Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.0% → 81.9%

Time: 33.6s

Alternatives: 21

Speedup: 0.5×

• 58.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 73.0% accurate, 1.0× speedup

Math

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

FPCore

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

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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

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) - (i * a)))) + (j * ((c * t) - (i * y)))
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) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

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(i * a)))) + Float64(j * Float64(Float64(c * t) - Float64(i * y))))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
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[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(c * t), $MachinePrecision] - N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 81.9% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
          (* j (- (* t c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (* c (- (* t 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 * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = c * ((t * 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 * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = c * ((t * 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 * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = c * ((t * 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(a * i) - Float64(z * c)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(t * 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 * ((a * i) - (z * c)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * ((t * 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[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(c * N[(N[(t * 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 i a)))) (*.f64 j (-.f64 (*.f64 c t) (*.f64 i y)))) < +inf.0

   1. Initial program 90.0%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf 57.9%

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

4. Final simplification 84.4%

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

Alternative 2: 29.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ t_2 := \left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{+135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-214}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.46 \cdot 10^{+243}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))) (t_2 (* (- i) (* y j))))
   (if (<= j -2.5e+135)
     t_2
     (if (<= j -4.1e-67)
       t_1
       (if (<= j -1.05e-304)
         (* x (* y z))
         (if (<= j 2.5e-214)
           (* i (* a b))
           (if (<= j 4.8e-145)
             (* z (* x y))
             (if (<= j 5.5e-88)
               t_1
               (if (<= j 1.5e+24)
                 (* b (- (* z c)))
                 (if (<= j 2e+43)
                   t_1
                   (if (<= j 2.8e+115)
                     t_2
                     (if (<= j 2.9e+203)
                       (* t (* c j))
                       (if (<= j 1.46e+243) t_2 (* c (* t j)))))))))))))))

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 * (t * -a);
	double t_2 = -i * (y * j);
	double tmp;
	if (j <= -2.5e+135) {
		tmp = t_2;
	} else if (j <= -4.1e-67) {
		tmp = t_1;
	} else if (j <= -1.05e-304) {
		tmp = x * (y * z);
	} else if (j <= 2.5e-214) {
		tmp = i * (a * b);
	} else if (j <= 4.8e-145) {
		tmp = z * (x * y);
	} else if (j <= 5.5e-88) {
		tmp = t_1;
	} else if (j <= 1.5e+24) {
		tmp = b * -(z * c);
	} else if (j <= 2e+43) {
		tmp = t_1;
	} else if (j <= 2.8e+115) {
		tmp = t_2;
	} else if (j <= 2.9e+203) {
		tmp = t * (c * j);
	} else if (j <= 1.46e+243) {
		tmp = t_2;
	} else {
		tmp = c * (t * 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (t * -a)
    t_2 = -i * (y * j)
    if (j <= (-2.5d+135)) then
        tmp = t_2
    else if (j <= (-4.1d-67)) then
        tmp = t_1
    else if (j <= (-1.05d-304)) then
        tmp = x * (y * z)
    else if (j <= 2.5d-214) then
        tmp = i * (a * b)
    else if (j <= 4.8d-145) then
        tmp = z * (x * y)
    else if (j <= 5.5d-88) then
        tmp = t_1
    else if (j <= 1.5d+24) then
        tmp = b * -(z * c)
    else if (j <= 2d+43) then
        tmp = t_1
    else if (j <= 2.8d+115) then
        tmp = t_2
    else if (j <= 2.9d+203) then
        tmp = t * (c * j)
    else if (j <= 1.46d+243) then
        tmp = t_2
    else
        tmp = c * (t * 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 t_1 = x * (t * -a);
	double t_2 = -i * (y * j);
	double tmp;
	if (j <= -2.5e+135) {
		tmp = t_2;
	} else if (j <= -4.1e-67) {
		tmp = t_1;
	} else if (j <= -1.05e-304) {
		tmp = x * (y * z);
	} else if (j <= 2.5e-214) {
		tmp = i * (a * b);
	} else if (j <= 4.8e-145) {
		tmp = z * (x * y);
	} else if (j <= 5.5e-88) {
		tmp = t_1;
	} else if (j <= 1.5e+24) {
		tmp = b * -(z * c);
	} else if (j <= 2e+43) {
		tmp = t_1;
	} else if (j <= 2.8e+115) {
		tmp = t_2;
	} else if (j <= 2.9e+203) {
		tmp = t * (c * j);
	} else if (j <= 1.46e+243) {
		tmp = t_2;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	t_2 = -i * (y * j)
	tmp = 0
	if j <= -2.5e+135:
		tmp = t_2
	elif j <= -4.1e-67:
		tmp = t_1
	elif j <= -1.05e-304:
		tmp = x * (y * z)
	elif j <= 2.5e-214:
		tmp = i * (a * b)
	elif j <= 4.8e-145:
		tmp = z * (x * y)
	elif j <= 5.5e-88:
		tmp = t_1
	elif j <= 1.5e+24:
		tmp = b * -(z * c)
	elif j <= 2e+43:
		tmp = t_1
	elif j <= 2.8e+115:
		tmp = t_2
	elif j <= 2.9e+203:
		tmp = t * (c * j)
	elif j <= 1.46e+243:
		tmp = t_2
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	t_2 = Float64(Float64(-i) * Float64(y * j))
	tmp = 0.0
	if (j <= -2.5e+135)
		tmp = t_2;
	elseif (j <= -4.1e-67)
		tmp = t_1;
	elseif (j <= -1.05e-304)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 2.5e-214)
		tmp = Float64(i * Float64(a * b));
	elseif (j <= 4.8e-145)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= 5.5e-88)
		tmp = t_1;
	elseif (j <= 1.5e+24)
		tmp = Float64(b * Float64(-Float64(z * c)));
	elseif (j <= 2e+43)
		tmp = t_1;
	elseif (j <= 2.8e+115)
		tmp = t_2;
	elseif (j <= 2.9e+203)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= 1.46e+243)
		tmp = t_2;
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	t_2 = -i * (y * j);
	tmp = 0.0;
	if (j <= -2.5e+135)
		tmp = t_2;
	elseif (j <= -4.1e-67)
		tmp = t_1;
	elseif (j <= -1.05e-304)
		tmp = x * (y * z);
	elseif (j <= 2.5e-214)
		tmp = i * (a * b);
	elseif (j <= 4.8e-145)
		tmp = z * (x * y);
	elseif (j <= 5.5e-88)
		tmp = t_1;
	elseif (j <= 1.5e+24)
		tmp = b * -(z * c);
	elseif (j <= 2e+43)
		tmp = t_1;
	elseif (j <= 2.8e+115)
		tmp = t_2;
	elseif (j <= 2.9e+203)
		tmp = t * (c * j);
	elseif (j <= 1.46e+243)
		tmp = t_2;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e+135], t$95$2, If[LessEqual[j, -4.1e-67], t$95$1, If[LessEqual[j, -1.05e-304], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e-214], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.8e-145], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.5e-88], t$95$1, If[LessEqual[j, 1.5e+24], N[(b * (-N[(z * c), $MachinePrecision])), $MachinePrecision], If[LessEqual[j, 2e+43], t$95$1, If[LessEqual[j, 2.8e+115], t$95$2, If[LessEqual[j, 2.9e+203], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.46e+243], t$95$2, N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if j < -2.50000000000000015e135 or 2.00000000000000003e43 < j < 2.8e115 or 2.90000000000000011e203 < j < 1.46000000000000009e243

   1. Initial program 72.0%

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

   3. Taylor expanded in c around inf 76.2%

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

      1. *-commutative 76.2%

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

      2. associate-*l* 74.3%

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

      3. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in i around inf 66.9%

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

      1. associate-*r* 66.9%

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

      2. neg-mul-1 66.9%

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

   8. Simplified 66.9%

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

   if -2.50000000000000015e135 < j < -4.0999999999999997e-67 or 4.8000000000000003e-145 < j < 5.49999999999999971e-88 or 1.49999999999999997e24 < j < 2.00000000000000003e43

   1. Initial program 76.3%

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

   3. Taylor expanded in j around 0 67.8%

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

      1. *-commutative 67.8%

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

      2. *-commutative 67.8%

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

   5. Simplified 67.8%

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

      1. add-cube-cbrt 67.7%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)} \]

      2. pow3 67.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - i \cdot a}\right)}^{3}} \]

      3. *-commutative 67.8%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot {\left(\sqrt[3]{c \cdot z - \color{blue}{a \cdot i}}\right)}^{3} \]

   7. Applied egg-rr 67.8%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - a \cdot i}\right)}^{3}} \]

   8. Taylor expanded in c around inf 68.9%

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

      1. *-commutative 68.9%

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

      2. associate-*l* 68.0%

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

   10. Simplified 68.0%

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

   11. Taylor expanded in z around 0 41.0%

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

       1. mul-1-neg 41.0%

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

       2. associate-*r* 44.3%

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

   13. Simplified 44.3%

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

   if -4.0999999999999997e-67 < j < -1.05000000000000004e-304

   1. Initial program 70.3%

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

   3. Taylor expanded in z around inf 53.6%

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

      1. *-commutative 53.6%

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

      2. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in y around inf 39.0%

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

   if -1.05000000000000004e-304 < j < 2.4999999999999999e-214

   1. Initial program 82.3%

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

   3. Taylor expanded in j around 0 86.6%

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

      1. *-commutative 86.6%

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

      2. *-commutative 86.6%

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

   5. Simplified 86.6%

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

      1. add-cube-cbrt 86.5%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)} \]

      2. pow3 86.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - i \cdot a}\right)}^{3}} \]

      3. *-commutative 86.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot {\left(\sqrt[3]{c \cdot z - \color{blue}{a \cdot i}}\right)}^{3} \]

   7. Applied egg-rr 86.4%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - a \cdot i}\right)}^{3}} \]

   8. Taylor expanded in i around inf 42.0%

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

      1. *-commutative 42.0%

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

      2. associate-*r* 38.7%

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

      3. *-commutative 38.7%

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

      4. associate-*l* 43.8%

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

   10. Simplified 43.8%

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

   if 2.4999999999999999e-214 < j < 4.8000000000000003e-145

   1. Initial program 74.0%

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

   3. Taylor expanded in z around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in y around inf 48.4%

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

      1. associate-*r* 54.7%

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

      2. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if 5.49999999999999971e-88 < j < 1.49999999999999997e24

   1. Initial program 87.3%

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

   3. Taylor expanded in c around inf 75.4%

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

      1. *-commutative 75.4%

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

      2. associate-*l* 75.4%

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

      3. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in b around inf 47.3%

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

      1. mul-1-neg 47.3%

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

      2. distribute-rgt-neg-in 47.3%

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

      3. distribute-rgt-neg-in 47.3%

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

   8. Simplified 47.3%

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

   if 2.8e115 < j < 2.90000000000000011e203

   1. Initial program 64.5%

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

   3. Taylor expanded in c around inf 58.1%

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

   4. Taylor expanded in j around inf 48.2%

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

      1. associate-*r* 53.8%

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

   6. Simplified 53.8%

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

   if 1.46000000000000009e243 < j

   1. Initial program 61.1%

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

   3. Taylor expanded in c around inf 87.7%

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

   4. Taylor expanded in j around inf 81.4%

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

      1. *-commutative 81.4%

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

   6. Simplified 81.4%

      \[\leadsto c \cdot \color{blue}{\left(t \cdot j\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+135}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq -4.1 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-304}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{-214}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-145}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq 5.5 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{+43}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+115}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{+203}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 1.46 \cdot 10^{+243}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t_1 - j \cdot \left(y \cdot i - t \cdot c\right)\\ t_4 := t_2 - c \cdot \left(z \cdot b\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+146}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-98}:\\ \;\;\;\;t_1 - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (- t_1 (* j (- (* y i) (* t c)))))
        (t_4 (- t_2 (* c (* z b)))))
   (if (<= x -3.2e+146)
     t_2
     (if (<= x -2.1e+45)
       t_3
       (if (<= x -1.3e+19)
         t_4
         (if (<= x -6.3e-86)
           (* a (- (* b i) (* x t)))
           (if (<= x -5.4e-114)
             (* y (- (* x z) (* i j)))
             (if (<= x 6e-180)
               t_3
               (if (<= x 8.5e-98)
                 (- t_1 (* a (* x t)))
                 (if (<= x 2.6e+27) t_3 t_4))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_1 - (j * ((y * i) - (t * c)));
	double t_4 = t_2 - (c * (z * b));
	double tmp;
	if (x <= -3.2e+146) {
		tmp = t_2;
	} else if (x <= -2.1e+45) {
		tmp = t_3;
	} else if (x <= -1.3e+19) {
		tmp = t_4;
	} else if (x <= -6.3e-86) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= -5.4e-114) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 6e-180) {
		tmp = t_3;
	} else if (x <= 8.5e-98) {
		tmp = t_1 - (a * (x * t));
	} else if (x <= 2.6e+27) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_1 - (j * ((y * i) - (t * c)))
    t_4 = t_2 - (c * (z * b))
    if (x <= (-3.2d+146)) then
        tmp = t_2
    else if (x <= (-2.1d+45)) then
        tmp = t_3
    else if (x <= (-1.3d+19)) then
        tmp = t_4
    else if (x <= (-6.3d-86)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= (-5.4d-114)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 6d-180) then
        tmp = t_3
    else if (x <= 8.5d-98) then
        tmp = t_1 - (a * (x * t))
    else if (x <= 2.6d+27) then
        tmp = t_3
    else
        tmp = t_4
    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 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_1 - (j * ((y * i) - (t * c)));
	double t_4 = t_2 - (c * (z * b));
	double tmp;
	if (x <= -3.2e+146) {
		tmp = t_2;
	} else if (x <= -2.1e+45) {
		tmp = t_3;
	} else if (x <= -1.3e+19) {
		tmp = t_4;
	} else if (x <= -6.3e-86) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= -5.4e-114) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 6e-180) {
		tmp = t_3;
	} else if (x <= 8.5e-98) {
		tmp = t_1 - (a * (x * t));
	} else if (x <= 2.6e+27) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_1 - (j * ((y * i) - (t * c)))
	t_4 = t_2 - (c * (z * b))
	tmp = 0
	if x <= -3.2e+146:
		tmp = t_2
	elif x <= -2.1e+45:
		tmp = t_3
	elif x <= -1.3e+19:
		tmp = t_4
	elif x <= -6.3e-86:
		tmp = a * ((b * i) - (x * t))
	elif x <= -5.4e-114:
		tmp = y * ((x * z) - (i * j))
	elif x <= 6e-180:
		tmp = t_3
	elif x <= 8.5e-98:
		tmp = t_1 - (a * (x * t))
	elif x <= 2.6e+27:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_1 - Float64(j * Float64(Float64(y * i) - Float64(t * c))))
	t_4 = Float64(t_2 - Float64(c * Float64(z * b)))
	tmp = 0.0
	if (x <= -3.2e+146)
		tmp = t_2;
	elseif (x <= -2.1e+45)
		tmp = t_3;
	elseif (x <= -1.3e+19)
		tmp = t_4;
	elseif (x <= -6.3e-86)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= -5.4e-114)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 6e-180)
		tmp = t_3;
	elseif (x <= 8.5e-98)
		tmp = Float64(t_1 - Float64(a * Float64(x * t)));
	elseif (x <= 2.6e+27)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_1 - (j * ((y * i) - (t * c)));
	t_4 = t_2 - (c * (z * b));
	tmp = 0.0;
	if (x <= -3.2e+146)
		tmp = t_2;
	elseif (x <= -2.1e+45)
		tmp = t_3;
	elseif (x <= -1.3e+19)
		tmp = t_4;
	elseif (x <= -6.3e-86)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= -5.4e-114)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 6e-180)
		tmp = t_3;
	elseif (x <= 8.5e-98)
		tmp = t_1 - (a * (x * t));
	elseif (x <= 2.6e+27)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $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$1 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.2e+146], t$95$2, If[LessEqual[x, -2.1e+45], t$95$3, If[LessEqual[x, -1.3e+19], t$95$4, If[LessEqual[x, -6.3e-86], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5.4e-114], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-180], t$95$3, If[LessEqual[x, 8.5e-98], N[(t$95$1 - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.6e+27], t$95$3, t$95$4]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < -3.2e146

   1. Initial program 75.7%

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

   3. Taylor expanded in c around inf 84.8%

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

      1. *-commutative 84.8%

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

      2. associate-*l* 82.0%

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

      3. *-commutative 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in x around inf 88.0%

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

      1. sub-neg 88.0%

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

      2. *-commutative 88.0%

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

      3. *-commutative 88.0%

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

      4. sub-neg 88.0%

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

   8. Simplified 88.0%

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

   if -3.2e146 < x < -2.09999999999999995e45 or -5.3999999999999999e-114 < x < 6.0000000000000001e-180 or 8.4999999999999997e-98 < x < 2.60000000000000009e27

   1. Initial program 80.3%

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

   3. Taylor expanded in x around 0 75.0%

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

      1. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -2.09999999999999995e45 < x < -1.3e19 or 2.60000000000000009e27 < x

   1. Initial program 75.1%

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

   3. Taylor expanded in j around 0 79.4%

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

      1. *-commutative 79.4%

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

      2. *-commutative 79.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in c around inf 76.7%

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

      1. *-commutative 73.7%

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

      2. associate-*l* 76.4%

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

      3. *-commutative 76.4%

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

   8. Simplified 78.1%

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

   if -1.3e19 < x < -6.2999999999999999e-86

   1. Initial program 63.3%

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

   3. Taylor expanded in a around -inf 57.8%

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

   if -6.2999999999999999e-86 < x < -5.3999999999999999e-114

   1. Initial program 58.5%

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

   3. Taylor expanded in c around inf 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*l* 66.8%

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

      3. *-commutative 66.8%

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

   5. Simplified 66.8%

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

   6. Taylor expanded in y around inf 76.1%

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

      1. +-commutative 76.1%

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

      2. mul-1-neg 76.1%

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

      3. unsub-neg 76.1%

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

      4. *-commutative 76.1%

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

      5. *-commutative 76.1%

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

   8. Simplified 76.1%

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

   if 6.0000000000000001e-180 < x < 8.4999999999999997e-98

   1. Initial program 58.4%

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

   3. Taylor expanded in j around 0 69.3%

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

      1. *-commutative 69.3%

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

      2. *-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in y around 0 74.4%

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

      1. associate-*r* 74.4%

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

      2. neg-mul-1 74.4%

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

      3. *-commutative 74.4%

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

   8. Simplified 74.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.2 \cdot 10^{+146}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{+45}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;x \leq -6.3 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-114}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-180}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-98}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 41.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-i\right) \cdot \left(y \cdot j\right)\\ t_2 := z \cdot \left(x \cdot y\right)\\ t_3 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_4 := c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{if}\;c \leq -1400000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -3.05 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-83}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.76 \cdot 10^{-208}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-223}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-274}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 3500:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (- i) (* y j)))
        (t_2 (* z (* x y)))
        (t_3 (* a (* x (- t))))
        (t_4 (* c (- (* t j) (* z b)))))
   (if (<= c -1400000.0)
     t_4
     (if (<= c -3.05e-80)
       t_2
       (if (<= c -1.3e-83)
         t_4
         (if (<= c -9e-180)
           t_1
           (if (<= c -1.76e-208)
             t_3
             (if (<= c -3.5e-223)
               t_1
               (if (<= c -1.7e-274)
                 t_2
                 (if (<= c 1.6e-32)
                   (* x (* y z))
                   (if (<= c 3500.0) t_3 t_4)))))))))))

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 * (y * j);
	double t_2 = z * (x * y);
	double t_3 = a * (x * -t);
	double t_4 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1400000.0) {
		tmp = t_4;
	} else if (c <= -3.05e-80) {
		tmp = t_2;
	} else if (c <= -1.3e-83) {
		tmp = t_4;
	} else if (c <= -9e-180) {
		tmp = t_1;
	} else if (c <= -1.76e-208) {
		tmp = t_3;
	} else if (c <= -3.5e-223) {
		tmp = t_1;
	} else if (c <= -1.7e-274) {
		tmp = t_2;
	} else if (c <= 1.6e-32) {
		tmp = x * (y * z);
	} else if (c <= 3500.0) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	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) :: tmp
    t_1 = -i * (y * j)
    t_2 = z * (x * y)
    t_3 = a * (x * -t)
    t_4 = c * ((t * j) - (z * b))
    if (c <= (-1400000.0d0)) then
        tmp = t_4
    else if (c <= (-3.05d-80)) then
        tmp = t_2
    else if (c <= (-1.3d-83)) then
        tmp = t_4
    else if (c <= (-9d-180)) then
        tmp = t_1
    else if (c <= (-1.76d-208)) then
        tmp = t_3
    else if (c <= (-3.5d-223)) then
        tmp = t_1
    else if (c <= (-1.7d-274)) then
        tmp = t_2
    else if (c <= 1.6d-32) then
        tmp = x * (y * z)
    else if (c <= 3500.0d0) then
        tmp = t_3
    else
        tmp = t_4
    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 * (y * j);
	double t_2 = z * (x * y);
	double t_3 = a * (x * -t);
	double t_4 = c * ((t * j) - (z * b));
	double tmp;
	if (c <= -1400000.0) {
		tmp = t_4;
	} else if (c <= -3.05e-80) {
		tmp = t_2;
	} else if (c <= -1.3e-83) {
		tmp = t_4;
	} else if (c <= -9e-180) {
		tmp = t_1;
	} else if (c <= -1.76e-208) {
		tmp = t_3;
	} else if (c <= -3.5e-223) {
		tmp = t_1;
	} else if (c <= -1.7e-274) {
		tmp = t_2;
	} else if (c <= 1.6e-32) {
		tmp = x * (y * z);
	} else if (c <= 3500.0) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = -i * (y * j)
	t_2 = z * (x * y)
	t_3 = a * (x * -t)
	t_4 = c * ((t * j) - (z * b))
	tmp = 0
	if c <= -1400000.0:
		tmp = t_4
	elif c <= -3.05e-80:
		tmp = t_2
	elif c <= -1.3e-83:
		tmp = t_4
	elif c <= -9e-180:
		tmp = t_1
	elif c <= -1.76e-208:
		tmp = t_3
	elif c <= -3.5e-223:
		tmp = t_1
	elif c <= -1.7e-274:
		tmp = t_2
	elif c <= 1.6e-32:
		tmp = x * (y * z)
	elif c <= 3500.0:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(-i) * Float64(y * j))
	t_2 = Float64(z * Float64(x * y))
	t_3 = Float64(a * Float64(x * Float64(-t)))
	t_4 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	tmp = 0.0
	if (c <= -1400000.0)
		tmp = t_4;
	elseif (c <= -3.05e-80)
		tmp = t_2;
	elseif (c <= -1.3e-83)
		tmp = t_4;
	elseif (c <= -9e-180)
		tmp = t_1;
	elseif (c <= -1.76e-208)
		tmp = t_3;
	elseif (c <= -3.5e-223)
		tmp = t_1;
	elseif (c <= -1.7e-274)
		tmp = t_2;
	elseif (c <= 1.6e-32)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 3500.0)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = -i * (y * j);
	t_2 = z * (x * y);
	t_3 = a * (x * -t);
	t_4 = c * ((t * j) - (z * b));
	tmp = 0.0;
	if (c <= -1400000.0)
		tmp = t_4;
	elseif (c <= -3.05e-80)
		tmp = t_2;
	elseif (c <= -1.3e-83)
		tmp = t_4;
	elseif (c <= -9e-180)
		tmp = t_1;
	elseif (c <= -1.76e-208)
		tmp = t_3;
	elseif (c <= -3.5e-223)
		tmp = t_1;
	elseif (c <= -1.7e-274)
		tmp = t_2;
	elseif (c <= 1.6e-32)
		tmp = x * (y * z);
	elseif (c <= 3500.0)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1400000.0], t$95$4, If[LessEqual[c, -3.05e-80], t$95$2, If[LessEqual[c, -1.3e-83], t$95$4, If[LessEqual[c, -9e-180], t$95$1, If[LessEqual[c, -1.76e-208], t$95$3, If[LessEqual[c, -3.5e-223], t$95$1, If[LessEqual[c, -1.7e-274], t$95$2, If[LessEqual[c, 1.6e-32], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3500.0], t$95$3, t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if c < -1.4e6 or -3.0500000000000001e-80 < c < -1.30000000000000004e-83 or 3500 < c

   1. Initial program 65.2%

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

   3. Taylor expanded in c around inf 66.0%

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

   if -1.4e6 < c < -3.0500000000000001e-80 or -3.50000000000000009e-223 < c < -1.6999999999999999e-274

   1. Initial program 86.6%

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

   3. Taylor expanded in z around inf 51.1%

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

      1. *-commutative 51.1%

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

      2. *-commutative 51.1%

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

   5. Simplified 51.1%

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

   6. Taylor expanded in y around inf 42.0%

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

      1. associate-*r* 51.4%

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

      2. *-commutative 51.4%

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

   8. Simplified 51.4%

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

   if -1.30000000000000004e-83 < c < -9.00000000000000019e-180 or -1.76000000000000008e-208 < c < -3.50000000000000009e-223

   1. Initial program 78.9%

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

   3. Taylor expanded in c around inf 75.2%

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

      1. *-commutative 75.2%

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

      2. associate-*l* 63.1%

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

      3. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in i around inf 48.7%

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

      1. associate-*r* 48.7%

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

      2. neg-mul-1 48.7%

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

   8. Simplified 48.7%

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

   if -9.00000000000000019e-180 < c < -1.76000000000000008e-208 or 1.6000000000000001e-32 < c < 3500

   1. Initial program 78.8%

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

   3. Taylor expanded in c around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*l* 78.5%

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

      3. *-commutative 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in a around inf 72.0%

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

      1. associate-*r* 72.0%

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

      2. neg-mul-1 72.0%

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

   8. Simplified 72.0%

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

   if -1.6999999999999999e-274 < c < 1.6000000000000001e-32

   1. Initial program 85.8%

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

   3. Taylor expanded in z around inf 37.7%

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

      1. *-commutative 37.7%

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

      2. *-commutative 37.7%

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

   5. Simplified 37.7%

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

   6. Taylor expanded in y around inf 39.3%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1400000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -3.05 \cdot 10^{-80}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-83}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;c \leq -9 \cdot 10^{-180}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq -1.76 \cdot 10^{-208}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq -3.5 \cdot 10^{-223}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;c \leq -1.7 \cdot 10^{-274}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;c \leq 1.6 \cdot 10^{-32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 3500:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 47.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.4 \cdot 10^{+123}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-147}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -3.15 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -3.4e+123)
     t_2
     (if (<= j -1.65e-147)
       (* c (- (* t j) (* z b)))
       (if (<= j -3.15e-260)
         (* z (* x y))
         (if (<= j -1.75e-301)
           t_1
           (if (<= j 5.8e-281)
             (* x (* y z))
             (if (<= j 4.4e-145)
               t_1
               (if (<= j 4.7e-88)
                 (* x (* t (- a)))
                 (if (<= j 8.2e+24) 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 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.4e+123) {
		tmp = t_2;
	} else if (j <= -1.65e-147) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -3.15e-260) {
		tmp = z * (x * y);
	} else if (j <= -1.75e-301) {
		tmp = t_1;
	} else if (j <= 5.8e-281) {
		tmp = x * (y * z);
	} else if (j <= 4.4e-145) {
		tmp = t_1;
	} else if (j <= 4.7e-88) {
		tmp = x * (t * -a);
	} else if (j <= 8.2e+24) {
		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 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-3.4d+123)) then
        tmp = t_2
    else if (j <= (-1.65d-147)) then
        tmp = c * ((t * j) - (z * b))
    else if (j <= (-3.15d-260)) then
        tmp = z * (x * y)
    else if (j <= (-1.75d-301)) then
        tmp = t_1
    else if (j <= 5.8d-281) then
        tmp = x * (y * z)
    else if (j <= 4.4d-145) then
        tmp = t_1
    else if (j <= 4.7d-88) then
        tmp = x * (t * -a)
    else if (j <= 8.2d+24) 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 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.4e+123) {
		tmp = t_2;
	} else if (j <= -1.65e-147) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= -3.15e-260) {
		tmp = z * (x * y);
	} else if (j <= -1.75e-301) {
		tmp = t_1;
	} else if (j <= 5.8e-281) {
		tmp = x * (y * z);
	} else if (j <= 4.4e-145) {
		tmp = t_1;
	} else if (j <= 4.7e-88) {
		tmp = x * (t * -a);
	} else if (j <= 8.2e+24) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -3.4e+123:
		tmp = t_2
	elif j <= -1.65e-147:
		tmp = c * ((t * j) - (z * b))
	elif j <= -3.15e-260:
		tmp = z * (x * y)
	elif j <= -1.75e-301:
		tmp = t_1
	elif j <= 5.8e-281:
		tmp = x * (y * z)
	elif j <= 4.4e-145:
		tmp = t_1
	elif j <= 4.7e-88:
		tmp = x * (t * -a)
	elif j <= 8.2e+24:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.4e+123)
		tmp = t_2;
	elseif (j <= -1.65e-147)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (j <= -3.15e-260)
		tmp = Float64(z * Float64(x * y));
	elseif (j <= -1.75e-301)
		tmp = t_1;
	elseif (j <= 5.8e-281)
		tmp = Float64(x * Float64(y * z));
	elseif (j <= 4.4e-145)
		tmp = t_1;
	elseif (j <= 4.7e-88)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 8.2e+24)
		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 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.4e+123)
		tmp = t_2;
	elseif (j <= -1.65e-147)
		tmp = c * ((t * j) - (z * b));
	elseif (j <= -3.15e-260)
		tmp = z * (x * y);
	elseif (j <= -1.75e-301)
		tmp = t_1;
	elseif (j <= 5.8e-281)
		tmp = x * (y * z);
	elseif (j <= 4.4e-145)
		tmp = t_1;
	elseif (j <= 4.7e-88)
		tmp = x * (t * -a);
	elseif (j <= 8.2e+24)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.4e+123], t$95$2, If[LessEqual[j, -1.65e-147], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.15e-260], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.75e-301], t$95$1, If[LessEqual[j, 5.8e-281], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.4e-145], t$95$1, If[LessEqual[j, 4.7e-88], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.2e+24], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -3.40000000000000001e123 or 8.2000000000000002e24 < j

   1. Initial program 70.2%

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

   3. Taylor expanded in c around inf 73.4%

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

      1. *-commutative 73.4%

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

      2. associate-*l* 72.7%

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

      3. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   6. Taylor expanded in j around inf 71.9%

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

   if -3.40000000000000001e123 < j < -1.64999999999999994e-147

   1. Initial program 70.2%

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

   3. Taylor expanded in c around inf 42.1%

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

   if -1.64999999999999994e-147 < j < -3.14999999999999989e-260

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf 66.4%

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

      1. *-commutative 66.4%

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

      2. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in y around inf 49.2%

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

      1. associate-*r* 53.2%

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

      2. *-commutative 53.2%

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

   8. Simplified 53.2%

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

   if -3.14999999999999989e-260 < j < -1.74999999999999996e-301 or 5.7999999999999998e-281 < j < 4.39999999999999998e-145 or 4.7e-88 < j < 8.2000000000000002e24

   1. Initial program 79.4%

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

   3. Taylor expanded in b around inf 54.7%

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

      1. *-commutative 54.7%

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

   5. Simplified 54.7%

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

   if -1.74999999999999996e-301 < j < 5.7999999999999998e-281

   1. Initial program 71.5%

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

   3. Taylor expanded in z around inf 58.1%

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

      1. *-commutative 58.1%

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

      2. *-commutative 58.1%

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

   5. Simplified 58.1%

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

   6. Taylor expanded in y around inf 49.6%

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

   if 4.39999999999999998e-145 < j < 4.7e-88

   1. Initial program 64.3%

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

   3. Taylor expanded in j around 0 73.4%

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

      1. *-commutative 73.4%

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

      2. *-commutative 73.4%

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

   5. Simplified 73.4%

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

      1. add-cube-cbrt 73.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)} \]

      2. pow3 73.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - i \cdot a}\right)}^{3}} \]

      3. *-commutative 73.4%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot {\left(\sqrt[3]{c \cdot z - \color{blue}{a \cdot i}}\right)}^{3} \]

   7. Applied egg-rr 73.4%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - a \cdot i}\right)}^{3}} \]

   8. Taylor expanded in c around inf 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*l* 82.8%

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

   10. Simplified 82.8%

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

   11. Taylor expanded in z around 0 64.1%

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

       1. mul-1-neg 64.1%

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

       2. associate-*r* 64.3%

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

   13. Simplified 64.3%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.4 \cdot 10^{+123}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-147}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq -3.15 \cdot 10^{-260}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-301}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.8 \cdot 10^{-281}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-145}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.7 \cdot 10^{-88}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right) - \left(c \cdot \left(z \cdot b\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{if}\;j \leq -1.25 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+250}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (-
          (* j (- (* t c) (* y i)))
          (+ (* c (* z b)) (* x (- (* t a) (* y z)))))))
   (if (<= j -1.25e-50)
     t_1
     (if (<= j 1.4e+58)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (if (<= j 2.2e+250) t_1 (* c (- (* t 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 = (j * ((t * c) - (y * i))) - ((c * (z * b)) + (x * ((t * a) - (y * z))));
	double tmp;
	if (j <= -1.25e-50) {
		tmp = t_1;
	} else if (j <= 1.4e+58) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 2.2e+250) {
		tmp = t_1;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	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 * ((t * c) - (y * i))) - ((c * (z * b)) + (x * ((t * a) - (y * z))))
    if (j <= (-1.25d-50)) then
        tmp = t_1
    else if (j <= 1.4d+58) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else if (j <= 2.2d+250) then
        tmp = t_1
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (j * ((t * c) - (y * i))) - ((c * (z * b)) + (x * ((t * a) - (y * z))));
	double tmp;
	if (j <= -1.25e-50) {
		tmp = t_1;
	} else if (j <= 1.4e+58) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else if (j <= 2.2e+250) {
		tmp = t_1;
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (j * ((t * c) - (y * i))) - ((c * (z * b)) + (x * ((t * a) - (y * z))))
	tmp = 0
	if j <= -1.25e-50:
		tmp = t_1
	elif j <= 1.4e+58:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	elif j <= 2.2e+250:
		tmp = t_1
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(Float64(c * Float64(z * b)) + Float64(x * Float64(Float64(t * a) - Float64(y * z)))))
	tmp = 0.0
	if (j <= -1.25e-50)
		tmp = t_1;
	elseif (j <= 1.4e+58)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 2.2e+250)
		tmp = t_1;
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) - ((c * (z * b)) + (x * ((t * a) - (y * z))));
	tmp = 0.0;
	if (j <= -1.25e-50)
		tmp = t_1;
	elseif (j <= 1.4e+58)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	elseif (j <= 2.2e+250)
		tmp = t_1;
	else
		tmp = c * ((t * 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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.25e-50], t$95$1, If[LessEqual[j, 1.4e+58], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.2e+250], t$95$1, N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.24999999999999992e-50 or 1.3999999999999999e58 < j < 2.20000000000000014e250

   1. Initial program 73.1%

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

   3. Taylor expanded in c around inf 76.9%

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

      1. *-commutative 76.9%

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

      2. associate-*l* 76.0%

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

      3. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   if -1.24999999999999992e-50 < j < 1.3999999999999999e58

   1. Initial program 76.9%

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

   3. Taylor expanded in j around 0 81.4%

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

      1. *-commutative 81.4%

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

      2. *-commutative 81.4%

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

   5. Simplified 81.4%

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

   if 2.20000000000000014e250 < j

   1. Initial program 55.1%

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

   3. Taylor expanded in c around inf 93.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{-50}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - \left(c \cdot \left(z \cdot b\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+250}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - \left(c \cdot \left(z \cdot b\right) + x \cdot \left(t \cdot a - y \cdot z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;x \leq -2.1 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -4500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.48 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= x -2.1e+173)
     t_1
     (if (<= x -9.5e+161)
       (* x (* t (- a)))
       (if (<= x -4500000.0)
         t_1
         (if (<= x 7e-251)
           t_2
           (if (<= x 1.48e-179)
             (* c (* t j))
             (if (<= x 2.5e+44) t_2 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 = z * (x * y);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -2.1e+173) {
		tmp = t_1;
	} else if (x <= -9.5e+161) {
		tmp = x * (t * -a);
	} else if (x <= -4500000.0) {
		tmp = t_1;
	} else if (x <= 7e-251) {
		tmp = t_2;
	} else if (x <= 1.48e-179) {
		tmp = c * (t * j);
	} else if (x <= 2.5e+44) {
		tmp = t_2;
	} 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) :: tmp
    t_1 = z * (x * y)
    t_2 = b * ((a * i) - (z * c))
    if (x <= (-2.1d+173)) then
        tmp = t_1
    else if (x <= (-9.5d+161)) then
        tmp = x * (t * -a)
    else if (x <= (-4500000.0d0)) then
        tmp = t_1
    else if (x <= 7d-251) then
        tmp = t_2
    else if (x <= 1.48d-179) then
        tmp = c * (t * j)
    else if (x <= 2.5d+44) then
        tmp = t_2
    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 = z * (x * y);
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (x <= -2.1e+173) {
		tmp = t_1;
	} else if (x <= -9.5e+161) {
		tmp = x * (t * -a);
	} else if (x <= -4500000.0) {
		tmp = t_1;
	} else if (x <= 7e-251) {
		tmp = t_2;
	} else if (x <= 1.48e-179) {
		tmp = c * (t * j);
	} else if (x <= 2.5e+44) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if x <= -2.1e+173:
		tmp = t_1
	elif x <= -9.5e+161:
		tmp = x * (t * -a)
	elif x <= -4500000.0:
		tmp = t_1
	elif x <= 7e-251:
		tmp = t_2
	elif x <= 1.48e-179:
		tmp = c * (t * j)
	elif x <= 2.5e+44:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (x <= -2.1e+173)
		tmp = t_1;
	elseif (x <= -9.5e+161)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= -4500000.0)
		tmp = t_1;
	elseif (x <= 7e-251)
		tmp = t_2;
	elseif (x <= 1.48e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 2.5e+44)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (x <= -2.1e+173)
		tmp = t_1;
	elseif (x <= -9.5e+161)
		tmp = x * (t * -a);
	elseif (x <= -4500000.0)
		tmp = t_1;
	elseif (x <= 7e-251)
		tmp = t_2;
	elseif (x <= 1.48e-179)
		tmp = c * (t * j);
	elseif (x <= 2.5e+44)
		tmp = t_2;
	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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.1e+173], t$95$1, If[LessEqual[x, -9.5e+161], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4500000.0], t$95$1, If[LessEqual[x, 7e-251], t$95$2, If[LessEqual[x, 1.48e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e+44], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1e173 or -9.50000000000000061e161 < x < -4.5e6 or 2.4999999999999998e44 < x

   1. Initial program 81.7%

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

   3. Taylor expanded in z around inf 51.8%

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

      1. *-commutative 51.8%

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

      2. *-commutative 51.8%

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

   5. Simplified 51.8%

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

   6. Taylor expanded in y around inf 47.0%

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

      1. associate-*r* 49.3%

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

      2. *-commutative 49.3%

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

   8. Simplified 49.3%

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

   if -2.1e173 < x < -9.50000000000000061e161

   1. Initial program 50.0%

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

   3. Taylor expanded in j around 0 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

   5. Simplified 50.0%

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

      1. add-cube-cbrt 50.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)} \]

      2. pow3 50.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - i \cdot a}\right)}^{3}} \]

      3. *-commutative 50.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot {\left(\sqrt[3]{c \cdot z - \color{blue}{a \cdot i}}\right)}^{3} \]

   7. Applied egg-rr 50.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - a \cdot i}\right)}^{3}} \]

   8. Taylor expanded in c around inf 83.3%

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

      1. *-commutative 83.3%

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

      2. associate-*l* 83.3%

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

   10. Simplified 83.3%

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

   11. Taylor expanded in z around 0 100.0%

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

       1. mul-1-neg 100.0%

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

       2. associate-*r* 100.0%

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

   13. Simplified 100.0%

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

   if -4.5e6 < x < 7.00000000000000069e-251 or 1.48000000000000006e-179 < x < 2.4999999999999998e44

   1. Initial program 69.2%

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

   3. Taylor expanded in b around inf 46.2%

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

      1. *-commutative 46.2%

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

   5. Simplified 46.2%

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

   if 7.00000000000000069e-251 < x < 1.48000000000000006e-179

   1. Initial program 64.3%

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

   3. Taylor expanded in c around inf 64.1%

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

   4. Taylor expanded in j around inf 63.5%

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

      1. *-commutative 63.5%

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

   6. Simplified 63.5%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -9.5 \cdot 10^{+161}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -4500000:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-251}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;x \leq 1.48 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+44}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;j \leq -5.4 \cdot 10^{+77}:\\ \;\;\;\;t_2 - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;j \leq -0.042:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-24} \lor \neg \left(j \leq 3.1 \cdot 10^{+57}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* a i) (* z c)))))
   (if (<= j -5.4e+77)
     (- t_2 (* j (- (* y i) (* t c))))
     (if (<= j -0.042)
       t_1
       (if (or (<= j -1.55e-24) (not (<= j 3.1e+57)))
         (* j (- (* t c) (* y i)))
         (+ 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));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (j <= -5.4e+77) {
		tmp = t_2 - (j * ((y * i) - (t * c)));
	} else if (j <= -0.042) {
		tmp = t_1;
	} else if ((j <= -1.55e-24) || !(j <= 3.1e+57)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1 + 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))
    t_2 = b * ((a * i) - (z * c))
    if (j <= (-5.4d+77)) then
        tmp = t_2 - (j * ((y * i) - (t * c)))
    else if (j <= (-0.042d0)) then
        tmp = t_1
    else if ((j <= (-1.55d-24)) .or. (.not. (j <= 3.1d+57))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = t_1 + 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));
	double t_2 = b * ((a * i) - (z * c));
	double tmp;
	if (j <= -5.4e+77) {
		tmp = t_2 - (j * ((y * i) - (t * c)));
	} else if (j <= -0.042) {
		tmp = t_1;
	} else if ((j <= -1.55e-24) || !(j <= 3.1e+57)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((a * i) - (z * c))
	tmp = 0
	if j <= -5.4e+77:
		tmp = t_2 - (j * ((y * i) - (t * c)))
	elif j <= -0.042:
		tmp = t_1
	elif (j <= -1.55e-24) or not (j <= 3.1e+57):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = t_1 + t_2
	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(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (j <= -5.4e+77)
		tmp = Float64(t_2 - Float64(j * Float64(Float64(y * i) - Float64(t * c))));
	elseif (j <= -0.042)
		tmp = t_1;
	elseif ((j <= -1.55e-24) || !(j <= 3.1e+57))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = Float64(t_1 + 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));
	t_2 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (j <= -5.4e+77)
		tmp = t_2 - (j * ((y * i) - (t * c)));
	elseif (j <= -0.042)
		tmp = t_1;
	elseif ((j <= -1.55e-24) || ~((j <= 3.1e+57)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = t_1 + t_2;
	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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.4e+77], N[(t$95$2 - N[(j * N[(N[(y * i), $MachinePrecision] - N[(t * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -0.042], t$95$1, If[Or[LessEqual[j, -1.55e-24], N[Not[LessEqual[j, 3.1e+57]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.3999999999999997e77

   1. Initial program 69.9%

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

   3. Taylor expanded in x around 0 72.7%

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

      1. *-commutative 72.7%

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

   5. Simplified 72.7%

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

   if -5.3999999999999997e77 < j < -0.0420000000000000026

   1. Initial program 71.1%

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

   3. Taylor expanded in c around inf 71.1%

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

      1. *-commutative 71.1%

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

      2. associate-*l* 71.1%

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

      3. *-commutative 71.1%

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

   5. Simplified 71.1%

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

   6. Taylor expanded in x around inf 71.4%

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

      1. sub-neg 71.4%

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

      2. *-commutative 71.4%

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

      3. *-commutative 71.4%

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

      4. sub-neg 71.4%

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

   8. Simplified 71.4%

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

   if -0.0420000000000000026 < j < -1.55e-24 or 3.10000000000000013e57 < j

   1. Initial program 68.2%

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

   3. Taylor expanded in c around inf 73.8%

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

      1. *-commutative 73.8%

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

      2. associate-*l* 75.4%

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

      3. *-commutative 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in j around inf 73.9%

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

   if -1.55e-24 < j < 3.10000000000000013e57

   1. Initial program 78.3%

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

   3. Taylor expanded in j around 0 82.0%

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

      1. *-commutative 82.0%

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

      2. *-commutative 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.4 \cdot 10^{+77}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - j \cdot \left(y \cdot i - t \cdot c\right)\\ \mathbf{elif}\;j \leq -0.042:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -1.55 \cdot 10^{-24} \lor \neg \left(j \leq 3.1 \cdot 10^{+57}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - c \cdot \left(z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1.1e+19)
     t_1
     (if (<= x -2.5e-77)
       (* a (- (* b i) (* x t)))
       (if (<= x 1.26e-176)
         (- (* j (- (* t c) (* y i))) (* b (* z c)))
         (if (<= x 2.7e+27)
           (- (* b (- (* a i) (* z c))) (* a (* x t)))
           (- t_1 (* c (* 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));
	double tmp;
	if (x <= -1.1e+19) {
		tmp = t_1;
	} else if (x <= -2.5e-77) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 1.26e-176) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 2.7e+27) {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	} else {
		tmp = t_1 - (c * (z * b));
	}
	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 <= (-1.1d+19)) then
        tmp = t_1
    else if (x <= (-2.5d-77)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= 1.26d-176) then
        tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
    else if (x <= 2.7d+27) then
        tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
    else
        tmp = t_1 - (c * (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1.1e+19) {
		tmp = t_1;
	} else if (x <= -2.5e-77) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 1.26e-176) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 2.7e+27) {
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	} else {
		tmp = t_1 - (c * (z * b));
	}
	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 <= -1.1e+19:
		tmp = t_1
	elif x <= -2.5e-77:
		tmp = a * ((b * i) - (x * t))
	elif x <= 1.26e-176:
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
	elif x <= 2.7e+27:
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t))
	else:
		tmp = t_1 - (c * (z * b))
	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 <= -1.1e+19)
		tmp = t_1;
	elseif (x <= -2.5e-77)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= 1.26e-176)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (x <= 2.7e+27)
		tmp = Float64(Float64(b * Float64(Float64(a * i) - Float64(z * c))) - Float64(a * Float64(x * t)));
	else
		tmp = Float64(t_1 - Float64(c * 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));
	tmp = 0.0;
	if (x <= -1.1e+19)
		tmp = t_1;
	elseif (x <= -2.5e-77)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= 1.26e-176)
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	elseif (x <= 2.7e+27)
		tmp = (b * ((a * i) - (z * c))) - (a * (x * t));
	else
		tmp = t_1 - (c * (z * b));
	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, -1.1e+19], t$95$1, If[LessEqual[x, -2.5e-77], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.26e-176], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+27], N[(N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.1e19

   1. Initial program 80.3%

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

   3. Taylor expanded in c around inf 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*l* 82.2%

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

      3. *-commutative 82.2%

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

   5. Simplified 82.2%

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

   6. Taylor expanded in x around inf 74.5%

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

      1. sub-neg 74.5%

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

      2. *-commutative 74.5%

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

      3. *-commutative 74.5%

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

      4. sub-neg 74.5%

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

   8. Simplified 74.5%

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

   if -1.1e19 < x < -2.49999999999999982e-77

   1. Initial program 61.4%

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

   3. Taylor expanded in a around -inf 60.6%

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

   if -2.49999999999999982e-77 < x < 1.25999999999999992e-176

   1. Initial program 68.8%

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

   3. Taylor expanded in c around inf 67.7%

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

      1. *-commutative 67.7%

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

      2. associate-*l* 65.2%

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

      3. *-commutative 65.2%

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

   5. Simplified 65.2%

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

   6. Taylor expanded in x around 0 66.6%

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

   if 1.25999999999999992e-176 < x < 2.6999999999999997e27

   1. Initial program 78.4%

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

   3. Taylor expanded in j around 0 70.9%

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

      1. *-commutative 70.9%

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

      2. *-commutative 70.9%

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

   5. Simplified 70.9%

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

   6. Taylor expanded in y around 0 66.3%

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

      1. associate-*r* 66.3%

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

      2. neg-mul-1 66.3%

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

      3. *-commutative 66.3%

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

   8. Simplified 66.3%

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

   if 2.6999999999999997e27 < x

   1. Initial program 75.5%

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

   3. Taylor expanded in j around 0 78.7%

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

      1. *-commutative 78.7%

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

      2. *-commutative 78.7%

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

   5. Simplified 78.7%

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

   6. Taylor expanded in c around inf 75.7%

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

      1. *-commutative 74.0%

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

      2. associate-*l* 75.5%

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

      3. *-commutative 75.5%

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

   8. Simplified 77.2%

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

4. Final simplification 70.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 1.26 \cdot 10^{-176}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+27}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.2 \cdot 10^{+127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-275}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-214}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* j (- (* t c) (* y i)))))
   (if (<= j -2.2e+127)
     t_3
     (if (<= j 2.1e-275)
       t_2
       (if (<= j 9.5e-214)
         t_1
         (if (<= j 8.2e-26) t_2 (if (<= j 9.5e+24) 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 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.2e+127) {
		tmp = t_3;
	} else if (j <= 2.1e-275) {
		tmp = t_2;
	} else if (j <= 9.5e-214) {
		tmp = t_1;
	} else if (j <= 8.2e-26) {
		tmp = t_2;
	} else if (j <= 9.5e+24) {
		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 = b * ((a * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-2.2d+127)) then
        tmp = t_3
    else if (j <= 2.1d-275) then
        tmp = t_2
    else if (j <= 9.5d-214) then
        tmp = t_1
    else if (j <= 8.2d-26) then
        tmp = t_2
    else if (j <= 9.5d+24) 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 = b * ((a * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.2e+127) {
		tmp = t_3;
	} else if (j <= 2.1e-275) {
		tmp = t_2;
	} else if (j <= 9.5e-214) {
		tmp = t_1;
	} else if (j <= 8.2e-26) {
		tmp = t_2;
	} else if (j <= 9.5e+24) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -2.2e+127:
		tmp = t_3
	elif j <= 2.1e-275:
		tmp = t_2
	elif j <= 9.5e-214:
		tmp = t_1
	elif j <= 8.2e-26:
		tmp = t_2
	elif j <= 9.5e+24:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.2e+127)
		tmp = t_3;
	elseif (j <= 2.1e-275)
		tmp = t_2;
	elseif (j <= 9.5e-214)
		tmp = t_1;
	elseif (j <= 8.2e-26)
		tmp = t_2;
	elseif (j <= 9.5e+24)
		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 = b * ((a * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.2e+127)
		tmp = t_3;
	elseif (j <= 2.1e-275)
		tmp = t_2;
	elseif (j <= 9.5e-214)
		tmp = t_1;
	elseif (j <= 8.2e-26)
		tmp = t_2;
	elseif (j <= 9.5e+24)
		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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.2e+127], t$95$3, If[LessEqual[j, 2.1e-275], t$95$2, If[LessEqual[j, 9.5e-214], t$95$1, If[LessEqual[j, 8.2e-26], t$95$2, If[LessEqual[j, 9.5e+24], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.2000000000000002e127 or 9.5000000000000001e24 < j

   1. Initial program 69.9%

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

   3. Taylor expanded in c around inf 73.1%

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

      1. *-commutative 73.1%

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

      2. associate-*l* 72.4%

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

      3. *-commutative 72.4%

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

   5. Simplified 72.4%

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

   6. Taylor expanded in j around inf 72.7%

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

   if -2.2000000000000002e127 < j < 2.09999999999999988e-275 or 9.4999999999999999e-214 < j < 8.1999999999999997e-26

   1. Initial program 73.2%

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

   3. Taylor expanded in c around inf 70.9%

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

      1. *-commutative 70.9%

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

      2. associate-*l* 70.3%

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

      3. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in x around inf 61.4%

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

      1. sub-neg 61.4%

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

      2. *-commutative 61.4%

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

      3. *-commutative 61.4%

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

      4. sub-neg 61.4%

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

   8. Simplified 61.4%

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

   if 2.09999999999999988e-275 < j < 9.4999999999999999e-214 or 8.1999999999999997e-26 < j < 9.5000000000000001e24

   1. Initial program 88.5%

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

   3. Taylor expanded in b around inf 66.9%

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

      1. *-commutative 66.9%

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

   5. Simplified 66.9%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.2 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{-214}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8.2 \cdot 10^{-26}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 9.5 \cdot 10^{+24}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.22 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -1e+19)
     t_1
     (if (<= x -2.22e-85)
       (* a (- (* b i) (* x t)))
       (if (<= x -2.15e-138)
         (* y (- (* x z) (* i j)))
         (if (<= x 1.25e-179)
           (* c (- (* t j) (* z b)))
           (if (<= x 5e+41) (* b (- (* a 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1e+19) {
		tmp = t_1;
	} else if (x <= -2.22e-85) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= -2.15e-138) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 1.25e-179) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 5e+41) {
		tmp = b * ((a * 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 = x * ((y * z) - (t * a))
    if (x <= (-1d+19)) then
        tmp = t_1
    else if (x <= (-2.22d-85)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= (-2.15d-138)) then
        tmp = y * ((x * z) - (i * j))
    else if (x <= 1.25d-179) then
        tmp = c * ((t * j) - (z * b))
    else if (x <= 5d+41) then
        tmp = b * ((a * 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -1e+19) {
		tmp = t_1;
	} else if (x <= -2.22e-85) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= -2.15e-138) {
		tmp = y * ((x * z) - (i * j));
	} else if (x <= 1.25e-179) {
		tmp = c * ((t * j) - (z * b));
	} else if (x <= 5e+41) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	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 <= -1e+19:
		tmp = t_1
	elif x <= -2.22e-85:
		tmp = a * ((b * i) - (x * t))
	elif x <= -2.15e-138:
		tmp = y * ((x * z) - (i * j))
	elif x <= 1.25e-179:
		tmp = c * ((t * j) - (z * b))
	elif x <= 5e+41:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	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 <= -1e+19)
		tmp = t_1;
	elseif (x <= -2.22e-85)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= -2.15e-138)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (x <= 1.25e-179)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (x <= 5e+41)
		tmp = Float64(b * Float64(Float64(a * 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 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -1e+19)
		tmp = t_1;
	elseif (x <= -2.22e-85)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= -2.15e-138)
		tmp = y * ((x * z) - (i * j));
	elseif (x <= 1.25e-179)
		tmp = c * ((t * j) - (z * b));
	elseif (x <= 5e+41)
		tmp = b * ((a * 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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+19], t$95$1, If[LessEqual[x, -2.22e-85], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.15e-138], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.25e-179], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5e+41], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1e19 or 5.00000000000000022e41 < x

   1. Initial program 79.1%

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

   3. Taylor expanded in c around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*l* 80.1%

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

      3. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in x around inf 75.1%

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

      1. sub-neg 75.1%

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

      2. *-commutative 75.1%

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

      3. *-commutative 75.1%

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

      4. sub-neg 75.1%

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

   8. Simplified 75.1%

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

   if -1e19 < x < -2.2199999999999999e-85

   1. Initial program 63.3%

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

   3. Taylor expanded in a around -inf 57.8%

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

   if -2.2199999999999999e-85 < x < -2.15e-138

   1. Initial program 62.9%

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

   3. Taylor expanded in c around inf 69.1%

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

      1. *-commutative 69.1%

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

      2. associate-*l* 69.1%

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

      3. *-commutative 69.1%

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

   5. Simplified 69.1%

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

   6. Taylor expanded in y around inf 69.8%

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

      1. +-commutative 69.8%

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

      2. mul-1-neg 69.8%

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

      3. unsub-neg 69.8%

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

      4. *-commutative 69.8%

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

      5. *-commutative 69.8%

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

   8. Simplified 69.8%

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

   if -2.15e-138 < x < 1.2499999999999999e-179

   1. Initial program 71.4%

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

   3. Taylor expanded in c around inf 54.9%

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

   if 1.2499999999999999e-179 < x < 5.00000000000000022e41

   1. Initial program 73.3%

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

   3. Taylor expanded in b around inf 59.1%

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

      1. *-commutative 59.1%

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

   5. Simplified 59.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.22 \cdot 10^{-85}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq -2.15 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 29.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+166}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -1e+173)
     t_1
     (if (<= x -5.4e+166)
       (* x (* t (- a)))
       (if (<= x -1.3e+19)
         t_1
         (if (<= x 1.5e-179)
           (* c (* t j))
           (if (<= x 1.6e+42) (* b (- (* 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 = z * (x * y);
	double tmp;
	if (x <= -1e+173) {
		tmp = t_1;
	} else if (x <= -5.4e+166) {
		tmp = x * (t * -a);
	} else if (x <= -1.3e+19) {
		tmp = t_1;
	} else if (x <= 1.5e-179) {
		tmp = c * (t * j);
	} else if (x <= 1.6e+42) {
		tmp = b * -(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 = z * (x * y)
    if (x <= (-1d+173)) then
        tmp = t_1
    else if (x <= (-5.4d+166)) then
        tmp = x * (t * -a)
    else if (x <= (-1.3d+19)) then
        tmp = t_1
    else if (x <= 1.5d-179) then
        tmp = c * (t * j)
    else if (x <= 1.6d+42) then
        tmp = b * -(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 = z * (x * y);
	double tmp;
	if (x <= -1e+173) {
		tmp = t_1;
	} else if (x <= -5.4e+166) {
		tmp = x * (t * -a);
	} else if (x <= -1.3e+19) {
		tmp = t_1;
	} else if (x <= 1.5e-179) {
		tmp = c * (t * j);
	} else if (x <= 1.6e+42) {
		tmp = b * -(z * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -1e+173:
		tmp = t_1
	elif x <= -5.4e+166:
		tmp = x * (t * -a)
	elif x <= -1.3e+19:
		tmp = t_1
	elif x <= 1.5e-179:
		tmp = c * (t * j)
	elif x <= 1.6e+42:
		tmp = b * -(z * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1e+173)
		tmp = t_1;
	elseif (x <= -5.4e+166)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (x <= -1.3e+19)
		tmp = t_1;
	elseif (x <= 1.5e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 1.6e+42)
		tmp = Float64(b * Float64(-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 = z * (x * y);
	tmp = 0.0;
	if (x <= -1e+173)
		tmp = t_1;
	elseif (x <= -5.4e+166)
		tmp = x * (t * -a);
	elseif (x <= -1.3e+19)
		tmp = t_1;
	elseif (x <= 1.5e-179)
		tmp = c * (t * j);
	elseif (x <= 1.6e+42)
		tmp = b * -(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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e+173], t$95$1, If[LessEqual[x, -5.4e+166], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.3e+19], t$95$1, If[LessEqual[x, 1.5e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.6e+42], N[(b * (-N[(z * c), $MachinePrecision])), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1e173 or -5.40000000000000023e166 < x < -1.3e19 or 1.60000000000000001e42 < x

   1. Initial program 80.7%

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

   3. Taylor expanded in z around inf 52.2%

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

      1. *-commutative 52.2%

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

      2. *-commutative 52.2%

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

   5. Simplified 52.2%

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

   6. Taylor expanded in y around inf 47.4%

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

      1. associate-*r* 49.7%

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

      2. *-commutative 49.7%

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

   8. Simplified 49.7%

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

   if -1e173 < x < -5.40000000000000023e166

   1. Initial program 50.0%

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

   3. Taylor expanded in j around 0 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

   5. Simplified 50.0%

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

      1. add-cube-cbrt 50.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)} \]

      2. pow3 50.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - i \cdot a}\right)}^{3}} \]

      3. *-commutative 50.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot {\left(\sqrt[3]{c \cdot z - \color{blue}{a \cdot i}}\right)}^{3} \]

   7. Applied egg-rr 50.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - a \cdot i}\right)}^{3}} \]

   8. Taylor expanded in c around inf 83.3%

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

      1. *-commutative 83.3%

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

      2. associate-*l* 83.3%

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

   10. Simplified 83.3%

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

   11. Taylor expanded in z around 0 100.0%

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

       1. mul-1-neg 100.0%

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

       2. associate-*r* 100.0%

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

   13. Simplified 100.0%

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

   if -1.3e19 < x < 1.50000000000000003e-179

   1. Initial program 67.9%

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

   3. Taylor expanded in c around inf 45.3%

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

   4. Taylor expanded in j around inf 30.5%

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

      1. *-commutative 30.5%

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

   6. Simplified 30.5%

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

   if 1.50000000000000003e-179 < x < 1.60000000000000001e42

   1. Initial program 73.3%

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

   3. Taylor expanded in c around inf 60.4%

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

      1. *-commutative 60.4%

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

      2. associate-*l* 58.4%

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

      3. *-commutative 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in b around inf 41.8%

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

      1. mul-1-neg 41.8%

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

      2. distribute-rgt-neg-in 41.8%

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

      3. distribute-rgt-neg-in 41.8%

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

   8. Simplified 41.8%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{+173}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{+166}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+42}:\\ \;\;\;\;b \cdot \left(-z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 56.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-180}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= x -2.4e+19)
     t_1
     (if (<= x -2.3e-76)
       (* a (- (* b i) (* x t)))
       (if (<= x 6e-180)
         (- (* j (- (* t c) (* y i))) (* b (* z c)))
         (if (<= x 5.6e+41) (* b (- (* a 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.4e+19) {
		tmp = t_1;
	} else if (x <= -2.3e-76) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 6e-180) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 5.6e+41) {
		tmp = b * ((a * 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 = x * ((y * z) - (t * a))
    if (x <= (-2.4d+19)) then
        tmp = t_1
    else if (x <= (-2.3d-76)) then
        tmp = a * ((b * i) - (x * t))
    else if (x <= 6d-180) then
        tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
    else if (x <= 5.6d+41) then
        tmp = b * ((a * 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 = x * ((y * z) - (t * a));
	double tmp;
	if (x <= -2.4e+19) {
		tmp = t_1;
	} else if (x <= -2.3e-76) {
		tmp = a * ((b * i) - (x * t));
	} else if (x <= 6e-180) {
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	} else if (x <= 5.6e+41) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	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 <= -2.4e+19:
		tmp = t_1
	elif x <= -2.3e-76:
		tmp = a * ((b * i) - (x * t))
	elif x <= 6e-180:
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c))
	elif x <= 5.6e+41:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	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 <= -2.4e+19)
		tmp = t_1;
	elseif (x <= -2.3e-76)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	elseif (x <= 6e-180)
		tmp = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) - Float64(b * Float64(z * c)));
	elseif (x <= 5.6e+41)
		tmp = Float64(b * Float64(Float64(a * 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 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (x <= -2.4e+19)
		tmp = t_1;
	elseif (x <= -2.3e-76)
		tmp = a * ((b * i) - (x * t));
	elseif (x <= 6e-180)
		tmp = (j * ((t * c) - (y * i))) - (b * (z * c));
	elseif (x <= 5.6e+41)
		tmp = b * ((a * 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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+19], t$95$1, If[LessEqual[x, -2.3e-76], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-180], N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.6e+41], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.4e19 or 5.5999999999999999e41 < x

   1. Initial program 79.1%

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

   3. Taylor expanded in c around inf 78.5%

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

      1. *-commutative 78.5%

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

      2. associate-*l* 80.1%

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

      3. *-commutative 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in x around inf 75.1%

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

      1. sub-neg 75.1%

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

      2. *-commutative 75.1%

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

      3. *-commutative 75.1%

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

      4. sub-neg 75.1%

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

   8. Simplified 75.1%

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

   if -2.4e19 < x < -2.30000000000000006e-76

   1. Initial program 61.4%

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

   3. Taylor expanded in a around -inf 60.6%

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

   if -2.30000000000000006e-76 < x < 6.0000000000000001e-180

   1. Initial program 70.7%

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

   3. Taylor expanded in c around inf 69.6%

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

      1. *-commutative 69.6%

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

      2. associate-*l* 66.9%

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

      3. *-commutative 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in x around 0 68.5%

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

   if 6.0000000000000001e-180 < x < 5.5999999999999999e41

   1. Initial program 72.0%

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

   3. Taylor expanded in b around inf 58.1%

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

      1. *-commutative 58.1%

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

   5. Simplified 58.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-76}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-180}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{+41}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 59.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -4.9 \cdot 10^{+135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;j \leq 1.08 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+252}:\\ \;\;\;\;t_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -4.9e+135)
     t_1
     (if (<= j 1.08e-24)
       (- (* x (- (* y z) (* t a))) (* c (* z b)))
       (if (<= j 3.5e+252) (- t_1 (* b (* z c))) (* c (- (* t 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -4.9e+135) {
		tmp = t_1;
	} else if (j <= 1.08e-24) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else if (j <= 3.5e+252) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	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 * ((t * c) - (y * i))
    if (j <= (-4.9d+135)) then
        tmp = t_1
    else if (j <= 1.08d-24) then
        tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
    else if (j <= 3.5d+252) then
        tmp = t_1 - (b * (z * c))
    else
        tmp = c * ((t * j) - (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -4.9e+135) {
		tmp = t_1;
	} else if (j <= 1.08e-24) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else if (j <= 3.5e+252) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = c * ((t * j) - (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -4.9e+135:
		tmp = t_1
	elif j <= 1.08e-24:
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
	elif j <= 3.5e+252:
		tmp = t_1 - (b * (z * c))
	else:
		tmp = c * ((t * j) - (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -4.9e+135)
		tmp = t_1;
	elseif (j <= 1.08e-24)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b)));
	elseif (j <= 3.5e+252)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	else
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -4.9e+135)
		tmp = t_1;
	elseif (j <= 1.08e-24)
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	elseif (j <= 3.5e+252)
		tmp = t_1 - (b * (z * c));
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.9e+135], t$95$1, If[LessEqual[j, 1.08e-24], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.5e+252], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.9000000000000001e135

   1. Initial program 65.7%

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

   3. Taylor expanded in c around inf 68.8%

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

      1. *-commutative 68.8%

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

      2. associate-*l* 65.9%

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

      3. *-commutative 65.9%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in j around inf 72.6%

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

   if -4.9000000000000001e135 < j < 1.08000000000000006e-24

   1. Initial program 75.2%

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

   3. Taylor expanded in j around 0 76.0%

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

      1. *-commutative 76.0%

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

      2. *-commutative 76.0%

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

   5. Simplified 76.0%

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

   6. Taylor expanded in c around inf 69.1%

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

      1. *-commutative 68.9%

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

      2. associate-*l* 68.5%

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

      3. *-commutative 68.5%

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

   8. Simplified 68.6%

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

   if 1.08000000000000006e-24 < j < 3.4999999999999999e252

   1. Initial program 81.0%

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

   3. Taylor expanded in c around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*l* 77.8%

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

      3. *-commutative 77.8%

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

   5. Simplified 77.8%

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

   6. Taylor expanded in x around 0 72.6%

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

   if 3.4999999999999999e252 < j

   1. Initial program 55.1%

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

   3. Taylor expanded in c around inf 93.1%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.9 \cdot 10^{+135}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.08 \cdot 10^{-24}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{+252}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 30.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+288}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+298}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* t (- a)))))
   (if (<= t -1.9e+82)
     t_1
     (if (<= t 2.3e+86)
       (* z (* x y))
       (if (<= t 3.7e+288)
         t_1
         (if (<= t 1.4e+298) (* c (* t j)) (* a (* 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 * (t * -a);
	double tmp;
	if (t <= -1.9e+82) {
		tmp = t_1;
	} else if (t <= 2.3e+86) {
		tmp = z * (x * y);
	} else if (t <= 3.7e+288) {
		tmp = t_1;
	} else if (t <= 1.4e+298) {
		tmp = c * (t * j);
	} else {
		tmp = a * (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 * (t * -a)
    if (t <= (-1.9d+82)) then
        tmp = t_1
    else if (t <= 2.3d+86) then
        tmp = z * (x * y)
    else if (t <= 3.7d+288) then
        tmp = t_1
    else if (t <= 1.4d+298) then
        tmp = c * (t * j)
    else
        tmp = a * (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 * (t * -a);
	double tmp;
	if (t <= -1.9e+82) {
		tmp = t_1;
	} else if (t <= 2.3e+86) {
		tmp = z * (x * y);
	} else if (t <= 3.7e+288) {
		tmp = t_1;
	} else if (t <= 1.4e+298) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (t * -a)
	tmp = 0
	if t <= -1.9e+82:
		tmp = t_1
	elif t <= 2.3e+86:
		tmp = z * (x * y)
	elif t <= 3.7e+288:
		tmp = t_1
	elif t <= 1.4e+298:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(t * Float64(-a)))
	tmp = 0.0
	if (t <= -1.9e+82)
		tmp = t_1;
	elseif (t <= 2.3e+86)
		tmp = Float64(z * Float64(x * y));
	elseif (t <= 3.7e+288)
		tmp = t_1;
	elseif (t <= 1.4e+298)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (t * -a);
	tmp = 0.0;
	if (t <= -1.9e+82)
		tmp = t_1;
	elseif (t <= 2.3e+86)
		tmp = z * (x * y);
	elseif (t <= 3.7e+288)
		tmp = t_1;
	elseif (t <= 1.4e+298)
		tmp = c * (t * j);
	else
		tmp = a * (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[(t * (-a)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+82], t$95$1, If[LessEqual[t, 2.3e+86], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.7e+288], t$95$1, If[LessEqual[t, 1.4e+298], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.90000000000000017e82 or 2.2999999999999999e86 < t < 3.6999999999999998e288

   1. Initial program 65.7%

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

   3. Taylor expanded in j around 0 63.0%

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

      1. *-commutative 63.0%

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

      2. *-commutative 63.0%

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

   5. Simplified 63.0%

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

      1. add-cube-cbrt 63.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)} \]

      2. pow3 63.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - i \cdot a}\right)}^{3}} \]

      3. *-commutative 63.0%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot {\left(\sqrt[3]{c \cdot z - \color{blue}{a \cdot i}}\right)}^{3} \]

   7. Applied egg-rr 63.0%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - a \cdot i}\right)}^{3}} \]

   8. Taylor expanded in c around inf 66.0%

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

      1. *-commutative 66.0%

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

      2. associate-*l* 62.3%

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

   10. Simplified 62.3%

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

   11. Taylor expanded in z around 0 46.7%

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

       1. mul-1-neg 46.7%

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

       2. associate-*r* 48.7%

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

   13. Simplified 48.7%

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

   if -1.90000000000000017e82 < t < 2.2999999999999999e86

   1. Initial program 80.9%

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

   3. Taylor expanded in z around inf 49.7%

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

      1. *-commutative 49.7%

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

      2. *-commutative 49.7%

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

   5. Simplified 49.7%

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

   6. Taylor expanded in y around inf 33.7%

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

      1. associate-*r* 34.2%

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

      2. *-commutative 34.2%

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

   8. Simplified 34.2%

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

   if 3.6999999999999998e288 < t < 1.40000000000000008e298

   1. Initial program 41.7%

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

   3. Taylor expanded in c around inf 100.0%

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

   4. Taylor expanded in j around inf 81.4%

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

      1. *-commutative 81.4%

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

   6. Simplified 81.4%

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

   if 1.40000000000000008e298 < t

   1. Initial program 36.9%

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

   3. Taylor expanded in b around inf 38.7%

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

      1. *-commutative 38.7%

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

   5. Simplified 38.7%

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

   6. Taylor expanded in i around inf 67.2%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+82}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+86}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{+288}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+298}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 50.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.2 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))))
   (if (<= b -4.2e+114)
     t_1
     (if (<= b -1.4e-39)
       (* j (- (* t c) (* y i)))
       (if (<= b 2.2e-35) (* t (- (* c j) (* 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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.2e+114) {
		tmp = t_1;
	} else if (b <= -1.4e-39) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 2.2e-35) {
		tmp = t * ((c * j) - (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 = b * ((a * i) - (z * c))
    if (b <= (-4.2d+114)) then
        tmp = t_1
    else if (b <= (-1.4d-39)) then
        tmp = j * ((t * c) - (y * i))
    else if (b <= 2.2d-35) then
        tmp = t * ((c * j) - (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 = b * ((a * i) - (z * c));
	double tmp;
	if (b <= -4.2e+114) {
		tmp = t_1;
	} else if (b <= -1.4e-39) {
		tmp = j * ((t * c) - (y * i));
	} else if (b <= 2.2e-35) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	tmp = 0
	if b <= -4.2e+114:
		tmp = t_1
	elif b <= -1.4e-39:
		tmp = j * ((t * c) - (y * i))
	elif b <= 2.2e-35:
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.2e+114)
		tmp = t_1;
	elseif (b <= -1.4e-39)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (b <= 2.2e-35)
		tmp = Float64(t * Float64(Float64(c * j) - 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 = b * ((a * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.2e+114)
		tmp = t_1;
	elseif (b <= -1.4e-39)
		tmp = j * ((t * c) - (y * i));
	elseif (b <= 2.2e-35)
		tmp = t * ((c * j) - (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[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.2e+114], t$95$1, If[LessEqual[b, -1.4e-39], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.2e-35], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.2000000000000001e114 or 2.19999999999999994e-35 < b

   1. Initial program 79.2%

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

   3. Taylor expanded in b around inf 60.4%

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

      1. *-commutative 60.4%

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

   5. Simplified 60.4%

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

   if -4.2000000000000001e114 < b < -1.4000000000000001e-39

   1. Initial program 62.0%

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

   3. Taylor expanded in c around inf 67.9%

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

      1. *-commutative 67.9%

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

      2. associate-*l* 62.3%

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

      3. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   6. Taylor expanded in j around inf 62.3%

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

   if -1.4000000000000001e-39 < b < 2.19999999999999994e-35

   1. Initial program 73.2%

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

   3. Taylor expanded in t around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

   5. Simplified 52.9%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.2 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.4 \cdot 10^{-39}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.2 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 29.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= x -1.1e+19)
     t_1
     (if (<= x 1.28e-179)
       (* c (* t j))
       (if (<= x 6.2e+43) (* i (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (x <= -1.1e+19) {
		tmp = t_1;
	} else if (x <= 1.28e-179) {
		tmp = c * (t * j);
	} else if (x <= 6.2e+43) {
		tmp = i * (a * b);
	} 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 = x * (y * z)
    if (x <= (-1.1d+19)) then
        tmp = t_1
    else if (x <= 1.28d-179) then
        tmp = c * (t * j)
    else if (x <= 6.2d+43) then
        tmp = i * (a * b)
    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 = x * (y * z);
	double tmp;
	if (x <= -1.1e+19) {
		tmp = t_1;
	} else if (x <= 1.28e-179) {
		tmp = c * (t * j);
	} else if (x <= 6.2e+43) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if x <= -1.1e+19:
		tmp = t_1
	elif x <= 1.28e-179:
		tmp = c * (t * j)
	elif x <= 6.2e+43:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (x <= -1.1e+19)
		tmp = t_1;
	elseif (x <= 1.28e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 6.2e+43)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (x <= -1.1e+19)
		tmp = t_1;
	elseif (x <= 1.28e-179)
		tmp = c * (t * j);
	elseif (x <= 6.2e+43)
		tmp = i * (a * b);
	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[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.1e+19], t$95$1, If[LessEqual[x, 1.28e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+43], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1e19 or 6.2000000000000003e43 < x

   1. Initial program 79.8%

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

   3. Taylor expanded in z around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around inf 46.3%

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

   if -1.1e19 < x < 1.28000000000000006e-179

   1. Initial program 67.9%

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

   3. Taylor expanded in c around inf 45.3%

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

   4. Taylor expanded in j around inf 30.5%

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

      1. *-commutative 30.5%

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

   6. Simplified 30.5%

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

   if 1.28000000000000006e-179 < x < 6.2000000000000003e43

   1. Initial program 71.8%

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

   3. Taylor expanded in j around 0 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

   5. Simplified 71.6%

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

      1. add-cube-cbrt 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)} \]

      2. pow3 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - i \cdot a}\right)}^{3}} \]

      3. *-commutative 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot {\left(\sqrt[3]{c \cdot z - \color{blue}{a \cdot i}}\right)}^{3} \]

   7. Applied egg-rr 71.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - a \cdot i}\right)}^{3}} \]

   8. Taylor expanded in i around inf 26.8%

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

      1. *-commutative 26.8%

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

      2. associate-*r* 28.7%

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

      3. *-commutative 28.7%

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

      4. associate-*l* 30.7%

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

   10. Simplified 30.7%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+19}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -1.55e+19)
     t_1
     (if (<= x 1.1e-179)
       (* c (* t j))
       (if (<= x 7.4e+43) (* i (* a b)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -1.55e+19) {
		tmp = t_1;
	} else if (x <= 1.1e-179) {
		tmp = c * (t * j);
	} else if (x <= 7.4e+43) {
		tmp = i * (a * b);
	} 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 = z * (x * y)
    if (x <= (-1.55d+19)) then
        tmp = t_1
    else if (x <= 1.1d-179) then
        tmp = c * (t * j)
    else if (x <= 7.4d+43) then
        tmp = i * (a * b)
    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 = z * (x * y);
	double tmp;
	if (x <= -1.55e+19) {
		tmp = t_1;
	} else if (x <= 1.1e-179) {
		tmp = c * (t * j);
	} else if (x <= 7.4e+43) {
		tmp = i * (a * b);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -1.55e+19:
		tmp = t_1
	elif x <= 1.1e-179:
		tmp = c * (t * j)
	elif x <= 7.4e+43:
		tmp = i * (a * b)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -1.55e+19)
		tmp = t_1;
	elseif (x <= 1.1e-179)
		tmp = Float64(c * Float64(t * j));
	elseif (x <= 7.4e+43)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (x <= -1.55e+19)
		tmp = t_1;
	elseif (x <= 1.1e-179)
		tmp = c * (t * j);
	elseif (x <= 7.4e+43)
		tmp = i * (a * b);
	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[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.55e+19], t$95$1, If[LessEqual[x, 1.1e-179], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e+43], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55e19 or 7.4000000000000002e43 < x

   1. Initial program 79.8%

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

   3. Taylor expanded in z around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around inf 46.3%

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

      1. associate-*r* 48.5%

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

      2. *-commutative 48.5%

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

   8. Simplified 48.5%

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

   if -1.55e19 < x < 1.10000000000000002e-179

   1. Initial program 67.9%

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

   3. Taylor expanded in c around inf 45.3%

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

   4. Taylor expanded in j around inf 30.5%

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

      1. *-commutative 30.5%

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

   6. Simplified 30.5%

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

   if 1.10000000000000002e-179 < x < 7.4000000000000002e43

   1. Initial program 71.8%

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

   3. Taylor expanded in j around 0 71.6%

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

      1. *-commutative 71.6%

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

      2. *-commutative 71.6%

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

   5. Simplified 71.6%

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

      1. add-cube-cbrt 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)} \]

      2. pow3 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - i \cdot a}\right)}^{3}} \]

      3. *-commutative 71.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot {\left(\sqrt[3]{c \cdot z - \color{blue}{a \cdot i}}\right)}^{3} \]

   7. Applied egg-rr 71.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - a \cdot i}\right)}^{3}} \]

   8. Taylor expanded in i around inf 26.8%

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

      1. *-commutative 26.8%

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

      2. associate-*r* 28.7%

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

      3. *-commutative 28.7%

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

      4. associate-*l* 30.7%

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

   10. Simplified 30.7%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-179}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.15e+118)
   (* b (* a i))
   (if (<= b 2e+40) (* c (* t j)) (* a (* b 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 (b <= -1.15e+118) {
		tmp = b * (a * i);
	} else if (b <= 2e+40) {
		tmp = c * (t * j);
	} else {
		tmp = a * (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) :: tmp
    if (b <= (-1.15d+118)) then
        tmp = b * (a * i)
    else if (b <= 2d+40) then
        tmp = c * (t * j)
    else
        tmp = a * (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 tmp;
	if (b <= -1.15e+118) {
		tmp = b * (a * i);
	} else if (b <= 2e+40) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.15e+118:
		tmp = b * (a * i)
	elif b <= 2e+40:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.15e+118)
		tmp = Float64(b * Float64(a * i));
	elseif (b <= 2e+40)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.15e+118)
		tmp = b * (a * i);
	elseif (b <= 2e+40)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.15e+118], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+40], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.15000000000000008e118

   1. Initial program 76.2%

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

   3. Taylor expanded in b around inf 71.3%

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

      1. *-commutative 71.3%

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

   5. Simplified 71.3%

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

   6. Taylor expanded in i around inf 33.5%

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

      1. *-commutative 33.5%

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

      2. associate-*l* 38.5%

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

   8. Simplified 38.5%

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

   if -1.15000000000000008e118 < b < 2.00000000000000006e40

   1. Initial program 72.8%

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

   3. Taylor expanded in c around inf 36.7%

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

   4. Taylor expanded in j around inf 28.5%

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

      1. *-commutative 28.5%

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

   6. Simplified 28.5%

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

   if 2.00000000000000006e40 < b

   1. Initial program 77.6%

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

   3. Taylor expanded in b around inf 61.2%

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

      1. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in i around inf 35.0%

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

4. Final simplification 31.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+118}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+40}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+100}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1.25e+100)
   (* i (* a b))
   (if (<= b 1.25e+42) (* c (* t j)) (* a (* b 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 (b <= -1.25e+100) {
		tmp = i * (a * b);
	} else if (b <= 1.25e+42) {
		tmp = c * (t * j);
	} else {
		tmp = a * (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) :: tmp
    if (b <= (-1.25d+100)) then
        tmp = i * (a * b)
    else if (b <= 1.25d+42) then
        tmp = c * (t * j)
    else
        tmp = a * (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 tmp;
	if (b <= -1.25e+100) {
		tmp = i * (a * b);
	} else if (b <= 1.25e+42) {
		tmp = c * (t * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1.25e+100:
		tmp = i * (a * b)
	elif b <= 1.25e+42:
		tmp = c * (t * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1.25e+100)
		tmp = Float64(i * Float64(a * b));
	elseif (b <= 1.25e+42)
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1.25e+100)
		tmp = i * (a * b);
	elseif (b <= 1.25e+42)
		tmp = c * (t * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1.25e+100], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.25e+42], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.25e100

   1. Initial program 75.5%

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

   3. Taylor expanded in j around 0 73.4%

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

      1. *-commutative 73.4%

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

      2. *-commutative 73.4%

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

   5. Simplified 73.4%

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

      1. add-cube-cbrt 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{\left(\left(\sqrt[3]{c \cdot z - i \cdot a} \cdot \sqrt[3]{c \cdot z - i \cdot a}\right) \cdot \sqrt[3]{c \cdot z - i \cdot a}\right)} \]

      2. pow3 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - i \cdot a}\right)}^{3}} \]

      3. *-commutative 73.2%

         \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot {\left(\sqrt[3]{c \cdot z - \color{blue}{a \cdot i}}\right)}^{3} \]

   7. Applied egg-rr 73.2%

      \[\leadsto x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \color{blue}{{\left(\sqrt[3]{c \cdot z - a \cdot i}\right)}^{3}} \]

   8. Taylor expanded in i around inf 36.1%

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

      1. *-commutative 36.1%

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

      2. associate-*r* 38.3%

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

      3. *-commutative 38.3%

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

      4. associate-*l* 40.7%

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

   10. Simplified 40.7%

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

   if -1.25e100 < b < 1.25000000000000002e42

   1. Initial program 72.9%

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

   3. Taylor expanded in c around inf 36.1%

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

   4. Taylor expanded in j around inf 27.8%

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

      1. *-commutative 27.8%

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

   6. Simplified 27.8%

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

   if 1.25000000000000002e42 < b

   1. Initial program 77.6%

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

   3. Taylor expanded in b around inf 61.2%

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

      1. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in i around inf 35.0%

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

4. Final simplification 31.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{+100}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{+42}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 21.8% accurate, 5.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 74.2%

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

3. Taylor expanded in b around inf 35.4%

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

   1. *-commutative 35.4%

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

5. Simplified 35.4%

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

6. Taylor expanded in i around inf 17.4%

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

7. Final simplification 17.4%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
8. Add Preprocessing

Developer target: 68.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ t_2 := x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{if}\;t < -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t < -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t < 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
          (/
           (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0)))
           (+ (* c t) (* i y)))))
        (t_2
         (-
          (* x (- (* z y) (* a t)))
          (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))
   (if (< t -8.120978919195912e-33)
     t_2
     (if (< t -4.712553818218485e-169)
       t_1
       (if (< t -7.633533346031584e-308)
         t_2
         (if (< t 1.0535888557455487e-139) 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 * ((c * z) - (i * a)))) + ((j * (pow((c * t), 2.0) - pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		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 * ((c * z) - (i * a)))) + ((j * (((c * t) ** 2.0d0) - ((i * y) ** 2.0d0))) / ((c * t) + (i * y)))
    t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
    if (t < (-8.120978919195912d-33)) then
        tmp = t_2
    else if (t < (-4.712553818218485d-169)) then
        tmp = t_1
    else if (t < (-7.633533346031584d-308)) then
        tmp = t_2
    else if (t < 1.0535888557455487d-139) 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 * ((c * z) - (i * a)))) + ((j * (Math.pow((c * t), 2.0) - Math.pow((i * y), 2.0))) / ((c * t) + (i * y)));
	double t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	double tmp;
	if (t < -8.120978919195912e-33) {
		tmp = t_2;
	} else if (t < -4.712553818218485e-169) {
		tmp = t_1;
	} else if (t < -7.633533346031584e-308) {
		tmp = t_2;
	} else if (t < 1.0535888557455487e-139) {
		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 * ((c * z) - (i * a)))) + ((j * (math.pow((c * t), 2.0) - math.pow((i * y), 2.0))) / ((c * t) + (i * y)))
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j))
	tmp = 0
	if t < -8.120978919195912e-33:
		tmp = t_2
	elif t < -4.712553818218485e-169:
		tmp = t_1
	elif t < -7.633533346031584e-308:
		tmp = t_2
	elif t < 1.0535888557455487e-139:
		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(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(c * z) - Float64(i * a)))) + Float64(Float64(j * Float64((Float64(c * t) ^ 2.0) - (Float64(i * y) ^ 2.0))) / Float64(Float64(c * t) + Float64(i * y))))
	t_2 = Float64(Float64(x * Float64(Float64(z * y) - Float64(a * t))) - Float64(Float64(b * Float64(Float64(z * c) - Float64(a * i))) - Float64(Float64(Float64(c * t) - Float64(y * i)) * j)))
	tmp = 0.0
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		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 * ((c * z) - (i * a)))) + ((j * (((c * t) ^ 2.0) - ((i * y) ^ 2.0))) / ((c * t) + (i * y)));
	t_2 = (x * ((z * y) - (a * t))) - ((b * ((z * c) - (a * i))) - (((c * t) - (y * i)) * j));
	tmp = 0.0;
	if (t < -8.120978919195912e-33)
		tmp = t_2;
	elseif (t < -4.712553818218485e-169)
		tmp = t_1;
	elseif (t < -7.633533346031584e-308)
		tmp = t_2;
	elseif (t < 1.0535888557455487e-139)
		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[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(c * z), $MachinePrecision] - N[(i * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(j * N[(N[Power[N[(c * t), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(i * y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * t), $MachinePrecision] + N[(i * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(z * y), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(c * t), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision] * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t, -8.120978919195912e-33], t$95$2, If[Less[t, -4.712553818218485e-169], t$95$1, If[Less[t, -7.633533346031584e-308], t$95$2, If[Less[t, 1.0535888557455487e-139], t$95$1, t$95$2]]]]]]

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

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