\left(b \cdot i\right) \cdot t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + \left(i \cdot \left(t \cdot b\right) + c \cdot \left(a \cdot j\right)\right)\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-296}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-178}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\\ \end{array} \]

Alternative 12: 50.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-175}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;i \leq 600000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+137} \lor \neg \left(i \leq 7 \cdot 10^{+174}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t))))
        (t_2 (* c (- (* a j) (* z b))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -8.5e+123)
     t_3
     (if (<= i -8.2e-69)
       t_2
       (if (<= i -5.2e-273)
         t_1
         (if (<= i 2.2e-175)
           t_2
           (if (<= i 600000000000.0)
             t_1
             (if (or (<= i 2.8e+137) (not (<= i 7e+174))) t_3 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -8.5e+123) {
		tmp = t_3;
	} else if (i <= -8.2e-69) {
		tmp = t_2;
	} else if (i <= -5.2e-273) {
		tmp = t_1;
	} else if (i <= 2.2e-175) {
		tmp = t_2;
	} else if (i <= 600000000000.0) {
		tmp = t_1;
	} else if ((i <= 2.8e+137) || !(i <= 7e+174)) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_3
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = c * ((a * j) - (z * b))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-8.5d+123)) then
        tmp = t_3
    else if (i <= (-8.2d-69)) then
        tmp = t_2
    else if (i <= (-5.2d-273)) then
        tmp = t_1
    else if (i <= 2.2d-175) then
        tmp = t_2
    else if (i <= 600000000000.0d0) then
        tmp = t_1
    else if ((i <= 2.8d+137) .or. (.not. (i <= 7d+174))) then
        tmp = t_3
    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 = a * ((c * j) - (x * t));
	double t_2 = c * ((a * j) - (z * b));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -8.5e+123) {
		tmp = t_3;
	} else if (i <= -8.2e-69) {
		tmp = t_2;
	} else if (i <= -5.2e-273) {
		tmp = t_1;
	} else if (i <= 2.2e-175) {
		tmp = t_2;
	} else if (i <= 600000000000.0) {
		tmp = t_1;
	} else if ((i <= 2.8e+137) || !(i <= 7e+174)) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = c * ((a * j) - (z * b))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -8.5e+123:
		tmp = t_3
	elif i <= -8.2e-69:
		tmp = t_2
	elif i <= -5.2e-273:
		tmp = t_1
	elif i <= 2.2e-175:
		tmp = t_2
	elif i <= 600000000000.0:
		tmp = t_1
	elif (i <= 2.8e+137) or not (i <= 7e+174):
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -8.5e+123)
		tmp = t_3;
	elseif (i <= -8.2e-69)
		tmp = t_2;
	elseif (i <= -5.2e-273)
		tmp = t_1;
	elseif (i <= 2.2e-175)
		tmp = t_2;
	elseif (i <= 600000000000.0)
		tmp = t_1;
	elseif ((i <= 2.8e+137) || !(i <= 7e+174))
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = c * ((a * j) - (z * b));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -8.5e+123)
		tmp = t_3;
	elseif (i <= -8.2e-69)
		tmp = t_2;
	elseif (i <= -5.2e-273)
		tmp = t_1;
	elseif (i <= 2.2e-175)
		tmp = t_2;
	elseif (i <= 600000000000.0)
		tmp = t_1;
	elseif ((i <= 2.8e+137) || ~((i <= 7e+174)))
		tmp = t_3;
	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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -8.5e+123], t$95$3, If[LessEqual[i, -8.2e-69], t$95$2, If[LessEqual[i, -5.2e-273], t$95$1, If[LessEqual[i, 2.2e-175], t$95$2, If[LessEqual[i, 600000000000.0], t$95$1, If[Or[LessEqual[i, 2.8e+137], N[Not[LessEqual[i, 7e+174]], $MachinePrecision]], t$95$3, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -8.5e123 or 6e11 < i < 2.80000000000000001e137 or 7.0000000000000003e174 < i

   1. Initial program 60.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 60.8%

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

      2. *-commutative 60.8%

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

      3. sub-neg 60.8%

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

      4. sub-neg 60.8%

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

      5. *-commutative 60.8%

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

   3. Simplified 60.8%

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

   4. Taylor expanded in i around inf 72.6%

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

      1. associate-*r* 72.6%

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

      2. neg-mul-1 72.6%

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

      3. cancel-sign-sub 72.6%

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

      4. +-commutative 72.6%

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

      5. mul-1-neg 72.6%

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

      6. unsub-neg 72.6%

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

      7. *-commutative 72.6%

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

   6. Simplified 72.6%

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

   if -8.5e123 < i < -8.1999999999999998e-69 or -5.19999999999999967e-273 < i < 2.2e-175 or 2.80000000000000001e137 < i < 7.0000000000000003e174

   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. Step-by-step derivation

      1. associate-+l- 64.5%

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

      2. *-commutative 64.5%

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

      3. sub-neg 64.5%

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

      4. sub-neg 64.5%

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

      5. *-commutative 64.5%

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

   3. Simplified 64.5%

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

   4. Taylor expanded in c around inf 58.8%

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

   if -8.1999999999999998e-69 < i < -5.19999999999999967e-273 or 2.2e-175 < i < 6e11

   1. Initial program 82.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 82.6%

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

      2. *-commutative 82.6%

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

      3. sub-neg 82.6%

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

      4. sub-neg 82.6%

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

      5. *-commutative 82.6%

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

   3. Simplified 82.6%

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

   4. Taylor expanded in a around inf 60.8%

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

      1. +-commutative 60.8%

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

      2. mul-1-neg 60.8%

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

      3. unsub-neg 60.8%

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

   6. Simplified 60.8%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-69}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-273}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{-175}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 600000000000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{+137} \lor \neg \left(i \leq 7 \cdot 10^{+174}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 13: 56.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.28 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-198}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j)))))
   (if (<= y -1.28e+98)
     t_1
     (if (<= y -2.75e+29)
       (* z (- (* x y) (* b c)))
       (if (<= y -3.5e-198)
         (* t (- (* b i) (* x a)))
         (if (<= y 1.85e+120)
           (+ (* a (* c j)) (* b (- (* t i) (* z c))))
           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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.28e+98) {
		tmp = t_1;
	} else if (y <= -2.75e+29) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= -3.5e-198) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.85e+120) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    if (y <= (-1.28d+98)) then
        tmp = t_1
    else if (y <= (-2.75d+29)) then
        tmp = z * ((x * y) - (b * c))
    else if (y <= (-3.5d-198)) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 1.85d+120) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.28e+98) {
		tmp = t_1;
	} else if (y <= -2.75e+29) {
		tmp = z * ((x * y) - (b * c));
	} else if (y <= -3.5e-198) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1.85e+120) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.28e+98:
		tmp = t_1
	elif y <= -2.75e+29:
		tmp = z * ((x * y) - (b * c))
	elif y <= -3.5e-198:
		tmp = t * ((b * i) - (x * a))
	elif y <= 1.85e+120:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.28e+98)
		tmp = t_1;
	elseif (y <= -2.75e+29)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (y <= -3.5e-198)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 1.85e+120)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.28e+98)
		tmp = t_1;
	elseif (y <= -2.75e+29)
		tmp = z * ((x * y) - (b * c));
	elseif (y <= -3.5e-198)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 1.85e+120)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.28e+98], t$95$1, If[LessEqual[y, -2.75e+29], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e-198], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e+120], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.28000000000000006e98 or 1.85000000000000012e120 < y

   1. Initial program 59.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 59.8%

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

      2. *-commutative 59.8%

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

      3. sub-neg 59.8%

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

      4. sub-neg 59.8%

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

      5. *-commutative 59.8%

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

   3. Simplified 59.8%

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

   4. Taylor expanded in y around inf 65.8%

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

      1. +-commutative 65.8%

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

      2. mul-1-neg 65.8%

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

      3. unsub-neg 65.8%

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

      4. *-commutative 65.8%

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

   6. Simplified 65.8%

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

   if -1.28000000000000006e98 < y < -2.75e29

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 57.1%

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

      2. *-commutative 57.1%

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

      3. sub-neg 57.1%

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

      4. sub-neg 57.1%

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

      5. *-commutative 57.1%

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

   3. Simplified 57.1%

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

   4. Taylor expanded in z around inf 72.1%

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

   if -2.75e29 < y < -3.50000000000000025e-198

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 80.2%

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

      2. *-commutative 80.2%

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

      3. sub-neg 80.2%

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

      4. sub-neg 80.2%

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

      5. *-commutative 80.2%

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

   3. Simplified 80.2%

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

   4. Taylor expanded in t around inf 60.6%

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

      1. associate-*r* 60.6%

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

      2. neg-mul-1 60.6%

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

      3. cancel-sign-sub 60.6%

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

      4. +-commutative 60.6%

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

      5. mul-1-neg 60.6%

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

      6. unsub-neg 60.6%

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

      7. *-commutative 60.6%

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

   6. Simplified 60.6%

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

   if -3.50000000000000025e-198 < y < 1.85000000000000012e120

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 75.9%

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

      2. *-commutative 75.9%

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

      3. sub-neg 75.9%

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

      4. sub-neg 75.9%

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

      5. *-commutative 75.9%

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

   3. Simplified 75.9%

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

   4. Taylor expanded in x around 0 66.8%

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

      1. *-commutative 66.8%

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

   6. Simplified 66.8%

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

   7. Taylor expanded in y around 0 62.7%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.28 \cdot 10^{+98}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+29}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-198}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+120}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]

Alternative 14: 58.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -3.15 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+213} \lor \neg \left(x \leq 1.7 \cdot 10^{+251}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -3.15e+115)
     t_1
     (if (<= x 3.4e-179)
       (+ (* a (* c j)) (* b (- (* t i) (* z c))))
       (if (<= x 6.5e+44)
         (- (* i (- (* t b) (* y j))) (* b (* z c)))
         (if (or (<= x 1.08e+213) (not (<= x 1.7e+251)))
           t_1
           (* z (- (* x y) (* b c)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.15e+115) {
		tmp = t_1;
	} else if (x <= 3.4e-179) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 6.5e+44) {
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	} else if ((x <= 1.08e+213) || !(x <= 1.7e+251)) {
		tmp = t_1;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (x <= (-3.15d+115)) then
        tmp = t_1
    else if (x <= 3.4d-179) then
        tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
    else if (x <= 6.5d+44) then
        tmp = (i * ((t * b) - (y * j))) - (b * (z * c))
    else if ((x <= 1.08d+213) .or. (.not. (x <= 1.7d+251))) then
        tmp = t_1
    else
        tmp = z * ((x * y) - (b * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -3.15e+115) {
		tmp = t_1;
	} else if (x <= 3.4e-179) {
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	} else if (x <= 6.5e+44) {
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	} else if ((x <= 1.08e+213) || !(x <= 1.7e+251)) {
		tmp = t_1;
	} else {
		tmp = z * ((x * y) - (b * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	tmp = 0
	if x <= -3.15e+115:
		tmp = t_1
	elif x <= 3.4e-179:
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)))
	elif x <= 6.5e+44:
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c))
	elif (x <= 1.08e+213) or not (x <= 1.7e+251):
		tmp = t_1
	else:
		tmp = z * ((x * y) - (b * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (x <= -3.15e+115)
		tmp = t_1;
	elseif (x <= 3.4e-179)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (x <= 6.5e+44)
		tmp = Float64(Float64(i * Float64(Float64(t * b) - Float64(y * j))) - Float64(b * Float64(z * c)));
	elseif ((x <= 1.08e+213) || !(x <= 1.7e+251))
		tmp = t_1;
	else
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -3.15e+115)
		tmp = t_1;
	elseif (x <= 3.4e-179)
		tmp = (a * (c * j)) + (b * ((t * i) - (z * c)));
	elseif (x <= 6.5e+44)
		tmp = (i * ((t * b) - (y * j))) - (b * (z * c));
	elseif ((x <= 1.08e+213) || ~((x <= 1.7e+251)))
		tmp = t_1;
	else
		tmp = z * ((x * y) - (b * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.15e+115], t$95$1, If[LessEqual[x, 3.4e-179], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.5e+44], N[(N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.08e+213], N[Not[LessEqual[x, 1.7e+251]], $MachinePrecision]], t$95$1, N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.1499999999999998e115 or 6.50000000000000018e44 < x < 1.08e213 or 1.70000000000000006e251 < x

   1. Initial program 73.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 73.0%

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

      2. *-commutative 73.0%

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

      3. sub-neg 73.0%

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

      4. sub-neg 73.0%

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

      5. *-commutative 73.0%

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

   3. Simplified 73.0%

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

   4. Taylor expanded in z around 0 76.9%

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

      1. mul-1-neg 76.9%

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

      2. *-commutative 76.9%

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

      3. associate-*l* 77.0%

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

      4. *-commutative 77.0%

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

   6. Simplified 77.0%

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

   7. Taylor expanded in x around inf 72.1%

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

      1. sub-neg 72.1%

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

      2. *-commutative 72.1%

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

      3. sub-neg 72.1%

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

   9. Simplified 72.1%

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

   if -3.1499999999999998e115 < x < 3.3999999999999997e-179

   1. Initial program 70.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 70.9%

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

      2. *-commutative 70.9%

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

      3. sub-neg 70.9%

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

      4. sub-neg 70.9%

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

      5. *-commutative 70.9%

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

   3. Simplified 70.9%

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

   4. Taylor expanded in x around 0 67.1%

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

      1. *-commutative 67.1%

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

   6. Simplified 67.1%

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

   7. Taylor expanded in y around 0 62.3%

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

   if 3.3999999999999997e-179 < x < 6.50000000000000018e44

   1. Initial program 67.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 67.7%

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

      2. *-commutative 67.7%

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

      3. sub-neg 67.7%

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

      4. sub-neg 67.7%

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

      5. *-commutative 67.7%

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

   3. Simplified 67.7%

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

   4. Taylor expanded in x around 0 59.5%

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

      1. *-commutative 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in a around 0 61.8%

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

   9. Simplified 69.3%

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

   if 1.08e213 < x < 1.70000000000000006e251

   1. Initial program 45.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 45.3%

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

      2. *-commutative 45.3%

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

      3. sub-neg 45.3%

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

      4. sub-neg 45.3%

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

      5. *-commutative 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in z around inf 74.2%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.15 \cdot 10^{+115}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-179}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{+213} \lor \neg \left(x \leq 1.7 \cdot 10^{+251}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]

Alternative 15: 43.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.55 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.05 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-211}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 4800000:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -2.55e-80)
     t_2
     (if (<= a -3.05e-286)
       t_1
       (if (<= a 1.6e-211)
         (* (* i j) (- y))
         (if (<= a 4.2e-140)
           t_1
           (if (<= a 4800000.0) (* i (- (* y j))) 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 = z * (b * -c);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.55e-80) {
		tmp = t_2;
	} else if (a <= -3.05e-286) {
		tmp = t_1;
	} else if (a <= 1.6e-211) {
		tmp = (i * j) * -y;
	} else if (a <= 4.2e-140) {
		tmp = t_1;
	} else if (a <= 4800000.0) {
		tmp = i * -(y * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 = z * (b * -c)
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-2.55d-80)) then
        tmp = t_2
    else if (a <= (-3.05d-286)) then
        tmp = t_1
    else if (a <= 1.6d-211) then
        tmp = (i * j) * -y
    else if (a <= 4.2d-140) then
        tmp = t_1
    else if (a <= 4800000.0d0) then
        tmp = i * -(y * j)
    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 = z * (b * -c);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.55e-80) {
		tmp = t_2;
	} else if (a <= -3.05e-286) {
		tmp = t_1;
	} else if (a <= 1.6e-211) {
		tmp = (i * j) * -y;
	} else if (a <= 4.2e-140) {
		tmp = t_1;
	} else if (a <= 4800000.0) {
		tmp = i * -(y * j);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.55e-80:
		tmp = t_2
	elif a <= -3.05e-286:
		tmp = t_1
	elif a <= 1.6e-211:
		tmp = (i * j) * -y
	elif a <= 4.2e-140:
		tmp = t_1
	elif a <= 4800000.0:
		tmp = i * -(y * j)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(-c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.55e-80)
		tmp = t_2;
	elseif (a <= -3.05e-286)
		tmp = t_1;
	elseif (a <= 1.6e-211)
		tmp = Float64(Float64(i * j) * Float64(-y));
	elseif (a <= 4.2e-140)
		tmp = t_1;
	elseif (a <= 4800000.0)
		tmp = Float64(i * Float64(-Float64(y * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * -c);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.55e-80)
		tmp = t_2;
	elseif (a <= -3.05e-286)
		tmp = t_1;
	elseif (a <= 1.6e-211)
		tmp = (i * j) * -y;
	elseif (a <= 4.2e-140)
		tmp = t_1;
	elseif (a <= 4800000.0)
		tmp = i * -(y * j);
	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[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.55e-80], t$95$2, If[LessEqual[a, -3.05e-286], t$95$1, If[LessEqual[a, 1.6e-211], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision], If[LessEqual[a, 4.2e-140], t$95$1, If[LessEqual[a, 4800000.0], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.55000000000000004e-80 or 4.8e6 < a

   1. Initial program 66.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 66.3%

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

      2. *-commutative 66.3%

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

      3. sub-neg 66.3%

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

      4. sub-neg 66.3%

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

      5. *-commutative 66.3%

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

   3. Simplified 66.3%

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

   4. Taylor expanded in a around inf 55.4%

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

      1. +-commutative 55.4%

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

      2. mul-1-neg 55.4%

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

      3. unsub-neg 55.4%

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

   6. Simplified 55.4%

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

   if -2.55000000000000004e-80 < a < -3.05000000000000016e-286 or 1.59999999999999993e-211 < a < 4.20000000000000035e-140

   1. Initial program 83.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 83.2%

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

      2. *-commutative 83.2%

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

      3. sub-neg 83.2%

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

      4. sub-neg 83.2%

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

      5. *-commutative 83.2%

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

   3. Simplified 83.2%

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

   4. Taylor expanded in z around inf 59.5%

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

   5. Taylor expanded in x around 0 47.3%

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

      1. mul-1-neg 47.3%

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

      2. distribute-lft-neg-out 47.3%

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

      3. *-commutative 47.3%

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

   7. Simplified 47.3%

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

   if -3.05000000000000016e-286 < a < 1.59999999999999993e-211

   1. Initial program 62.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.3%

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

      2. *-commutative 62.3%

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

      3. sub-neg 62.3%

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

      4. sub-neg 62.3%

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

      5. *-commutative 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in y around inf 45.1%

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

      1. +-commutative 45.1%

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

      2. mul-1-neg 45.1%

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

      3. unsub-neg 45.1%

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

      4. *-commutative 45.1%

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

   6. Simplified 45.1%

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

   7. Taylor expanded in z around 0 35.3%

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

      1. neg-mul-1 35.3%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-rgt-neg-in 35.3%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   9. Simplified 35.3%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   if 4.20000000000000035e-140 < a < 4.8e6

   1. Initial program 72.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 72.5%

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

      2. *-commutative 72.5%

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

      3. sub-neg 72.5%

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

      4. sub-neg 72.5%

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

      5. *-commutative 72.5%

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

   3. Simplified 72.5%

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

   4. Taylor expanded in i around inf 63.4%

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

      1. associate-*r* 63.4%

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

      2. neg-mul-1 63.4%

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

      3. cancel-sign-sub 63.4%

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

      4. +-commutative 63.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 63.4%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 63.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 63.4%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   6. Simplified 63.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   7. Taylor expanded in b around 0 46.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 46.6%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 46.6%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. *-commutative 46.6%

         \[\leadsto -\color{blue}{\left(y \cdot j\right)} \cdot i \]

      4. distribute-rgt-neg-in 46.6%

         \[\leadsto \color{blue}{\left(y \cdot j\right) \cdot \left(-i\right)} \]

   9. Simplified 46.6%

      \[\leadsto \color{blue}{\left(y \cdot j\right) \cdot \left(-i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.55 \cdot 10^{-80}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -3.05 \cdot 10^{-286}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{-211}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-140}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;a \leq 4800000:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]

Alternative 16: 52.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -7.5 \cdot 10^{+88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* c (- (* a j) (* z b)))))
   (if (<= c -7.5e+88)
     t_3
     (if (<= c -5.5e-141)
       t_2
       (if (<= c -1.02e-250)
         t_1
         (if (<= c 3.5e-294) t_2 (if (<= c 4.5e+43) 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 = t * ((b * i) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -7.5e+88) {
		tmp = t_3;
	} else if (c <= -5.5e-141) {
		tmp = t_2;
	} else if (c <= -1.02e-250) {
		tmp = t_1;
	} else if (c <= 3.5e-294) {
		tmp = t_2;
	} else if (c <= 4.5e+43) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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) :: t_3
    real(8) :: tmp
    t_1 = t * ((b * i) - (x * a))
    t_2 = x * ((y * z) - (t * a))
    t_3 = c * ((a * j) - (z * b))
    if (c <= (-7.5d+88)) then
        tmp = t_3
    else if (c <= (-5.5d-141)) then
        tmp = t_2
    else if (c <= (-1.02d-250)) then
        tmp = t_1
    else if (c <= 3.5d-294) then
        tmp = t_2
    else if (c <= 4.5d+43) then
        tmp = t_1
    else
        tmp = t_3
    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 = t * ((b * i) - (x * a));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -7.5e+88) {
		tmp = t_3;
	} else if (c <= -5.5e-141) {
		tmp = t_2;
	} else if (c <= -1.02e-250) {
		tmp = t_1;
	} else if (c <= 3.5e-294) {
		tmp = t_2;
	} else if (c <= 4.5e+43) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = x * ((y * z) - (t * a))
	t_3 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -7.5e+88:
		tmp = t_3
	elif c <= -5.5e-141:
		tmp = t_2
	elif c <= -1.02e-250:
		tmp = t_1
	elif c <= 3.5e-294:
		tmp = t_2
	elif c <= 4.5e+43:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -7.5e+88)
		tmp = t_3;
	elseif (c <= -5.5e-141)
		tmp = t_2;
	elseif (c <= -1.02e-250)
		tmp = t_1;
	elseif (c <= 3.5e-294)
		tmp = t_2;
	elseif (c <= 4.5e+43)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((b * i) - (x * a));
	t_2 = x * ((y * z) - (t * a));
	t_3 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -7.5e+88)
		tmp = t_3;
	elseif (c <= -5.5e-141)
		tmp = t_2;
	elseif (c <= -1.02e-250)
		tmp = t_1;
	elseif (c <= 3.5e-294)
		tmp = t_2;
	elseif (c <= 4.5e+43)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -7.5e+88], t$95$3, If[LessEqual[c, -5.5e-141], t$95$2, If[LessEqual[c, -1.02e-250], t$95$1, If[LessEqual[c, 3.5e-294], t$95$2, If[LessEqual[c, 4.5e+43], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if c < -7.50000000000000031e88 or 4.5e43 < c

   1. Initial program 61.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 61.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 61.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 68.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   if -7.50000000000000031e88 < c < -5.4999999999999998e-141 or -1.02000000000000001e-250 < c < 3.50000000000000032e-294

   1. Initial program 75.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 75.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 75.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 75.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 75.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 75.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 73.1%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 73.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 73.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 78.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 78.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 78.8%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in x around inf 59.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   8. Step-by-step derivation

      1. sub-neg 59.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)} \]

      2. *-commutative 59.9%

         \[\leadsto x \cdot \left(y \cdot z + \left(-\color{blue}{t \cdot a}\right)\right) \]

      3. sub-neg 59.9%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} \]

   9. Simplified 59.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]

   if -5.4999999999999998e-141 < c < -1.02000000000000001e-250 or 3.50000000000000032e-294 < c < 4.5e43

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 78.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 78.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 78.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 78.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 78.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 78.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in t around inf 60.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 60.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \]

      2. neg-mul-1 60.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-b\right)} \cdot i\right) \]

      3. cancel-sign-sub 60.8%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \]

      4. +-commutative 60.8%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)} \]

      5. mul-1-neg 60.8%

         \[\leadsto t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right) \]

      6. unsub-neg 60.8%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)} \]

      7. *-commutative 60.8%

         \[\leadsto t \cdot \left(b \cdot i - \color{blue}{x \cdot a}\right) \]

   6. Simplified 60.8%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i - x \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -7.5 \cdot 10^{+88}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq -1.02 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 3.5 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 4.5 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 17: 52.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_2 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1.12 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))) (t_2 (* c (- (* a j) (* z b)))))
   (if (<= c -1.12e+89)
     t_2
     (if (<= c -5.6e-141)
       (* y (- (* x z) (* i j)))
       (if (<= c -1.12e-250)
         t_1
         (if (<= c 2.1e-294)
           (* x (- (* y z) (* t a)))
           (if (<= c 3e+43) 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 = t * ((b * i) - (x * a));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.12e+89) {
		tmp = t_2;
	} else if (c <= -5.6e-141) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= -1.12e-250) {
		tmp = t_1;
	} else if (c <= 2.1e-294) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3e+43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 = t * ((b * i) - (x * a))
    t_2 = c * ((a * j) - (z * b))
    if (c <= (-1.12d+89)) then
        tmp = t_2
    else if (c <= (-5.6d-141)) then
        tmp = y * ((x * z) - (i * j))
    else if (c <= (-1.12d-250)) then
        tmp = t_1
    else if (c <= 2.1d-294) then
        tmp = x * ((y * z) - (t * a))
    else if (c <= 3d+43) then
        tmp = 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 = t * ((b * i) - (x * a));
	double t_2 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -1.12e+89) {
		tmp = t_2;
	} else if (c <= -5.6e-141) {
		tmp = y * ((x * z) - (i * j));
	} else if (c <= -1.12e-250) {
		tmp = t_1;
	} else if (c <= 2.1e-294) {
		tmp = x * ((y * z) - (t * a));
	} else if (c <= 3e+43) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	t_2 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -1.12e+89:
		tmp = t_2
	elif c <= -5.6e-141:
		tmp = y * ((x * z) - (i * j))
	elif c <= -1.12e-250:
		tmp = t_1
	elif c <= 2.1e-294:
		tmp = x * ((y * z) - (t * a))
	elif c <= 3e+43:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	t_2 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1.12e+89)
		tmp = t_2;
	elseif (c <= -5.6e-141)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (c <= -1.12e-250)
		tmp = t_1;
	elseif (c <= 2.1e-294)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (c <= 3e+43)
		tmp = 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 = t * ((b * i) - (x * a));
	t_2 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -1.12e+89)
		tmp = t_2;
	elseif (c <= -5.6e-141)
		tmp = y * ((x * z) - (i * j));
	elseif (c <= -1.12e-250)
		tmp = t_1;
	elseif (c <= 2.1e-294)
		tmp = x * ((y * z) - (t * a));
	elseif (c <= 3e+43)
		tmp = 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[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.12e+89], t$95$2, If[LessEqual[c, -5.6e-141], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.12e-250], t$95$1, If[LessEqual[c, 2.1e-294], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3e+43], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.11999999999999995e89 or 3.00000000000000017e43 < c

   1. Initial program 61.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 61.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 61.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 68.4%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   if -1.11999999999999995e89 < c < -5.60000000000000023e-141

   1. Initial program 71.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.5%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in y around inf 62.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 62.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 62.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 62.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 62.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   6. Simplified 62.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   if -5.60000000000000023e-141 < c < -1.11999999999999996e-250 or 2.09999999999999984e-294 < c < 3.00000000000000017e43

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 78.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 78.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 78.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 78.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 78.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 78.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in t around inf 60.8%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 60.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \]

      2. neg-mul-1 60.8%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-b\right)} \cdot i\right) \]

      3. cancel-sign-sub 60.8%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \]

      4. +-commutative 60.8%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)} \]

      5. mul-1-neg 60.8%

         \[\leadsto t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right) \]

      6. unsub-neg 60.8%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)} \]

      7. *-commutative 60.8%

         \[\leadsto t \cdot \left(b \cdot i - \color{blue}{x \cdot a}\right) \]

   6. Simplified 60.8%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i - x \cdot a\right)} \]

   if -1.11999999999999996e-250 < c < 2.09999999999999984e-294

   1. Initial program 90.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 90.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 90.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 90.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 90.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 90.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 90.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 90.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 90.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 90.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 100.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 100.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 100.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in x around inf 80.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
   8. Step-by-step derivation

      1. sub-neg 80.6%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z + \left(-a \cdot t\right)\right)} \]

      2. *-commutative 80.6%

         \[\leadsto x \cdot \left(y \cdot z + \left(-\color{blue}{t \cdot a}\right)\right) \]

      3. sub-neg 80.6%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot z - t \cdot a\right)} \]

   9. Simplified 80.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.12 \cdot 10^{+89}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;c \leq -1.12 \cdot 10^{-250}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;c \leq 2.1 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;c \leq 3 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 18: 29.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+140}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* b (- c)))))
   (if (<= y -4.4e+114)
     (* x (* y z))
     (if (<= y -3.2e-18)
       t_1
       (if (<= y -2e-308)
         (* a (* c j))
         (if (<= y 7.6e-144)
           t_1
           (if (<= y 1.4e+49)
             (* c (* a j))
             (if (<= y 4.3e+140) (* t (* b i)) (* (* i j) (- 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 = z * (b * -c);
	double tmp;
	if (y <= -4.4e+114) {
		tmp = x * (y * z);
	} else if (y <= -3.2e-18) {
		tmp = t_1;
	} else if (y <= -2e-308) {
		tmp = a * (c * j);
	} else if (y <= 7.6e-144) {
		tmp = t_1;
	} else if (y <= 1.4e+49) {
		tmp = c * (a * j);
	} else if (y <= 4.3e+140) {
		tmp = t * (b * i);
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (b * -c)
    if (y <= (-4.4d+114)) then
        tmp = x * (y * z)
    else if (y <= (-3.2d-18)) then
        tmp = t_1
    else if (y <= (-2d-308)) then
        tmp = a * (c * j)
    else if (y <= 7.6d-144) then
        tmp = t_1
    else if (y <= 1.4d+49) then
        tmp = c * (a * j)
    else if (y <= 4.3d+140) then
        tmp = t * (b * i)
    else
        tmp = (i * j) * -y
    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 = z * (b * -c);
	double tmp;
	if (y <= -4.4e+114) {
		tmp = x * (y * z);
	} else if (y <= -3.2e-18) {
		tmp = t_1;
	} else if (y <= -2e-308) {
		tmp = a * (c * j);
	} else if (y <= 7.6e-144) {
		tmp = t_1;
	} else if (y <= 1.4e+49) {
		tmp = c * (a * j);
	} else if (y <= 4.3e+140) {
		tmp = t * (b * i);
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (b * -c)
	tmp = 0
	if y <= -4.4e+114:
		tmp = x * (y * z)
	elif y <= -3.2e-18:
		tmp = t_1
	elif y <= -2e-308:
		tmp = a * (c * j)
	elif y <= 7.6e-144:
		tmp = t_1
	elif y <= 1.4e+49:
		tmp = c * (a * j)
	elif y <= 4.3e+140:
		tmp = t * (b * i)
	else:
		tmp = (i * j) * -y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(b * Float64(-c)))
	tmp = 0.0
	if (y <= -4.4e+114)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -3.2e-18)
		tmp = t_1;
	elseif (y <= -2e-308)
		tmp = Float64(a * Float64(c * j));
	elseif (y <= 7.6e-144)
		tmp = t_1;
	elseif (y <= 1.4e+49)
		tmp = Float64(c * Float64(a * j));
	elseif (y <= 4.3e+140)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(Float64(i * j) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (b * -c);
	tmp = 0.0;
	if (y <= -4.4e+114)
		tmp = x * (y * z);
	elseif (y <= -3.2e-18)
		tmp = t_1;
	elseif (y <= -2e-308)
		tmp = a * (c * j);
	elseif (y <= 7.6e-144)
		tmp = t_1;
	elseif (y <= 1.4e+49)
		tmp = c * (a * j);
	elseif (y <= 4.3e+140)
		tmp = t * (b * i);
	else
		tmp = (i * j) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+114], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.2e-18], t$95$1, If[LessEqual[y, -2e-308], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e-144], t$95$1, If[LessEqual[y, 1.4e+49], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+140], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -4.4000000000000001e114

   1. Initial program 56.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 56.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 56.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 56.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 56.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 56.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 56.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 62.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 62.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 61.1%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in z around inf 46.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -4.4000000000000001e114 < y < -3.1999999999999999e-18 or -1.9999999999999998e-308 < y < 7.59999999999999985e-144

   1. Initial program 76.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 76.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 76.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 76.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 76.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 53.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

   5. Taylor expanded in x around 0 46.4%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 46.4%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-lft-neg-out 46.4%

         \[\leadsto z \cdot \color{blue}{\left(\left(-b\right) \cdot c\right)} \]

      3. *-commutative 46.4%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   7. Simplified 46.4%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   if -3.1999999999999999e-18 < y < -1.9999999999999998e-308

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 76.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 76.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 76.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 76.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 76.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 53.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 53.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 53.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 33.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.0%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 33.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if 7.59999999999999985e-144 < y < 1.3999999999999999e49

   1. Initial program 70.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 70.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 70.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 70.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 70.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 70.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 75.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 75.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 75.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 79.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 79.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 79.4%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in c around inf 44.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. associate-*l* 48.2%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   9. Simplified 48.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if 1.3999999999999999e49 < y < 4.30000000000000002e140

   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. Step-by-step derivation

      1. associate-+l- 73.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 56.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 56.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 56.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 56.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 56.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 56.0%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 56.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 56.0%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   6. Simplified 56.0%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   7. Taylor expanded in b around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 49.3%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

   9. Simplified 49.3%

      \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

   if 4.30000000000000002e140 < y

   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. Step-by-step derivation

      1. associate-+l- 66.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 66.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 66.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 66.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 66.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in y around inf 67.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 67.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 67.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 67.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 67.1%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   6. Simplified 67.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around 0 43.1%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 43.1%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-rgt-neg-in 43.1%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   9. Simplified 43.1%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 43.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+114}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-18}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-144}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+140}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]

Alternative 19: 29.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-141}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+140}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -3.1e+106)
   (* x (* y z))
   (if (<= y -9.2e-20)
     (* z (* b (- c)))
     (if (<= y -9.5e-308)
       (* a (* c j))
       (if (<= y 1.15e-141)
         (* b (* z (- c)))
         (if (<= y 1.5e+49)
           (* c (* a j))
           (if (<= y 4.3e+140) (* t (* b i)) (* (* i j) (- 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 (y <= -3.1e+106) {
		tmp = x * (y * z);
	} else if (y <= -9.2e-20) {
		tmp = z * (b * -c);
	} else if (y <= -9.5e-308) {
		tmp = a * (c * j);
	} else if (y <= 1.15e-141) {
		tmp = b * (z * -c);
	} else if (y <= 1.5e+49) {
		tmp = c * (a * j);
	} else if (y <= 4.3e+140) {
		tmp = t * (b * i);
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 <= (-3.1d+106)) then
        tmp = x * (y * z)
    else if (y <= (-9.2d-20)) then
        tmp = z * (b * -c)
    else if (y <= (-9.5d-308)) then
        tmp = a * (c * j)
    else if (y <= 1.15d-141) then
        tmp = b * (z * -c)
    else if (y <= 1.5d+49) then
        tmp = c * (a * j)
    else if (y <= 4.3d+140) then
        tmp = t * (b * i)
    else
        tmp = (i * j) * -y
    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 <= -3.1e+106) {
		tmp = x * (y * z);
	} else if (y <= -9.2e-20) {
		tmp = z * (b * -c);
	} else if (y <= -9.5e-308) {
		tmp = a * (c * j);
	} else if (y <= 1.15e-141) {
		tmp = b * (z * -c);
	} else if (y <= 1.5e+49) {
		tmp = c * (a * j);
	} else if (y <= 4.3e+140) {
		tmp = t * (b * i);
	} else {
		tmp = (i * j) * -y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -3.1e+106:
		tmp = x * (y * z)
	elif y <= -9.2e-20:
		tmp = z * (b * -c)
	elif y <= -9.5e-308:
		tmp = a * (c * j)
	elif y <= 1.15e-141:
		tmp = b * (z * -c)
	elif y <= 1.5e+49:
		tmp = c * (a * j)
	elif y <= 4.3e+140:
		tmp = t * (b * i)
	else:
		tmp = (i * j) * -y
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -3.1e+106)
		tmp = Float64(x * Float64(y * z));
	elseif (y <= -9.2e-20)
		tmp = Float64(z * Float64(b * Float64(-c)));
	elseif (y <= -9.5e-308)
		tmp = Float64(a * Float64(c * j));
	elseif (y <= 1.15e-141)
		tmp = Float64(b * Float64(z * Float64(-c)));
	elseif (y <= 1.5e+49)
		tmp = Float64(c * Float64(a * j));
	elseif (y <= 4.3e+140)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(Float64(i * j) * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -3.1e+106)
		tmp = x * (y * z);
	elseif (y <= -9.2e-20)
		tmp = z * (b * -c);
	elseif (y <= -9.5e-308)
		tmp = a * (c * j);
	elseif (y <= 1.15e-141)
		tmp = b * (z * -c);
	elseif (y <= 1.5e+49)
		tmp = c * (a * j);
	elseif (y <= 4.3e+140)
		tmp = t * (b * i);
	else
		tmp = (i * j) * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -3.1e+106], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.2e-20], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-308], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-141], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+49], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.3e+140], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(N[(i * j), $MachinePrecision] * (-y)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -3.0999999999999999e106

   1. Initial program 56.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 56.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 56.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 56.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 56.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 56.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 56.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 62.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 62.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 62.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 61.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 61.1%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in z around inf 46.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -3.0999999999999999e106 < y < -9.1999999999999997e-20

   1. Initial program 68.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 68.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 68.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 68.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 68.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 68.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 68.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 54.1%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

   5. Taylor expanded in x around 0 44.2%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 44.2%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-lft-neg-out 44.2%

         \[\leadsto z \cdot \color{blue}{\left(\left(-b\right) \cdot c\right)} \]

      3. *-commutative 44.2%

         \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   7. Simplified 44.2%

      \[\leadsto z \cdot \color{blue}{\left(c \cdot \left(-b\right)\right)} \]

   if -9.1999999999999997e-20 < y < -9.49999999999999963e-308

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 76.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 76.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 76.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 76.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 76.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 76.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 53.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 53.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 53.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 53.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 53.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 33.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 33.0%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 33.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -9.49999999999999963e-308 < y < 1.14999999999999997e-141

   1. Initial program 80.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 80.0%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 80.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 80.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 80.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 80.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 80.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around inf 52.6%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]

   5. Taylor expanded in x around 0 52.4%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(c \cdot z\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 52.4%

         \[\leadsto \color{blue}{\left(-1 \cdot b\right) \cdot \left(c \cdot z\right)} \]

      2. neg-mul-1 52.4%

         \[\leadsto \color{blue}{\left(-b\right)} \cdot \left(c \cdot z\right) \]

      3. *-commutative 52.4%

         \[\leadsto \left(-b\right) \cdot \color{blue}{\left(z \cdot c\right)} \]

   7. Simplified 52.4%

      \[\leadsto \color{blue}{\left(-b\right) \cdot \left(z \cdot c\right)} \]

   if 1.14999999999999997e-141 < y < 1.5000000000000001e49

   1. Initial program 70.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 70.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 70.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 70.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 70.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 70.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 70.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 75.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 75.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 75.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 79.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 79.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 79.4%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in c around inf 44.5%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.5%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. associate-*l* 48.2%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   9. Simplified 48.2%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   if 1.5000000000000001e49 < y < 4.30000000000000002e140

   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. Step-by-step derivation

      1. associate-+l- 73.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 56.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 56.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 56.0%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 56.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 56.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 56.0%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 56.0%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 56.0%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   6. Simplified 56.0%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   7. Taylor expanded in b around inf 45.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 49.3%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

   9. Simplified 49.3%

      \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

   if 4.30000000000000002e140 < y

   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. Step-by-step derivation

      1. associate-+l- 66.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 66.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 66.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 66.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 66.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 66.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in y around inf 67.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   5. Step-by-step derivation

      1. +-commutative 67.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 67.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 67.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 67.1%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

   6. Simplified 67.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - i \cdot j\right)} \]

   7. Taylor expanded in z around 0 43.1%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   8. Step-by-step derivation

      1. neg-mul-1 43.1%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-rgt-neg-in 43.1%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   9. Simplified 43.1%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+106}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-20}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-308}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-141}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+49}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+140}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(i \cdot j\right) \cdot \left(-y\right)\\ \end{array} \]

Alternative 20: 50.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -5.2 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-297}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+106}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -5.2e-25)
     t_2
     (if (<= b -2e-246)
       t_1
       (if (<= b 1.95e-297) (* i (- (* y j))) (if (<= b 6.5e+106) 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.2e-25) {
		tmp = t_2;
	} else if (b <= -2e-246) {
		tmp = t_1;
	} else if (b <= 1.95e-297) {
		tmp = i * -(y * j);
	} else if (b <= 6.5e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-5.2d-25)) then
        tmp = t_2
    else if (b <= (-2d-246)) then
        tmp = t_1
    else if (b <= 1.95d-297) then
        tmp = i * -(y * j)
    else if (b <= 6.5d+106) then
        tmp = 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -5.2e-25) {
		tmp = t_2;
	} else if (b <= -2e-246) {
		tmp = t_1;
	} else if (b <= 1.95e-297) {
		tmp = i * -(y * j);
	} else if (b <= 6.5e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -5.2e-25:
		tmp = t_2
	elif b <= -2e-246:
		tmp = t_1
	elif b <= 1.95e-297:
		tmp = i * -(y * j)
	elif b <= 6.5e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -5.2e-25)
		tmp = t_2;
	elseif (b <= -2e-246)
		tmp = t_1;
	elseif (b <= 1.95e-297)
		tmp = Float64(i * Float64(-Float64(y * j)));
	elseif (b <= 6.5e+106)
		tmp = 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 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -5.2e-25)
		tmp = t_2;
	elseif (b <= -2e-246)
		tmp = t_1;
	elseif (b <= 1.95e-297)
		tmp = i * -(y * j);
	elseif (b <= 6.5e+106)
		tmp = 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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -5.2e-25], t$95$2, If[LessEqual[b, -2e-246], t$95$1, If[LessEqual[b, 1.95e-297], N[(i * (-N[(y * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[b, 6.5e+106], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -5.2e-25 or 6.5000000000000003e106 < b

   1. Initial program 72.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 72.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 72.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 72.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 72.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 72.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 72.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 62.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if -5.2e-25 < b < -1.99999999999999991e-246 or 1.9500000000000001e-297 < b < 6.5000000000000003e106

   1. Initial program 69.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 69.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 69.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 69.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 69.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 69.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 69.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 54.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 54.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 54.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 54.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 54.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -1.99999999999999991e-246 < b < 1.9500000000000001e-297

   1. Initial program 52.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 52.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 52.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 52.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 52.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 52.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 52.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 72.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 72.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 72.3%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 72.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 72.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 72.3%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 72.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 72.3%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   6. Simplified 72.3%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   7. Taylor expanded in b around 0 58.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 58.6%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 58.6%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. *-commutative 58.6%

         \[\leadsto -\color{blue}{\left(y \cdot j\right)} \cdot i \]

      4. distribute-rgt-neg-in 58.6%

         \[\leadsto \color{blue}{\left(y \cdot j\right) \cdot \left(-i\right)} \]

   9. Simplified 58.6%

      \[\leadsto \color{blue}{\left(y \cdot j\right) \cdot \left(-i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -5.2 \cdot 10^{-25}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2 \cdot 10^{-246}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-297}:\\ \;\;\;\;i \cdot \left(-y \cdot j\right)\\ \mathbf{elif}\;b \leq 6.5 \cdot 10^{+106}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]

Alternative 21: 51.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{+23}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1e+122)
     t_1
     (if (<= j -1.4e+23)
       (* c (- (* a j) (* z b)))
       (if (<= j -1.8e-85)
         (* a (- (* c j) (* x t)))
         (if (<= j 3.5e+138) (* b (- (* t i) (* z c))) 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1e+122) {
		tmp = t_1;
	} else if (j <= -1.4e+23) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -1.8e-85) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= 3.5e+138) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-1d+122)) then
        tmp = t_1
    else if (j <= (-1.4d+23)) then
        tmp = c * ((a * j) - (z * b))
    else if (j <= (-1.8d-85)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= 3.5d+138) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1e+122) {
		tmp = t_1;
	} else if (j <= -1.4e+23) {
		tmp = c * ((a * j) - (z * b));
	} else if (j <= -1.8e-85) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= 3.5e+138) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1e+122:
		tmp = t_1
	elif j <= -1.4e+23:
		tmp = c * ((a * j) - (z * b))
	elif j <= -1.8e-85:
		tmp = a * ((c * j) - (x * t))
	elif j <= 3.5e+138:
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1e+122)
		tmp = t_1;
	elseif (j <= -1.4e+23)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (j <= -1.8e-85)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= 3.5e+138)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1e+122)
		tmp = t_1;
	elseif (j <= -1.4e+23)
		tmp = c * ((a * j) - (z * b));
	elseif (j <= -1.8e-85)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= 3.5e+138)
		tmp = b * ((t * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1e+122], t$95$1, If[LessEqual[j, -1.4e+23], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.8e-85], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e+138], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.00000000000000001e122 or 3.4999999999999998e138 < j

   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. Step-by-step derivation

      1. associate-+l- 66.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 66.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 66.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 66.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 66.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 66.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 70.6%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 70.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 70.6%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 74.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 74.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 74.4%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in j around inf 76.0%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   if -1.00000000000000001e122 < j < -1.4e23

   1. Initial program 57.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 57.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 57.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 57.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 57.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 57.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 57.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 65.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   if -1.4e23 < j < -1.7999999999999999e-85

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 74.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 46.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 46.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 46.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 46.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 46.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   if -1.7999999999999999e-85 < j < 3.4999999999999998e138

   1. Initial program 73.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 73.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in b around inf 51.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1 \cdot 10^{+122}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.4 \cdot 10^{+23}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -1.8 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+138}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]

Alternative 22: 50.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -4.4 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b)))))
   (if (<= c -4.4e+29)
     t_1
     (if (<= c -5.6e-141)
       (* x (* y z))
       (if (<= c 7e+43) (* t (- (* b i) (* x a))) 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 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -4.4e+29) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 7e+43) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    if (c <= (-4.4d+29)) then
        tmp = t_1
    else if (c <= (-5.6d-141)) then
        tmp = x * (y * z)
    else if (c <= 7d+43) then
        tmp = t * ((b * i) - (x * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double tmp;
	if (c <= -4.4e+29) {
		tmp = t_1;
	} else if (c <= -5.6e-141) {
		tmp = x * (y * z);
	} else if (c <= 7e+43) {
		tmp = t * ((b * i) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	tmp = 0
	if c <= -4.4e+29:
		tmp = t_1
	elif c <= -5.6e-141:
		tmp = x * (y * z)
	elif c <= 7e+43:
		tmp = t * ((b * i) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -4.4e+29)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 7e+43)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	tmp = 0.0;
	if (c <= -4.4e+29)
		tmp = t_1;
	elseif (c <= -5.6e-141)
		tmp = x * (y * z);
	elseif (c <= 7e+43)
		tmp = t * ((b * i) - (x * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -4.4e+29], t$95$1, If[LessEqual[c, -5.6e-141], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7e+43], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.4000000000000003e29 or 7.0000000000000002e43 < c

   1. Initial program 61.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 61.4%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 61.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 61.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 61.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 61.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 61.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in c around inf 65.0%

      \[\leadsto \color{blue}{c \cdot \left(a \cdot j - b \cdot z\right)} \]

   if -4.4000000000000003e29 < c < -5.60000000000000023e-141

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 74.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 77.5%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 77.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 77.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 80.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 80.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 80.5%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in z around inf 52.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -5.60000000000000023e-141 < c < 7.0000000000000002e43

   1. Initial program 79.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 79.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 79.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 79.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 79.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 79.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in t around inf 57.9%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 57.9%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \]

      2. neg-mul-1 57.9%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x\right) - \color{blue}{\left(-b\right)} \cdot i\right) \]

      3. cancel-sign-sub 57.9%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x\right) + b \cdot i\right)} \]

      4. +-commutative 57.9%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i + -1 \cdot \left(a \cdot x\right)\right)} \]

      5. mul-1-neg 57.9%

         \[\leadsto t \cdot \left(b \cdot i + \color{blue}{\left(-a \cdot x\right)}\right) \]

      6. unsub-neg 57.9%

         \[\leadsto t \cdot \color{blue}{\left(b \cdot i - a \cdot x\right)} \]

      7. *-commutative 57.9%

         \[\leadsto t \cdot \left(b \cdot i - \color{blue}{x \cdot a}\right) \]

   6. Simplified 57.9%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i - x \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.4 \cdot 10^{+29}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -5.6 \cdot 10^{-141}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 7 \cdot 10^{+43}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \end{array} \]

Alternative 23: 31.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 22500000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= c -9.5e+95)
     t_1
     (if (<= c -8e-176)
       (* x (* y z))
       (if (<= c 22500000000000.0) (* a (* x (- t))) 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 = a * (c * j);
	double tmp;
	if (c <= -9.5e+95) {
		tmp = t_1;
	} else if (c <= -8e-176) {
		tmp = x * (y * z);
	} else if (c <= 22500000000000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (c <= (-9.5d+95)) then
        tmp = t_1
    else if (c <= (-8d-176)) then
        tmp = x * (y * z)
    else if (c <= 22500000000000.0d0) then
        tmp = a * (x * -t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -9.5e+95) {
		tmp = t_1;
	} else if (c <= -8e-176) {
		tmp = x * (y * z);
	} else if (c <= 22500000000000.0) {
		tmp = a * (x * -t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if c <= -9.5e+95:
		tmp = t_1
	elif c <= -8e-176:
		tmp = x * (y * z)
	elif c <= 22500000000000.0:
		tmp = a * (x * -t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (c <= -9.5e+95)
		tmp = t_1;
	elseif (c <= -8e-176)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 22500000000000.0)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (c <= -9.5e+95)
		tmp = t_1;
	elseif (c <= -8e-176)
		tmp = x * (y * z);
	elseif (c <= 22500000000000.0)
		tmp = a * (x * -t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -9.5e+95], t$95$1, If[LessEqual[c, -8e-176], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 22500000000000.0], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -9.5000000000000004e95 or 2.25e13 < c

   1. Initial program 61.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 61.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 61.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 61.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 61.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 61.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 61.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 42.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 42.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 42.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 42.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 42.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 40.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 40.3%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -9.5000000000000004e95 < c < -8e-176

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 69.3%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 73.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 73.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 73.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in z around inf 46.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -8e-176 < c < 2.25e13

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 80.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 80.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 80.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 80.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 80.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 80.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 42.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 42.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 42.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 42.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 42.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around 0 34.9%

      \[\leadsto a \cdot \color{blue}{\left(-1 \cdot \left(t \cdot x\right)\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 34.9%

         \[\leadsto a \cdot \color{blue}{\left(-t \cdot x\right)} \]

      2. distribute-lft-neg-out 34.9%

         \[\leadsto a \cdot \color{blue}{\left(\left(-t\right) \cdot x\right)} \]

      3. *-commutative 34.9%

         \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]

   9. Simplified 34.9%

      \[\leadsto a \cdot \color{blue}{\left(x \cdot \left(-t\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -8 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 22500000000000:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 24: 30.8% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -1.55 \cdot 10^{+100}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1650000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))))
   (if (<= c -1.55e+100)
     t_1
     (if (<= c -9.2e-176)
       (* x (* y z))
       (if (<= c 1650000.0) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -1.55e+100) {
		tmp = t_1;
	} else if (c <= -9.2e-176) {
		tmp = x * (y * z);
	} else if (c <= 1650000.0) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (c * j)
    if (c <= (-1.55d+100)) then
        tmp = t_1
    else if (c <= (-9.2d-176)) then
        tmp = x * (y * z)
    else if (c <= 1650000.0d0) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (c * j);
	double tmp;
	if (c <= -1.55e+100) {
		tmp = t_1;
	} else if (c <= -9.2e-176) {
		tmp = x * (y * z);
	} else if (c <= 1650000.0) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (c * j)
	tmp = 0
	if c <= -1.55e+100:
		tmp = t_1
	elif c <= -9.2e-176:
		tmp = x * (y * z)
	elif c <= 1650000.0:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(c * j))
	tmp = 0.0
	if (c <= -1.55e+100)
		tmp = t_1;
	elseif (c <= -9.2e-176)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 1650000.0)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (c * j);
	tmp = 0.0;
	if (c <= -1.55e+100)
		tmp = t_1;
	elseif (c <= -9.2e-176)
		tmp = x * (y * z);
	elseif (c <= 1650000.0)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.55e+100], t$95$1, If[LessEqual[c, -9.2e-176], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1650000.0], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -1.55000000000000003e100 or 1.65e6 < c

   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. Step-by-step derivation

      1. associate-+l- 61.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 61.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 61.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 61.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 61.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 61.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 43.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 43.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 43.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 43.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 43.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 39.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 39.7%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 39.7%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -1.55000000000000003e100 < c < -9.2000000000000005e-176

   1. Initial program 71.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 71.2%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 71.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 69.3%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 69.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 73.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 73.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 73.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in z around inf 46.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -9.2000000000000005e-176 < c < 1.65e6

   1. Initial program 79.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 79.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 79.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 46.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 46.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 46.2%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 46.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 46.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 46.2%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 46.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 46.2%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   6. Simplified 46.2%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   7. Taylor expanded in b around inf 31.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.55 \cdot 10^{+100}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -9.2 \cdot 10^{-176}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 1650000:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]

Alternative 25: 30.3% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -5.6 \cdot 10^{-6} \lor \neg \left(j \leq 2.65 \cdot 10^{+138}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -5.6e-6) (not (<= j 2.65e+138))) (* a (* c 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 ((j <= -5.6e-6) || !(j <= 2.65e+138)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 ((j <= (-5.6d-6)) .or. (.not. (j <= 2.65d+138))) then
        tmp = a * (c * j)
    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 ((j <= -5.6e-6) || !(j <= 2.65e+138)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -5.6e-6) or not (j <= 2.65e+138):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -5.6e-6) || !(j <= 2.65e+138))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -5.6e-6) || ~((j <= 2.65e+138)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -5.6e-6], N[Not[LessEqual[j, 2.65e+138]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -5.59999999999999975e-6 or 2.64999999999999992e138 < j

   1. Initial program 63.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 63.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 63.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 63.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 63.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 63.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 63.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 50.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 45.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 45.0%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 45.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -5.59999999999999975e-6 < j < 2.64999999999999992e138

   1. Initial program 74.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 74.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 74.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 74.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 36.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 36.6%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 36.6%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 36.6%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 36.6%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 36.6%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 36.6%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 36.6%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   6. Simplified 36.6%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   7. Taylor expanded in b around inf 29.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.6 \cdot 10^{-6} \lor \neg \left(j \leq 2.65 \cdot 10^{+138}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]

Alternative 26: 30.5% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{-5}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+129}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.3e-5)
   (* a (* c j))
   (if (<= j 2.4e+129) (* b (* t i)) (* c (* a 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 (j <= -1.3e-5) {
		tmp = a * (c * j);
	} else if (j <= 2.4e+129) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 (j <= (-1.3d-5)) then
        tmp = a * (c * j)
    else if (j <= 2.4d+129) then
        tmp = b * (t * i)
    else
        tmp = c * (a * j)
    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 (j <= -1.3e-5) {
		tmp = a * (c * j);
	} else if (j <= 2.4e+129) {
		tmp = b * (t * i);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.3e-5:
		tmp = a * (c * j)
	elif j <= 2.4e+129:
		tmp = b * (t * i)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.3e-5)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 2.4e+129)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -1.3e-5)
		tmp = a * (c * j);
	elseif (j <= 2.4e+129)
		tmp = b * (t * i);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.3e-5], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.4e+129], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.29999999999999992e-5

   1. Initial program 65.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 65.8%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 65.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 65.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 65.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 65.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 65.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 50.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 43.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 43.0%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 43.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -1.29999999999999992e-5 < j < 2.3999999999999999e129

   1. Initial program 73.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 73.9%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.9%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 36.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 36.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 36.4%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 36.4%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 36.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 36.4%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 36.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 36.4%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   6. Simplified 36.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   7. Taylor expanded in b around inf 29.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if 2.3999999999999999e129 < j

   1. Initial program 62.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 67.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 67.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 67.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 74.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in c around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. associate-*l* 50.9%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   9. Simplified 50.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{-5}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.4 \cdot 10^{+129}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 27: 30.8% accurate, 3.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+131}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -3.8e+20)
   (* a (* c j))
   (if (<= j 2.2e+131) (* i (* t b)) (* c (* a 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 (j <= -3.8e+20) {
		tmp = a * (c * j);
	} else if (j <= 2.2e+131) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 (j <= (-3.8d+20)) then
        tmp = a * (c * j)
    else if (j <= 2.2d+131) then
        tmp = i * (t * b)
    else
        tmp = c * (a * j)
    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 (j <= -3.8e+20) {
		tmp = a * (c * j);
	} else if (j <= 2.2e+131) {
		tmp = i * (t * b);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -3.8e+20:
		tmp = a * (c * j)
	elif j <= 2.2e+131:
		tmp = i * (t * b)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -3.8e+20)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 2.2e+131)
		tmp = Float64(i * Float64(t * b));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -3.8e+20)
		tmp = a * (c * j);
	elseif (j <= 2.2e+131)
		tmp = i * (t * b);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -3.8e+20], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.2e+131], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.8e20

   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. Step-by-step derivation

      1. associate-+l- 66.7%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 66.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 66.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 66.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 66.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 66.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in a around inf 50.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   5. Step-by-step derivation

      1. +-commutative 50.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 50.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 50.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   6. Simplified 50.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

   7. Taylor expanded in c around inf 44.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 44.0%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   9. Simplified 44.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -3.8e20 < j < 2.1999999999999999e131

   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. Step-by-step derivation

      1. associate-+l- 73.3%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 73.3%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 73.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in i around inf 36.5%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 36.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-1 \cdot b\right) \cdot t}\right) \]

      2. neg-mul-1 36.5%

         \[\leadsto i \cdot \left(-1 \cdot \left(j \cdot y\right) - \color{blue}{\left(-b\right)} \cdot t\right) \]

      3. cancel-sign-sub 36.5%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]

      4. +-commutative 36.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      5. mul-1-neg 36.5%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      6. unsub-neg 36.5%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

      7. *-commutative 36.5%

         \[\leadsto i \cdot \left(b \cdot t - \color{blue}{y \cdot j}\right) \]

   6. Simplified 36.5%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - y \cdot j\right)} \]

   7. Taylor expanded in b around inf 29.9%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]
   8. Step-by-step derivation

      1. *-commutative 29.9%

         \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   9. Simplified 29.9%

      \[\leadsto i \cdot \color{blue}{\left(t \cdot b\right)} \]

   if 2.1999999999999999e131 < j

   1. Initial program 62.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Step-by-step derivation

      1. associate-+l- 62.1%

         \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

      2. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

      3. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

      4. sub-neg 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

      5. *-commutative 62.1%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

   3. Simplified 62.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

   4. Taylor expanded in z around 0 67.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]
   5. Step-by-step derivation

      1. mul-1-neg 67.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-b \cdot \left(i \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      2. *-commutative 67.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{\left(i \cdot t\right) \cdot b}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      3. associate-*l* 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-\color{blue}{i \cdot \left(t \cdot b\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

      4. *-commutative 74.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\left(-i \cdot \color{blue}{\left(b \cdot t\right)}\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   6. Simplified 74.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(\color{blue}{\left(-i \cdot \left(b \cdot t\right)\right)} - j \cdot \left(a \cdot c - y \cdot i\right)\right) \]

   7. Taylor expanded in c around inf 46.3%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   8. Step-by-step derivation

      1. *-commutative 46.3%

         \[\leadsto \color{blue}{\left(c \cdot j\right) \cdot a} \]

      2. associate-*l* 50.9%

         \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]

   9. Simplified 50.9%

      \[\leadsto \color{blue}{c \cdot \left(j \cdot a\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{+20}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+131}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]

Alternative 28: 23.1% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 = a * (c * j)
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 a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Step-by-step derivation

   1. associate-+l- 69.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(c \cdot z - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)} \]

   2. *-commutative 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right) \]

   3. sub-neg 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a + \left(-y \cdot i\right)\right)}\right) \]

   4. sub-neg 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \color{blue}{\left(c \cdot a - y \cdot i\right)}\right) \]

   5. *-commutative 69.9%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(\color{blue}{a \cdot c} - y \cdot i\right)\right) \]

3. Simplified 69.9%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot z - t \cdot a\right) - \left(b \cdot \left(z \cdot c - t \cdot i\right) - j \cdot \left(a \cdot c - y \cdot i\right)\right)} \]

4. Taylor expanded in a around inf 40.0%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
5. Step-by-step derivation

   1. +-commutative 40.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 40.0%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 40.0%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

6. Simplified 40.0%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j - t \cdot x\right)} \]

7. Taylor expanded in c around inf 25.1%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
8. Step-by-step derivation

   1. *-commutative 25.1%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

9. Simplified 25.1%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

10. Final simplification 25.1%

    \[\leadsto a \cdot \left(c \cdot j\right) \]

Developer target: 58.6% accurate, 0.1× 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

real(8) function code(x, y, z, t, a, b, c, i, j)
    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 2023279 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))