Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.8% → 82.1%

Time: 16.7s

Alternatives: 17

Speedup: 0.5×

• 58.2% 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: 73.8% 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: 82.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(Float64(z * c) - Float64(a * i)))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	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 * ((z * c) - (a * i)))) + (j * ((t * c) - (y * i)));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = a * ((b * i) - (x * t));
	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[(z * c), $MachinePrecision] - N[(a * i), $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[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $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 89.5%

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

   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. Step-by-step derivation

      1. add-cube-cbrt 0.0%

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

      2. pow3 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

   4. Applied egg-rr 0.0%

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

   5. Taylor expanded in a around inf 60.7%

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

      1. associate-*r* 60.7%

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

      2. neg-mul-1 60.7%

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

      3. cancel-sign-sub 60.7%

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

      4. +-commutative 60.7%

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

      5. *-commutative 60.7%

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

      6. mul-1-neg 60.7%

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

      7. unsub-neg 60.7%

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

   7. Simplified 60.7%

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

4. Final simplification 84.1%

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

Alternative 2: 62.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot \frac{c \cdot j - x \cdot a}{b} + \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{if}\;a \leq -5.4 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (+ (* t (/ (- (* c j) (* x a)) b)) (- (* a i) (* z c))))))
   (if (<= a -5.4e+147)
     t_1
     (if (<= a 1.5e-77)
       (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
       (if (<= a 1.7e+120) t_1 (* a (- (* b i) (* x t))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * (((c * j) - (x * a)) / b)) + ((a * i) - (z * c)));
	double tmp;
	if (a <= -5.4e+147) {
		tmp = t_1;
	} else if (a <= 1.5e-77) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else if (a <= 1.7e+120) {
		tmp = t_1;
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	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 * ((t * (((c * j) - (x * a)) / b)) + ((a * i) - (z * c)))
    if (a <= (-5.4d+147)) then
        tmp = t_1
    else if (a <= 1.5d-77) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else if (a <= 1.7d+120) then
        tmp = t_1
    else
        tmp = a * ((b * i) - (x * t))
    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 * ((t * (((c * j) - (x * a)) / b)) + ((a * i) - (z * c)));
	double tmp;
	if (a <= -5.4e+147) {
		tmp = t_1;
	} else if (a <= 1.5e-77) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else if (a <= 1.7e+120) {
		tmp = t_1;
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * (((c * j) - (x * a)) / b)) + ((a * i) - (z * c)))
	tmp = 0
	if a <= -5.4e+147:
		tmp = t_1
	elif a <= 1.5e-77:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	elif a <= 1.7e+120:
		tmp = t_1
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * Float64(Float64(Float64(c * j) - Float64(x * a)) / b)) + Float64(Float64(a * i) - Float64(z * c))))
	tmp = 0.0
	if (a <= -5.4e+147)
		tmp = t_1;
	elseif (a <= 1.5e-77)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	elseif (a <= 1.7e+120)
		tmp = t_1;
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * (((c * j) - (x * a)) / b)) + ((a * i) - (z * c)));
	tmp = 0.0;
	if (a <= -5.4e+147)
		tmp = t_1;
	elseif (a <= 1.5e-77)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	elseif (a <= 1.7e+120)
		tmp = t_1;
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * N[(N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] + N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.4e+147], t$95$1, If[LessEqual[a, 1.5e-77], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e+120], t$95$1, N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.39999999999999995e147 or 1.50000000000000008e-77 < a < 1.69999999999999999e120

   1. Initial program 67.8%

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

   3. Taylor expanded in y around 0 60.1%

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

      1. mul-1-neg 60.1%

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

      2. associate-*r* 61.6%

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

      3. *-commutative 61.6%

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

      4. associate-*l* 62.9%

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

      5. distribute-rgt-neg-in 62.9%

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

      6. mul-1-neg 62.9%

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

      7. *-commutative 62.9%

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

      8. associate-*r* 61.5%

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

      9. *-commutative 61.5%

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

      10. associate-*l* 62.9%

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

      11. distribute-lft-in 67.5%

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

      12. +-commutative 67.5%

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

      13. mul-1-neg 67.5%

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

      14. unsub-neg 67.5%

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

      15. *-commutative 67.5%

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

      16. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in b around -inf 69.3%

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

      1. associate-*r* 69.3%

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

      2. neg-mul-1 69.3%

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

      3. distribute-lft-out-- 69.3%

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

      4. associate-/l* 72.3%

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

      5. *-commutative 72.3%

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

      6. *-commutative 72.3%

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

   8. Simplified 72.3%

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

   if -5.39999999999999995e147 < a < 1.50000000000000008e-77

   1. Initial program 81.8%

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

   3. Taylor expanded in b around 0 72.8%

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

   if 1.69999999999999999e120 < a

   1. Initial program 55.0%

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

      1. add-cube-cbrt 54.9%

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

      2. pow3 54.9%

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

      3. *-commutative 54.9%

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

      4. *-commutative 54.9%

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

   4. Applied egg-rr 54.9%

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

   5. Taylor expanded in a around inf 81.6%

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

      1. associate-*r* 81.6%

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

      2. neg-mul-1 81.6%

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

      3. cancel-sign-sub 81.6%

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

      4. +-commutative 81.6%

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

      5. *-commutative 81.6%

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

      6. mul-1-neg 81.6%

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

      7. unsub-neg 81.6%

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

   7. Simplified 81.6%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.4 \cdot 10^{+147}:\\ \;\;\;\;b \cdot \left(t \cdot \frac{c \cdot j - x \cdot a}{b} + \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-77}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot \frac{c \cdot j - x \cdot a}{b} + \left(a \cdot i - z \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* b i) (* x t)))))
   (if (<= a -4e+200)
     t_1
     (if (<= a 5e-80)
       (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))
       (if (<= a 1.25e+121)
         (- (* t (- (* c j) (* x a))) (* b (- (* z c) (* a i))))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4e+200) {
		tmp = t_1;
	} else if (a <= 5e-80) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else if (a <= 1.25e+121) {
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((b * i) - (x * t))
    if (a <= (-4d+200)) then
        tmp = t_1
    else if (a <= 5d-80) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
    else if (a <= 1.25d+121) then
        tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -4e+200) {
		tmp = t_1;
	} else if (a <= 5e-80) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	} else if (a <= 1.25e+121) {
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -4e+200:
		tmp = t_1
	elif a <= 5e-80:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	elif a <= 1.25e+121:
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4e+200)
		tmp = t_1;
	elseif (a <= 5e-80)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	elseif (a <= 1.25e+121)
		tmp = Float64(Float64(t * Float64(Float64(c * j) - Float64(x * a))) - Float64(b * Float64(Float64(z * c) - Float64(a * i))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -4e+200)
		tmp = t_1;
	elseif (a <= 5e-80)
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	elseif (a <= 1.25e+121)
		tmp = (t * ((c * j) - (x * a))) - (b * ((z * c) - (a * i)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4e+200], t$95$1, If[LessEqual[a, 5e-80], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.25e+121], N[(N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(N[(z * c), $MachinePrecision] - N[(a * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.9999999999999999e200 or 1.25000000000000002e121 < a

   1. Initial program 50.4%

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

      1. add-cube-cbrt 50.3%

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

      2. pow3 50.3%

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

      3. *-commutative 50.3%

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

      4. *-commutative 50.3%

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

   4. Applied egg-rr 50.3%

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

   5. Taylor expanded in a around inf 76.3%

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

      1. associate-*r* 76.3%

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

      2. neg-mul-1 76.3%

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

      3. cancel-sign-sub 76.3%

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

      4. +-commutative 76.3%

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

      5. *-commutative 76.3%

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

      6. mul-1-neg 76.3%

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

      7. unsub-neg 76.3%

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

   7. Simplified 76.3%

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

   if -3.9999999999999999e200 < a < 5e-80

   1. Initial program 81.6%

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

   3. Taylor expanded in b around 0 72.0%

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

   if 5e-80 < a < 1.25000000000000002e121

   1. Initial program 82.5%

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

   3. Taylor expanded in y around 0 67.7%

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

      1. mul-1-neg 67.7%

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

      2. associate-*r* 73.4%

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

      3. *-commutative 73.4%

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

      4. associate-*l* 73.3%

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

      5. distribute-rgt-neg-in 73.3%

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

      6. mul-1-neg 73.3%

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

      7. *-commutative 73.3%

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

      8. associate-*r* 70.5%

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

      9. *-commutative 70.5%

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

      10. associate-*l* 73.3%

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

      11. distribute-lft-in 76.3%

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

      12. +-commutative 76.3%

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

      13. mul-1-neg 76.3%

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

      14. unsub-neg 76.3%

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

      15. *-commutative 76.3%

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

      16. *-commutative 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{+200}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-80}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+121}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right) - b \cdot \left(z \cdot c - a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.8 \cdot 10^{+69} \lor \neg \left(i \leq 1.1 \cdot 10^{+114}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.8e+69) (not (<= i 1.1e+114)))
   (* i (- (* a b) (* y j)))
   (+ (* x (- (* y z) (* t a))) (* j (- (* t c) (* y i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.8e+69) || !(i <= 1.1e+114)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 ((i <= (-1.8d+69)) .or. (.not. (i <= 1.1d+114))) then
        tmp = i * ((a * b) - (y * j))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * 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 ((i <= -1.8e+69) || !(i <= 1.1e+114)) {
		tmp = i * ((a * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.8e+69) or not (i <= 1.1e+114):
		tmp = i * ((a * b) - (y * j))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.8e+69) || !(i <= 1.1e+114))
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(t * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.8e+69) || ~((i <= 1.1e+114)))
		tmp = i * ((a * b) - (y * j));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((t * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.8e+69], N[Not[LessEqual[i, 1.1e+114]], $MachinePrecision]], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.8000000000000001e69 or 1.1e114 < i

   1. Initial program 56.8%

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

   3. Taylor expanded in i around inf 73.1%

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

      1. distribute-lft-out-- 73.1%

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

      2. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   if -1.8000000000000001e69 < i < 1.1e114

   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 0 71.0%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.8 \cdot 10^{+69} \lor \neg \left(i \leq 1.1 \cdot 10^{+114}\right):\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot c - y \cdot i\\ \mathbf{if}\;j \leq -4.4 \cdot 10^{+41}:\\ \;\;\;\;j \cdot t\_1\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(a \cdot \left(i - c \cdot \frac{z}{a}\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot j\right) \cdot \frac{t\_1}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t c) (* y i))))
   (if (<= j -4.4e+41)
     (* j t_1)
     (if (<= j -6.5e-102)
       (* b (* a (- i (* c (/ z a)))))
       (if (<= j 1.65e+38) (* x (- (* y z) (* t a))) (* (* a j) (/ t_1 a)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double tmp;
	if (j <= -4.4e+41) {
		tmp = j * t_1;
	} else if (j <= -6.5e-102) {
		tmp = b * (a * (i - (c * (z / a))));
	} else if (j <= 1.65e+38) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = (a * j) * (t_1 / a);
	}
	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 = (t * c) - (y * i)
    if (j <= (-4.4d+41)) then
        tmp = j * t_1
    else if (j <= (-6.5d-102)) then
        tmp = b * (a * (i - (c * (z / a))))
    else if (j <= 1.65d+38) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = (a * j) * (t_1 / a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * c) - (y * i);
	double tmp;
	if (j <= -4.4e+41) {
		tmp = j * t_1;
	} else if (j <= -6.5e-102) {
		tmp = b * (a * (i - (c * (z / a))));
	} else if (j <= 1.65e+38) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = (a * j) * (t_1 / a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * c) - (y * i)
	tmp = 0
	if j <= -4.4e+41:
		tmp = j * t_1
	elif j <= -6.5e-102:
		tmp = b * (a * (i - (c * (z / a))))
	elif j <= 1.65e+38:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = (a * j) * (t_1 / a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * c) - Float64(y * i))
	tmp = 0.0
	if (j <= -4.4e+41)
		tmp = Float64(j * t_1);
	elseif (j <= -6.5e-102)
		tmp = Float64(b * Float64(a * Float64(i - Float64(c * Float64(z / a)))));
	elseif (j <= 1.65e+38)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = Float64(Float64(a * j) * Float64(t_1 / a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * c) - (y * i);
	tmp = 0.0;
	if (j <= -4.4e+41)
		tmp = j * t_1;
	elseif (j <= -6.5e-102)
		tmp = b * (a * (i - (c * (z / a))));
	elseif (j <= 1.65e+38)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = (a * j) * (t_1 / a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -4.4e+41], N[(j * t$95$1), $MachinePrecision], If[LessEqual[j, -6.5e-102], N[(b * N[(a * N[(i - N[(c * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.65e+38], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(a * j), $MachinePrecision] * N[(t$95$1 / a), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -4.3999999999999998e41

   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 j around inf 83.3%

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

   if -4.3999999999999998e41 < j < -6.5000000000000003e-102

   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 b around inf 59.0%

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

      1. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in a around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

      3. associate-/l* 62.2%

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

   8. Simplified 62.2%

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

   if -6.5000000000000003e-102 < j < 1.65e38

   1. Initial program 73.6%

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

      1. add-cube-cbrt 73.5%

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

      2. pow3 73.5%

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

      3. *-commutative 73.5%

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

      4. *-commutative 73.5%

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

   4. Applied egg-rr 73.5%

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

   5. Taylor expanded in x around inf 53.8%

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

      1. *-commutative 53.8%

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

   7. Simplified 53.8%

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

   if 1.65e38 < j

   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. Step-by-step derivation

      1. add-cube-cbrt 68.4%

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

      2. pow3 68.4%

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

      3. *-commutative 68.4%

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

      4. *-commutative 68.4%

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

   4. Applied egg-rr 68.4%

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

   5. Taylor expanded in a around inf 50.8%

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

      1. +-commutative 50.8%

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

      2. mul-1-neg 50.8%

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

      3. unsub-neg 50.8%

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

      4. associate-/l* 57.0%

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

      5. associate-/l* 59.0%

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

      6. +-commutative 59.0%

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

      7. mul-1-neg 59.0%

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

      8. *-commutative 59.0%

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

      9. unsub-neg 59.0%

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

      10. associate-/l* 59.0%

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

      11. associate-/l* 59.0%

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

   7. Simplified 59.0%

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

   8. Taylor expanded in j around inf 49.5%

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

      1. div-sub 51.6%

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

      2. associate-*r* 63.4%

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

      3. *-commutative 63.4%

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

   10. Simplified 63.4%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -4.4 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(a \cdot \left(i - c \cdot \frac{z}{a}\right)\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(a \cdot j\right) \cdot \frac{t \cdot c - y \cdot i}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -1.45 \cdot 10^{+86}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 3.55 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= c -1.45e+86)
     t_1
     (if (<= c -5.5e+19)
       (* t (* x (- a)))
       (if (<= c -1.3e-275)
         (* x (* y z))
         (if (<= c 3.55e+71) (* b (* a i)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -1.45e+86) {
		tmp = t_1;
	} else if (c <= -5.5e+19) {
		tmp = t * (x * -a);
	} else if (c <= -1.3e-275) {
		tmp = x * (y * z);
	} else if (c <= 3.55e+71) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (c <= (-1.45d+86)) then
        tmp = t_1
    else if (c <= (-5.5d+19)) then
        tmp = t * (x * -a)
    else if (c <= (-1.3d-275)) then
        tmp = x * (y * z)
    else if (c <= 3.55d+71) then
        tmp = b * (a * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -1.45e+86) {
		tmp = t_1;
	} else if (c <= -5.5e+19) {
		tmp = t * (x * -a);
	} else if (c <= -1.3e-275) {
		tmp = x * (y * z);
	} else if (c <= 3.55e+71) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if c <= -1.45e+86:
		tmp = t_1
	elif c <= -5.5e+19:
		tmp = t * (x * -a)
	elif c <= -1.3e-275:
		tmp = x * (y * z)
	elif c <= 3.55e+71:
		tmp = b * (a * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -1.45e+86)
		tmp = t_1;
	elseif (c <= -5.5e+19)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (c <= -1.3e-275)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 3.55e+71)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (c <= -1.45e+86)
		tmp = t_1;
	elseif (c <= -5.5e+19)
		tmp = t * (x * -a);
	elseif (c <= -1.3e-275)
		tmp = x * (y * z);
	elseif (c <= 3.55e+71)
		tmp = b * (a * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -1.45e+86], t$95$1, If[LessEqual[c, -5.5e+19], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.3e-275], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 3.55e+71], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.44999999999999995e86 or 3.54999999999999993e71 < c

   1. Initial program 65.3%

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

   3. Taylor expanded in t around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

      4. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in c around inf 44.5%

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

      1. *-commutative 44.5%

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

   8. Simplified 44.5%

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

   if -1.44999999999999995e86 < c < -5.5e19

   1. Initial program 54.1%

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

   3. Taylor expanded in t around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

      4. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in c around 0 48.6%

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

      1. mul-1-neg 48.6%

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

      2. distribute-rgt-neg-in 48.6%

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

   8. Simplified 48.6%

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

   if -5.5e19 < c < -1.29999999999999996e-275

   1. Initial program 80.6%

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

      1. add-cube-cbrt 80.4%

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

      2. pow3 80.4%

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

      3. *-commutative 80.4%

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

      4. *-commutative 80.4%

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

   4. Applied egg-rr 80.4%

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

   5. Taylor expanded in x around inf 51.4%

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

      1. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in y around inf 32.1%

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

   if -1.29999999999999996e-275 < c < 3.54999999999999993e71

   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 44.6%

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

      1. *-commutative 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in a around inf 39.4%

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

      1. *-commutative 39.4%

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

   8. Simplified 39.4%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.45 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -5.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;c \leq -1.3 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 3.55 \cdot 10^{+71}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.85 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(a \cdot \left(i - c \cdot \frac{z}{a}\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.85e+45)
     t_1
     (if (<= j -6.6e-102)
       (* b (* a (- i (* c (/ z a)))))
       (if (<= j 5e+37) (* x (- (* y z) (* t 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.85e+45) {
		tmp = t_1;
	} else if (j <= -6.6e-102) {
		tmp = b * (a * (i - (c * (z / a))));
	} else if (j <= 5e+37) {
		tmp = x * ((y * z) - (t * 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 = j * ((t * c) - (y * i))
    if (j <= (-1.85d+45)) then
        tmp = t_1
    else if (j <= (-6.6d-102)) then
        tmp = b * (a * (i - (c * (z / a))))
    else if (j <= 5d+37) then
        tmp = x * ((y * z) - (t * 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.85e+45) {
		tmp = t_1;
	} else if (j <= -6.6e-102) {
		tmp = b * (a * (i - (c * (z / a))));
	} else if (j <= 5e+37) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	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 <= -1.85e+45:
		tmp = t_1
	elif j <= -6.6e-102:
		tmp = b * (a * (i - (c * (z / a))))
	elif j <= 5e+37:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	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 <= -1.85e+45)
		tmp = t_1;
	elseif (j <= -6.6e-102)
		tmp = Float64(b * Float64(a * Float64(i - Float64(c * Float64(z / a)))));
	elseif (j <= 5e+37)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * 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 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.85e+45)
		tmp = t_1;
	elseif (j <= -6.6e-102)
		tmp = b * (a * (i - (c * (z / a))));
	elseif (j <= 5e+37)
		tmp = x * ((y * z) - (t * 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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.85e+45], t$95$1, If[LessEqual[j, -6.6e-102], N[(b * N[(a * N[(i - N[(c * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e+37], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.84999999999999989e45 or 4.99999999999999989e37 < j

   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 j around inf 73.7%

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

   if -1.84999999999999989e45 < j < -6.6e-102

   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 b around inf 59.0%

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

      1. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   6. Taylor expanded in a around inf 65.1%

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

      1. mul-1-neg 65.1%

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

      2. unsub-neg 65.1%

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

      3. associate-/l* 62.2%

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

   8. Simplified 62.2%

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

   if -6.6e-102 < j < 4.99999999999999989e37

   1. Initial program 73.6%

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

      1. add-cube-cbrt 73.5%

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

      2. pow3 73.5%

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

      3. *-commutative 73.5%

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

      4. *-commutative 73.5%

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

   4. Applied egg-rr 73.5%

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

   5. Taylor expanded in x around inf 53.8%

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

      1. *-commutative 53.8%

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

   7. Simplified 53.8%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.85 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -6.6 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(a \cdot \left(i - c \cdot \frac{z}{a}\right)\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.7e+41)
     t_1
     (if (<= j -9.5e-102)
       (* b (- (* a i) (* z c)))
       (if (<= j 3.2e+37) (* x (- (* y z) (* t 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.7e+41) {
		tmp = t_1;
	} else if (j <= -9.5e-102) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 3.2e+37) {
		tmp = x * ((y * z) - (t * 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 = j * ((t * c) - (y * i))
    if (j <= (-1.7d+41)) then
        tmp = t_1
    else if (j <= (-9.5d-102)) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 3.2d+37) then
        tmp = x * ((y * z) - (t * 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.7e+41) {
		tmp = t_1;
	} else if (j <= -9.5e-102) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 3.2e+37) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	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 <= -1.7e+41:
		tmp = t_1
	elif j <= -9.5e-102:
		tmp = b * ((a * i) - (z * c))
	elif j <= 3.2e+37:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	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 <= -1.7e+41)
		tmp = t_1;
	elseif (j <= -9.5e-102)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 3.2e+37)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * 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 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.7e+41)
		tmp = t_1;
	elseif (j <= -9.5e-102)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 3.2e+37)
		tmp = x * ((y * z) - (t * 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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e+41], t$95$1, If[LessEqual[j, -9.5e-102], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e+37], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.69999999999999999e41 or 3.20000000000000014e37 < j

   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 j around inf 73.7%

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

   if -1.69999999999999999e41 < j < -9.50000000000000025e-102

   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 b around inf 59.0%

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

      1. *-commutative 59.0%

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

   5. Simplified 59.0%

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

   if -9.50000000000000025e-102 < j < 3.20000000000000014e37

   1. Initial program 73.6%

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

      1. add-cube-cbrt 73.5%

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

      2. pow3 73.5%

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

      3. *-commutative 73.5%

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

      4. *-commutative 73.5%

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

   4. Applied egg-rr 73.5%

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

   5. Taylor expanded in x around inf 53.8%

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

      1. *-commutative 53.8%

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

   7. Simplified 53.8%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+41}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -9.5 \cdot 10^{-102}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-224}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -1.95e+86)
   (* t (* c j))
   (if (<= c -1.4e-224)
     (* a (* x (- t)))
     (if (<= c 2e+119) (* b (* a i)) (* z (* b (- c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.95e+86) {
		tmp = t * (c * j);
	} else if (c <= -1.4e-224) {
		tmp = a * (x * -t);
	} else if (c <= 2e+119) {
		tmp = b * (a * i);
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-1.95d+86)) then
        tmp = t * (c * j)
    else if (c <= (-1.4d-224)) then
        tmp = a * (x * -t)
    else if (c <= 2d+119) then
        tmp = b * (a * i)
    else
        tmp = z * (b * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -1.95e+86) {
		tmp = t * (c * j);
	} else if (c <= -1.4e-224) {
		tmp = a * (x * -t);
	} else if (c <= 2e+119) {
		tmp = b * (a * i);
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -1.95e+86:
		tmp = t * (c * j)
	elif c <= -1.4e-224:
		tmp = a * (x * -t)
	elif c <= 2e+119:
		tmp = b * (a * i)
	else:
		tmp = z * (b * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -1.95e+86)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= -1.4e-224)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (c <= 2e+119)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(z * Float64(b * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -1.95e+86)
		tmp = t * (c * j);
	elseif (c <= -1.4e-224)
		tmp = a * (x * -t);
	elseif (c <= 2e+119)
		tmp = b * (a * i);
	else
		tmp = z * (b * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -1.95e+86], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -1.4e-224], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2e+119], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -1.9500000000000001e86

   1. Initial program 65.8%

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

   3. Taylor expanded in t around inf 52.8%

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

      1. +-commutative 52.8%

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

      2. mul-1-neg 52.8%

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

      3. unsub-neg 52.8%

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

      4. *-commutative 52.8%

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

   5. Simplified 52.8%

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

   6. Taylor expanded in c around inf 50.5%

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

      1. *-commutative 50.5%

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

   8. Simplified 50.5%

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

   if -1.9500000000000001e86 < c < -1.3999999999999999e-224

   1. Initial program 75.9%

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

   3. Taylor expanded in t around inf 32.9%

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

      1. +-commutative 32.9%

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

      2. mul-1-neg 32.9%

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

      3. unsub-neg 32.9%

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

      4. *-commutative 32.9%

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

   5. Simplified 32.9%

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

   6. Taylor expanded in c around 0 34.6%

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

      1. associate-*r* 34.6%

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

      2. neg-mul-1 34.6%

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

   8. Simplified 34.6%

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

   if -1.3999999999999999e-224 < c < 1.99999999999999989e119

   1. Initial program 79.0%

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

   3. Taylor expanded in b around inf 38.0%

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

      1. *-commutative 38.0%

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

   5. Simplified 38.0%

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

   6. Taylor expanded in a around inf 34.2%

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

      1. *-commutative 34.2%

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

   8. Simplified 34.2%

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

   if 1.99999999999999989e119 < c

   1. Initial program 57.4%

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

   3. Taylor expanded in b around inf 42.8%

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

      1. *-commutative 42.8%

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

   5. Simplified 42.8%

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

   6. Taylor expanded in a around 0 42.9%

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

      1. mul-1-neg 42.9%

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

      2. *-commutative 42.9%

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

      3. distribute-rgt-neg-in 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in c around 0 42.9%

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

       1. mul-1-neg 42.9%

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

       2. associate-*r* 50.3%

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

       3. distribute-lft-neg-in 50.3%

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

       4. *-commutative 50.3%

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

       5. distribute-rgt-neg-in 50.3%

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

   11. Simplified 50.3%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.95 \cdot 10^{+86}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -1.4 \cdot 10^{-224}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 2 \cdot 10^{+119}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;c \leq -3.7 \cdot 10^{+85}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-221}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 2.75 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= c -3.7e+85)
     t_1
     (if (<= c -1.25e-221)
       (* a (* x (- t)))
       (if (<= c 2.75e+63) (* b (* a i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -3.7e+85) {
		tmp = t_1;
	} else if (c <= -1.25e-221) {
		tmp = a * (x * -t);
	} else if (c <= 2.75e+63) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (c <= (-3.7d+85)) then
        tmp = t_1
    else if (c <= (-1.25d-221)) then
        tmp = a * (x * -t)
    else if (c <= 2.75d+63) then
        tmp = b * (a * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (c <= -3.7e+85) {
		tmp = t_1;
	} else if (c <= -1.25e-221) {
		tmp = a * (x * -t);
	} else if (c <= 2.75e+63) {
		tmp = b * (a * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if c <= -3.7e+85:
		tmp = t_1
	elif c <= -1.25e-221:
		tmp = a * (x * -t)
	elif c <= 2.75e+63:
		tmp = b * (a * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (c <= -3.7e+85)
		tmp = t_1;
	elseif (c <= -1.25e-221)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (c <= 2.75e+63)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (c <= -3.7e+85)
		tmp = t_1;
	elseif (c <= -1.25e-221)
		tmp = a * (x * -t);
	elseif (c <= 2.75e+63)
		tmp = b * (a * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[c, -3.7e+85], t$95$1, If[LessEqual[c, -1.25e-221], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 2.75e+63], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if c < -3.7000000000000002e85 or 2.75000000000000002e63 < c

   1. Initial program 65.3%

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

   3. Taylor expanded in t around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

      4. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   6. Taylor expanded in c around inf 44.5%

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

      1. *-commutative 44.5%

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

   8. Simplified 44.5%

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

   if -3.7000000000000002e85 < c < -1.24999999999999999e-221

   1. Initial program 75.9%

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

   3. Taylor expanded in t around inf 32.9%

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

      1. +-commutative 32.9%

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

      2. mul-1-neg 32.9%

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

      3. unsub-neg 32.9%

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

      4. *-commutative 32.9%

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

   5. Simplified 32.9%

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

   6. Taylor expanded in c around 0 34.6%

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

      1. associate-*r* 34.6%

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

      2. neg-mul-1 34.6%

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

   8. Simplified 34.6%

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

   if -1.24999999999999999e-221 < c < 2.75000000000000002e63

   1. Initial program 77.5%

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

   3. Taylor expanded in b around inf 41.1%

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

      1. *-commutative 41.1%

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

   5. Simplified 41.1%

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

   6. Taylor expanded in a around inf 36.8%

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

      1. *-commutative 36.8%

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

   8. Simplified 36.8%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -3.7 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq -1.25 \cdot 10^{-221}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;c \leq 2.75 \cdot 10^{+63}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.45 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-273}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+78}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -2.45e+51)
   (* c (* t j))
   (if (<= c -3.6e-273)
     (* x (* y z))
     (if (<= c 6.8e+78) (* b (* a i)) (* t (* c j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.45e+51) {
		tmp = c * (t * j);
	} else if (c <= -3.6e-273) {
		tmp = x * (y * z);
	} else if (c <= 6.8e+78) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-2.45d+51)) then
        tmp = c * (t * j)
    else if (c <= (-3.6d-273)) then
        tmp = x * (y * z)
    else if (c <= 6.8d+78) then
        tmp = b * (a * i)
    else
        tmp = t * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -2.45e+51) {
		tmp = c * (t * j);
	} else if (c <= -3.6e-273) {
		tmp = x * (y * z);
	} else if (c <= 6.8e+78) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -2.45e+51:
		tmp = c * (t * j)
	elif c <= -3.6e-273:
		tmp = x * (y * z)
	elif c <= 6.8e+78:
		tmp = b * (a * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -2.45e+51)
		tmp = Float64(c * Float64(t * j));
	elseif (c <= -3.6e-273)
		tmp = Float64(x * Float64(y * z));
	elseif (c <= 6.8e+78)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -2.45e+51)
		tmp = c * (t * j);
	elseif (c <= -3.6e-273)
		tmp = x * (y * z);
	elseif (c <= 6.8e+78)
		tmp = b * (a * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -2.45e+51], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, -3.6e-273], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 6.8e+78], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if c < -2.44999999999999992e51

   1. Initial program 62.1%

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

   3. Taylor expanded in t around inf 53.7%

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

      1. +-commutative 53.7%

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

      2. mul-1-neg 53.7%

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

      3. unsub-neg 53.7%

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

      4. *-commutative 53.7%

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

   5. Simplified 53.7%

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

   6. Taylor expanded in x around inf 55.7%

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

   7. Taylor expanded in c around inf 43.8%

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

   8. Taylor expanded in t around 0 45.6%

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

   if -2.44999999999999992e51 < c < -3.59999999999999993e-273

   1. Initial program 79.6%

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

      1. add-cube-cbrt 79.4%

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

      2. pow3 79.3%

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

      3. *-commutative 79.3%

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

      4. *-commutative 79.3%

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

   4. Applied egg-rr 79.3%

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

   5. Taylor expanded in x around inf 51.4%

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

      1. *-commutative 51.4%

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

   7. Simplified 51.4%

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

   8. Taylor expanded in y around inf 31.2%

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

   if -3.59999999999999993e-273 < c < 6.80000000000000014e78

   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 44.6%

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

      1. *-commutative 44.6%

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

   5. Simplified 44.6%

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

   6. Taylor expanded in a around inf 39.4%

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

      1. *-commutative 39.4%

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

   8. Simplified 39.4%

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

   if 6.80000000000000014e78 < c

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

      4. *-commutative 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in c around inf 39.7%

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

      1. *-commutative 39.7%

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

   8. Simplified 39.7%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.45 \cdot 10^{+51}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq -3.6 \cdot 10^{-273}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;c \leq 6.8 \cdot 10^{+78}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 50.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+102} \lor \neg \left(a \leq 1.7 \cdot 10^{-77}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -3e+102) (not (<= a 1.7e-77)))
   (* a (- (* b i) (* x t)))
   (* j (- (* t c) (* y i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -3e+102) || !(a <= 1.7e-77)) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = j * ((t * c) - (y * 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 ((a <= (-3d+102)) .or. (.not. (a <= 1.7d-77))) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = j * ((t * c) - (y * 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 ((a <= -3e+102) || !(a <= 1.7e-77)) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = j * ((t * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -3e+102) or not (a <= 1.7e-77):
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = j * ((t * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -3e+102) || !(a <= 1.7e-77))
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -3e+102) || ~((a <= 1.7e-77)))
		tmp = a * ((b * i) - (x * t));
	else
		tmp = j * ((t * c) - (y * i));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -3e+102], N[Not[LessEqual[a, 1.7e-77]], $MachinePrecision]], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -2.9999999999999998e102 or 1.69999999999999991e-77 < a

   1. Initial program 63.2%

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

      1. add-cube-cbrt 63.2%

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

      2. pow3 63.2%

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

      3. *-commutative 63.2%

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

      4. *-commutative 63.2%

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

   4. Applied egg-rr 63.2%

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

   5. Taylor expanded in a around inf 66.3%

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

      1. associate-*r* 66.3%

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

      2. neg-mul-1 66.3%

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

      3. cancel-sign-sub 66.3%

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

      4. +-commutative 66.3%

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

      5. *-commutative 66.3%

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

      6. mul-1-neg 66.3%

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

      7. unsub-neg 66.3%

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

   7. Simplified 66.3%

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

   if -2.9999999999999998e102 < a < 1.69999999999999991e-77

   1. Initial program 81.2%

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

   3. Taylor expanded in j around inf 52.2%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{+102} \lor \neg \left(a \leq 1.7 \cdot 10^{-77}\right):\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+153} \lor \neg \left(c \leq 3.1 \cdot 10^{+60}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -2.4e+153) (not (<= c 3.1e+60)))
   (* c (- (* t j) (* z b)))
   (* a (- (* b i) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -2.4e+153) || !(c <= 3.1e+60)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	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 ((c <= (-2.4d+153)) .or. (.not. (c <= 3.1d+60))) then
        tmp = c * ((t * j) - (z * b))
    else
        tmp = a * ((b * i) - (x * t))
    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 ((c <= -2.4e+153) || !(c <= 3.1e+60)) {
		tmp = c * ((t * j) - (z * b));
	} else {
		tmp = a * ((b * i) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -2.4e+153) or not (c <= 3.1e+60):
		tmp = c * ((t * j) - (z * b))
	else:
		tmp = a * ((b * i) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -2.4e+153) || !(c <= 3.1e+60))
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	else
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -2.4e+153) || ~((c <= 3.1e+60)))
		tmp = c * ((t * j) - (z * b));
	else
		tmp = a * ((b * i) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -2.4e+153], N[Not[LessEqual[c, 3.1e+60]], $MachinePrecision]], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -2.39999999999999992e153 or 3.1000000000000001e60 < c

   1. Initial program 62.5%

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

   3. Taylor expanded in c around inf 67.2%

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

      1. *-commutative 67.2%

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

      2. *-commutative 67.2%

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

   5. Simplified 67.2%

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

   if -2.39999999999999992e153 < c < 3.1000000000000001e60

   1. Initial program 77.0%

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

      1. add-cube-cbrt 76.8%

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

      2. pow3 76.8%

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

      3. *-commutative 76.8%

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

      4. *-commutative 76.8%

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

   4. Applied egg-rr 76.8%

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

   5. Taylor expanded in a around inf 48.2%

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

      1. associate-*r* 48.2%

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

      2. neg-mul-1 48.2%

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

      3. cancel-sign-sub 48.2%

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

      4. +-commutative 48.2%

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

      5. *-commutative 48.2%

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

      6. mul-1-neg 48.2%

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

      7. unsub-neg 48.2%

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

   7. Simplified 48.2%

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

4. Final simplification 53.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -2.4 \cdot 10^{+153} \lor \neg \left(c \leq 3.1 \cdot 10^{+60}\right):\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 42.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -4.6e+116)
   (* t (* c j))
   (if (<= c 1.8e+128) (* a (- (* b i) (* x t))) (* z (* b (- c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -4.6e+116) {
		tmp = t * (c * j);
	} else if (c <= 1.8e+128) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-4.6d+116)) then
        tmp = t * (c * j)
    else if (c <= 1.8d+128) then
        tmp = a * ((b * i) - (x * t))
    else
        tmp = z * (b * -c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -4.6e+116) {
		tmp = t * (c * j);
	} else if (c <= 1.8e+128) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = z * (b * -c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -4.6e+116:
		tmp = t * (c * j)
	elif c <= 1.8e+128:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = z * (b * -c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -4.6e+116)
		tmp = Float64(t * Float64(c * j));
	elseif (c <= 1.8e+128)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = Float64(z * Float64(b * Float64(-c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -4.6e+116)
		tmp = t * (c * j);
	elseif (c <= 1.8e+128)
		tmp = a * ((b * i) - (x * t));
	else
		tmp = z * (b * -c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -4.6e+116], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.8e+128], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.5999999999999999e116

   1. Initial program 61.7%

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

   3. Taylor expanded in t around inf 54.3%

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

      1. +-commutative 54.3%

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

      2. mul-1-neg 54.3%

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

      3. unsub-neg 54.3%

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

      4. *-commutative 54.3%

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

   5. Simplified 54.3%

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

   6. Taylor expanded in c around inf 54.3%

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

      1. *-commutative 54.3%

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

   8. Simplified 54.3%

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

   if -4.5999999999999999e116 < c < 1.80000000000000014e128

   1. Initial program 78.0%

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

      1. add-cube-cbrt 77.8%

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

      2. pow3 77.8%

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

      3. *-commutative 77.8%

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

      4. *-commutative 77.8%

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

   4. Applied egg-rr 77.8%

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

   5. Taylor expanded in a around inf 46.9%

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

      1. associate-*r* 46.9%

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

      2. neg-mul-1 46.9%

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

      3. cancel-sign-sub 46.9%

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

      4. +-commutative 46.9%

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

      5. *-commutative 46.9%

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

      6. mul-1-neg 46.9%

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

      7. unsub-neg 46.9%

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

   7. Simplified 46.9%

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

   if 1.80000000000000014e128 < c

   1. Initial program 57.4%

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

   3. Taylor expanded in b around inf 42.8%

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

      1. *-commutative 42.8%

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

   5. Simplified 42.8%

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

   6. Taylor expanded in a around 0 42.9%

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

      1. mul-1-neg 42.9%

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

      2. *-commutative 42.9%

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

      3. distribute-rgt-neg-in 42.9%

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

   8. Simplified 42.9%

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

   9. Taylor expanded in c around 0 42.9%

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

       1. mul-1-neg 42.9%

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

       2. associate-*r* 50.3%

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

       3. distribute-lft-neg-in 50.3%

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

       4. *-commutative 50.3%

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

       5. distribute-rgt-neg-in 50.3%

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

   11. Simplified 50.3%

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

4. Final simplification 48.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+116}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;c \leq 1.8 \cdot 10^{+128}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -1.18 \cdot 10^{-11} \lor \neg \left(c \leq 6.8 \cdot 10^{+73}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -1.18e-11) (not (<= c 6.8e+73))) (* c (* t j)) (* b (* a 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 ((c <= -1.18e-11) || !(c <= 6.8e+73)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * 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 ((c <= (-1.18d-11)) .or. (.not. (c <= 6.8d+73))) then
        tmp = c * (t * j)
    else
        tmp = b * (a * 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 ((c <= -1.18e-11) || !(c <= 6.8e+73)) {
		tmp = c * (t * j);
	} else {
		tmp = b * (a * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -1.18e-11) or not (c <= 6.8e+73):
		tmp = c * (t * j)
	else:
		tmp = b * (a * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -1.18e-11) || !(c <= 6.8e+73))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(b * Float64(a * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -1.18e-11) || ~((c <= 6.8e+73)))
		tmp = c * (t * j);
	else
		tmp = b * (a * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -1.18e-11], N[Not[LessEqual[c, 6.8e+73]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -1.18e-11 or 6.8000000000000003e73 < c

   1. Initial program 66.0%

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

   3. Taylor expanded in t around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in x around inf 51.5%

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

   7. Taylor expanded in c around inf 39.4%

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

   8. Taylor expanded in t around 0 39.4%

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

   if -1.18e-11 < c < 6.8000000000000003e73

   1. Initial program 78.0%

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

   3. Taylor expanded in b around inf 37.0%

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

      1. *-commutative 37.0%

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

   5. Simplified 37.0%

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

   6. Taylor expanded in a around inf 32.7%

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

      1. *-commutative 32.7%

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

   8. Simplified 32.7%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -1.18 \cdot 10^{-11} \lor \neg \left(c \leq 6.8 \cdot 10^{+73}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= c -4.2e-11)
   (* c (* t j))
   (if (<= c 7.6e+67) (* b (* a i)) (* t (* c j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -4.2e-11) {
		tmp = c * (t * j);
	} else if (c <= 7.6e+67) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (c <= (-4.2d-11)) then
        tmp = c * (t * j)
    else if (c <= 7.6d+67) then
        tmp = b * (a * i)
    else
        tmp = t * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (c <= -4.2e-11) {
		tmp = c * (t * j);
	} else if (c <= 7.6e+67) {
		tmp = b * (a * i);
	} else {
		tmp = t * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if c <= -4.2e-11:
		tmp = c * (t * j)
	elif c <= 7.6e+67:
		tmp = b * (a * i)
	else:
		tmp = t * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (c <= -4.2e-11)
		tmp = Float64(c * Float64(t * j));
	elseif (c <= 7.6e+67)
		tmp = Float64(b * Float64(a * i));
	else
		tmp = Float64(t * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (c <= -4.2e-11)
		tmp = c * (t * j);
	elseif (c <= 7.6e+67)
		tmp = b * (a * i);
	else
		tmp = t * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[c, -4.2e-11], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 7.6e+67], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if c < -4.1999999999999997e-11

   1. Initial program 66.8%

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

   3. Taylor expanded in t around inf 51.6%

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

      1. +-commutative 51.6%

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

      2. mul-1-neg 51.6%

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

      3. unsub-neg 51.6%

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

      4. *-commutative 51.6%

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

   5. Simplified 51.6%

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

   6. Taylor expanded in x around inf 53.2%

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

   7. Taylor expanded in c around inf 39.1%

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

   8. Taylor expanded in t around 0 40.5%

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

   if -4.1999999999999997e-11 < c < 7.60000000000000041e67

   1. Initial program 78.0%

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

   3. Taylor expanded in b around inf 37.0%

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

      1. *-commutative 37.0%

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

   5. Simplified 37.0%

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

   6. Taylor expanded in a around inf 32.7%

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

      1. *-commutative 32.7%

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

   8. Simplified 32.7%

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

   if 7.60000000000000041e67 < c

   1. Initial program 65.0%

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

   3. Taylor expanded in t around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

      4. *-commutative 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in c around inf 39.7%

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

      1. *-commutative 39.7%

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

   8. Simplified 39.7%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.2 \cdot 10^{-11}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;c \leq 7.6 \cdot 10^{+67}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 22.4% 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 72.7%

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

3. Taylor expanded in b around inf 33.8%

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

   1. *-commutative 33.8%

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

5. Simplified 33.8%

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

6. Taylor expanded in a around inf 24.0%

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

Developer Target 1: 69.2% 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 2024144 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< t -1015122364899489/125000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -942510763643697/2000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -238547917063487/3125000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 10535888557455487/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* 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)))))