Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.4% → 82.0%

Time: 20.7s

Alternatives: 22

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: 73.4% 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: 82.0% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (j * ((t * c) - (y * i))) + ((x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c))));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = c * ((t * j) - (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in c around inf 57.4%

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

4. Final simplification 86.3%

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

Alternative 2: 49.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ t_2 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_3 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{+208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-200}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-277}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-107}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a))))
        (t_2 (* c (- (* t j) (* z b))))
        (t_3 (* a (- (* b i) (* x t)))))
   (if (<= a -7e+208)
     t_3
     (if (<= a -2.2e+123)
       (* x (- (* y z) (* t a)))
       (if (<= a -5.4e+40)
         t_1
         (if (<= a -2.2e-132)
           (* b (- (* a i) (* z c)))
           (if (<= a -1.25e-200)
             t_1
             (if (<= a -1.2e-277)
               t_2
               (if (<= a 1.85e-249)
                 (* y (- (* x z) (* i j)))
                 (if (<= a 5e-107)
                   t_2
                   (if (<= a 1.9e+99) (* z (- (* x y) (* b c))) t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7e+208) {
		tmp = t_3;
	} else if (a <= -2.2e+123) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -5.4e+40) {
		tmp = t_1;
	} else if (a <= -2.2e-132) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= -1.25e-200) {
		tmp = t_1;
	} else if (a <= -1.2e-277) {
		tmp = t_2;
	} else if (a <= 1.85e-249) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 5e-107) {
		tmp = t_2;
	} else if (a <= 1.9e+99) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    t_2 = c * ((t * j) - (z * b))
    t_3 = a * ((b * i) - (x * t))
    if (a <= (-7d+208)) then
        tmp = t_3
    else if (a <= (-2.2d+123)) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= (-5.4d+40)) then
        tmp = t_1
    else if (a <= (-2.2d-132)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= (-1.25d-200)) then
        tmp = t_1
    else if (a <= (-1.2d-277)) then
        tmp = t_2
    else if (a <= 1.85d-249) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 5d-107) then
        tmp = t_2
    else if (a <= 1.9d+99) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double t_2 = c * ((t * j) - (z * b));
	double t_3 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7e+208) {
		tmp = t_3;
	} else if (a <= -2.2e+123) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -5.4e+40) {
		tmp = t_1;
	} else if (a <= -2.2e-132) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= -1.25e-200) {
		tmp = t_1;
	} else if (a <= -1.2e-277) {
		tmp = t_2;
	} else if (a <= 1.85e-249) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 5e-107) {
		tmp = t_2;
	} else if (a <= 1.9e+99) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	t_2 = c * ((t * j) - (z * b))
	t_3 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -7e+208:
		tmp = t_3
	elif a <= -2.2e+123:
		tmp = x * ((y * z) - (t * a))
	elif a <= -5.4e+40:
		tmp = t_1
	elif a <= -2.2e-132:
		tmp = b * ((a * i) - (z * c))
	elif a <= -1.25e-200:
		tmp = t_1
	elif a <= -1.2e-277:
		tmp = t_2
	elif a <= 1.85e-249:
		tmp = y * ((x * z) - (i * j))
	elif a <= 5e-107:
		tmp = t_2
	elif a <= 1.9e+99:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	t_2 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_3 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7e+208)
		tmp = t_3;
	elseif (a <= -2.2e+123)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= -5.4e+40)
		tmp = t_1;
	elseif (a <= -2.2e-132)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= -1.25e-200)
		tmp = t_1;
	elseif (a <= -1.2e-277)
		tmp = t_2;
	elseif (a <= 1.85e-249)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 5e-107)
		tmp = t_2;
	elseif (a <= 1.9e+99)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	t_2 = c * ((t * j) - (z * b));
	t_3 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -7e+208)
		tmp = t_3;
	elseif (a <= -2.2e+123)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= -5.4e+40)
		tmp = t_1;
	elseif (a <= -2.2e-132)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= -1.25e-200)
		tmp = t_1;
	elseif (a <= -1.2e-277)
		tmp = t_2;
	elseif (a <= 1.85e-249)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 5e-107)
		tmp = t_2;
	elseif (a <= 1.9e+99)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e+208], t$95$3, If[LessEqual[a, -2.2e+123], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.4e+40], t$95$1, If[LessEqual[a, -2.2e-132], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.25e-200], t$95$1, If[LessEqual[a, -1.2e-277], t$95$2, If[LessEqual[a, 1.85e-249], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5e-107], t$95$2, If[LessEqual[a, 1.9e+99], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if a < -7.00000000000000033e208 or 1.9e99 < a

   1. Initial program 75.5%

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

   3. Taylor expanded in a around inf 77.2%

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

      1. distribute-lft-out-- 77.2%

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

   5. Simplified 77.2%

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

   if -7.00000000000000033e208 < a < -2.19999999999999992e123

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -2.19999999999999992e123 < a < -5.40000000000000019e40 or -2.19999999999999991e-132 < a < -1.24999999999999998e-200

   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 t around inf 64.0%

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

      1. +-commutative 64.0%

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

      2. mul-1-neg 64.0%

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

      3. unsub-neg 64.0%

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

   5. Simplified 64.0%

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

   if -5.40000000000000019e40 < a < -2.19999999999999991e-132

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 67.4%

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

   if -1.24999999999999998e-200 < a < -1.2e-277 or 1.84999999999999988e-249 < a < 4.99999999999999971e-107

   1. Initial program 75.1%

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

   3. Taylor expanded in c around inf 73.5%

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

   if -1.2e-277 < a < 1.84999999999999988e-249

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if 4.99999999999999971e-107 < a < 1.9e99

   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 z around inf 58.7%

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

      1. *-commutative 58.7%

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

   5. Simplified 58.7%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{+123}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -5.4 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq -2.2 \cdot 10^{-132}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-200}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-277}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{-249}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-107}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 48.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(t \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{+208}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(y \cdot \left(c \cdot \frac{t}{y} - i\right)\right)\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-200}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-278}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* t j) (* z b)))) (t_2 (* a (- (* b i) (* x t)))))
   (if (<= a -7e+208)
     t_2
     (if (<= a -5e+124)
       (* x (- (* y z) (* t a)))
       (if (<= a -1e+38)
         (* j (* y (- (* c (/ t y)) i)))
         (if (<= a -8.6e-122)
           (* b (- (* a i) (* z c)))
           (if (<= a -1.6e-200)
             (* t (- (* c j) (* x a)))
             (if (<= a -5.3e-278)
               t_1
               (if (<= a 1.05e-254)
                 (* y (- (* x z) (* i j)))
                 (if (<= a 3.4e-112)
                   t_1
                   (if (<= a 7.5e+101) (* z (- (* x y) (* b c))) 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 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7e+208) {
		tmp = t_2;
	} else if (a <= -5e+124) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -1e+38) {
		tmp = j * (y * ((c * (t / y)) - i));
	} else if (a <= -8.6e-122) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= -1.6e-200) {
		tmp = t * ((c * j) - (x * a));
	} else if (a <= -5.3e-278) {
		tmp = t_1;
	} else if (a <= 1.05e-254) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 3.4e-112) {
		tmp = t_1;
	} else if (a <= 7.5e+101) {
		tmp = z * ((x * y) - (b * c));
	} 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 = c * ((t * j) - (z * b))
    t_2 = a * ((b * i) - (x * t))
    if (a <= (-7d+208)) then
        tmp = t_2
    else if (a <= (-5d+124)) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= (-1d+38)) then
        tmp = j * (y * ((c * (t / y)) - i))
    else if (a <= (-8.6d-122)) then
        tmp = b * ((a * i) - (z * c))
    else if (a <= (-1.6d-200)) then
        tmp = t * ((c * j) - (x * a))
    else if (a <= (-5.3d-278)) then
        tmp = t_1
    else if (a <= 1.05d-254) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 3.4d-112) then
        tmp = t_1
    else if (a <= 7.5d+101) then
        tmp = z * ((x * y) - (b * c))
    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 = c * ((t * j) - (z * b));
	double t_2 = a * ((b * i) - (x * t));
	double tmp;
	if (a <= -7e+208) {
		tmp = t_2;
	} else if (a <= -5e+124) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -1e+38) {
		tmp = j * (y * ((c * (t / y)) - i));
	} else if (a <= -8.6e-122) {
		tmp = b * ((a * i) - (z * c));
	} else if (a <= -1.6e-200) {
		tmp = t * ((c * j) - (x * a));
	} else if (a <= -5.3e-278) {
		tmp = t_1;
	} else if (a <= 1.05e-254) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 3.4e-112) {
		tmp = t_1;
	} else if (a <= 7.5e+101) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((t * j) - (z * b))
	t_2 = a * ((b * i) - (x * t))
	tmp = 0
	if a <= -7e+208:
		tmp = t_2
	elif a <= -5e+124:
		tmp = x * ((y * z) - (t * a))
	elif a <= -1e+38:
		tmp = j * (y * ((c * (t / y)) - i))
	elif a <= -8.6e-122:
		tmp = b * ((a * i) - (z * c))
	elif a <= -1.6e-200:
		tmp = t * ((c * j) - (x * a))
	elif a <= -5.3e-278:
		tmp = t_1
	elif a <= 1.05e-254:
		tmp = y * ((x * z) - (i * j))
	elif a <= 3.4e-112:
		tmp = t_1
	elif a <= 7.5e+101:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(t * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(b * i) - Float64(x * t)))
	tmp = 0.0
	if (a <= -7e+208)
		tmp = t_2;
	elseif (a <= -5e+124)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= -1e+38)
		tmp = Float64(j * Float64(y * Float64(Float64(c * Float64(t / y)) - i)));
	elseif (a <= -8.6e-122)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (a <= -1.6e-200)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (a <= -5.3e-278)
		tmp = t_1;
	elseif (a <= 1.05e-254)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 3.4e-112)
		tmp = t_1;
	elseif (a <= 7.5e+101)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((t * j) - (z * b));
	t_2 = a * ((b * i) - (x * t));
	tmp = 0.0;
	if (a <= -7e+208)
		tmp = t_2;
	elseif (a <= -5e+124)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= -1e+38)
		tmp = j * (y * ((c * (t / y)) - i));
	elseif (a <= -8.6e-122)
		tmp = b * ((a * i) - (z * c));
	elseif (a <= -1.6e-200)
		tmp = t * ((c * j) - (x * a));
	elseif (a <= -5.3e-278)
		tmp = t_1;
	elseif (a <= 1.05e-254)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 3.4e-112)
		tmp = t_1;
	elseif (a <= 7.5e+101)
		tmp = z * ((x * y) - (b * c));
	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[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -7e+208], t$95$2, If[LessEqual[a, -5e+124], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1e+38], N[(j * N[(y * N[(N[(c * N[(t / y), $MachinePrecision]), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -8.6e-122], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.6e-200], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.3e-278], t$95$1, If[LessEqual[a, 1.05e-254], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.4e-112], t$95$1, If[LessEqual[a, 7.5e+101], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if a < -7.00000000000000033e208 or 7.4999999999999995e101 < a

   1. Initial program 75.5%

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

   3. Taylor expanded in a around inf 77.2%

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

      1. distribute-lft-out-- 77.2%

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

   5. Simplified 77.2%

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

   if -7.00000000000000033e208 < a < -4.9999999999999996e124

   1. Initial program 87.4%

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

   3. Taylor expanded in x around inf 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -4.9999999999999996e124 < a < -9.99999999999999977e37

   1. Initial program 71.1%

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

      1. *-commutative 71.1%

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

      2. *-commutative 71.1%

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

      3. add-cube-cbrt 71.0%

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

      4. pow3 70.9%

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

      5. *-commutative 70.9%

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

      6. *-commutative 70.9%

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

   4. Applied egg-rr 70.9%

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

   5. Taylor expanded in j around inf 51.4%

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

   6. Taylor expanded in y around inf 58.4%

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

      1. associate-/l* 58.4%

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

   8. Simplified 58.4%

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

   if -9.99999999999999977e37 < a < -8.60000000000000037e-122

   1. Initial program 83.1%

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

   3. Taylor expanded in b around inf 67.4%

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

   if -8.60000000000000037e-122 < a < -1.59999999999999991e-200

   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 t around inf 77.2%

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

      1. +-commutative 77.2%

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

      2. mul-1-neg 77.2%

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

      3. unsub-neg 77.2%

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

   5. Simplified 77.2%

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

   if -1.59999999999999991e-200 < a < -5.3e-278 or 1.04999999999999998e-254 < a < 3.3999999999999998e-112

   1. Initial program 75.1%

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

   3. Taylor expanded in c around inf 73.5%

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

   if -5.3e-278 < a < 1.04999999999999998e-254

   1. Initial program 76.2%

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

   3. Taylor expanded in y around inf 59.9%

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

      1. +-commutative 59.9%

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

      2. mul-1-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. *-commutative 59.9%

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

   5. Simplified 59.9%

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

   if 3.3999999999999998e-112 < a < 7.4999999999999995e101

   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 z around inf 58.7%

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

      1. *-commutative 58.7%

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

   5. Simplified 58.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - b \cdot c\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{+124}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -1 \cdot 10^{+38}:\\ \;\;\;\;j \cdot \left(y \cdot \left(c \cdot \frac{t}{y} - i\right)\right)\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-122}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{-200}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;a \leq -5.3 \cdot 10^{-278}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{-254}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{-112}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 28.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot c\right) \cdot \left(-b\right)\\ t_2 := b \cdot \left(a \cdot i\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+28}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-287}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+243}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* (* z c) (- b))) (t_2 (* b (* a i))))
   (if (<= t -2.5e+28)
     (* j (* t c))
     (if (<= t -1.35e-30)
       t_1
       (if (<= t -1.95e-221)
         t_2
         (if (<= t -5.6e-279)
           (* y (* x z))
           (if (<= t 1.3e-287)
             t_2
             (if (<= t 1.4e-96)
               t_1
               (if (<= t 5.5e+35)
                 (* i (* a b))
                 (if (<= t 1.05e+175)
                   t_1
                   (if (<= t 3.2e+243)
                     (* a (* x (- t)))
                     (* x (* t (- 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 = (z * c) * -b;
	double t_2 = b * (a * i);
	double tmp;
	if (t <= -2.5e+28) {
		tmp = j * (t * c);
	} else if (t <= -1.35e-30) {
		tmp = t_1;
	} else if (t <= -1.95e-221) {
		tmp = t_2;
	} else if (t <= -5.6e-279) {
		tmp = y * (x * z);
	} else if (t <= 1.3e-287) {
		tmp = t_2;
	} else if (t <= 1.4e-96) {
		tmp = t_1;
	} else if (t <= 5.5e+35) {
		tmp = i * (a * b);
	} else if (t <= 1.05e+175) {
		tmp = t_1;
	} else if (t <= 3.2e+243) {
		tmp = a * (x * -t);
	} else {
		tmp = x * (t * -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) :: t_2
    real(8) :: tmp
    t_1 = (z * c) * -b
    t_2 = b * (a * i)
    if (t <= (-2.5d+28)) then
        tmp = j * (t * c)
    else if (t <= (-1.35d-30)) then
        tmp = t_1
    else if (t <= (-1.95d-221)) then
        tmp = t_2
    else if (t <= (-5.6d-279)) then
        tmp = y * (x * z)
    else if (t <= 1.3d-287) then
        tmp = t_2
    else if (t <= 1.4d-96) then
        tmp = t_1
    else if (t <= 5.5d+35) then
        tmp = i * (a * b)
    else if (t <= 1.05d+175) then
        tmp = t_1
    else if (t <= 3.2d+243) then
        tmp = a * (x * -t)
    else
        tmp = x * (t * -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 = (z * c) * -b;
	double t_2 = b * (a * i);
	double tmp;
	if (t <= -2.5e+28) {
		tmp = j * (t * c);
	} else if (t <= -1.35e-30) {
		tmp = t_1;
	} else if (t <= -1.95e-221) {
		tmp = t_2;
	} else if (t <= -5.6e-279) {
		tmp = y * (x * z);
	} else if (t <= 1.3e-287) {
		tmp = t_2;
	} else if (t <= 1.4e-96) {
		tmp = t_1;
	} else if (t <= 5.5e+35) {
		tmp = i * (a * b);
	} else if (t <= 1.05e+175) {
		tmp = t_1;
	} else if (t <= 3.2e+243) {
		tmp = a * (x * -t);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * c) * -b
	t_2 = b * (a * i)
	tmp = 0
	if t <= -2.5e+28:
		tmp = j * (t * c)
	elif t <= -1.35e-30:
		tmp = t_1
	elif t <= -1.95e-221:
		tmp = t_2
	elif t <= -5.6e-279:
		tmp = y * (x * z)
	elif t <= 1.3e-287:
		tmp = t_2
	elif t <= 1.4e-96:
		tmp = t_1
	elif t <= 5.5e+35:
		tmp = i * (a * b)
	elif t <= 1.05e+175:
		tmp = t_1
	elif t <= 3.2e+243:
		tmp = a * (x * -t)
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * c) * Float64(-b))
	t_2 = Float64(b * Float64(a * i))
	tmp = 0.0
	if (t <= -2.5e+28)
		tmp = Float64(j * Float64(t * c));
	elseif (t <= -1.35e-30)
		tmp = t_1;
	elseif (t <= -1.95e-221)
		tmp = t_2;
	elseif (t <= -5.6e-279)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 1.3e-287)
		tmp = t_2;
	elseif (t <= 1.4e-96)
		tmp = t_1;
	elseif (t <= 5.5e+35)
		tmp = Float64(i * Float64(a * b));
	elseif (t <= 1.05e+175)
		tmp = t_1;
	elseif (t <= 3.2e+243)
		tmp = Float64(a * Float64(x * Float64(-t)));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * c) * -b;
	t_2 = b * (a * i);
	tmp = 0.0;
	if (t <= -2.5e+28)
		tmp = j * (t * c);
	elseif (t <= -1.35e-30)
		tmp = t_1;
	elseif (t <= -1.95e-221)
		tmp = t_2;
	elseif (t <= -5.6e-279)
		tmp = y * (x * z);
	elseif (t <= 1.3e-287)
		tmp = t_2;
	elseif (t <= 1.4e-96)
		tmp = t_1;
	elseif (t <= 5.5e+35)
		tmp = i * (a * b);
	elseif (t <= 1.05e+175)
		tmp = t_1;
	elseif (t <= 3.2e+243)
		tmp = a * (x * -t);
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+28], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e-30], t$95$1, If[LessEqual[t, -1.95e-221], t$95$2, If[LessEqual[t, -5.6e-279], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.3e-287], t$95$2, If[LessEqual[t, 1.4e-96], t$95$1, If[LessEqual[t, 5.5e+35], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+175], t$95$1, If[LessEqual[t, 3.2e+243], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -2.49999999999999979e28

   1. Initial program 76.5%

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

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. add-cube-cbrt 76.2%

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

      4. pow3 76.3%

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

      5. *-commutative 76.3%

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

      6. *-commutative 76.3%

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

   4. Applied egg-rr 76.3%

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

   5. Taylor expanded in j around inf 53.7%

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

   6. Taylor expanded in c around inf 39.8%

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

      1. *-commutative 39.8%

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

      2. associate-*l* 45.9%

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

      3. *-commutative 45.9%

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

   8. Simplified 45.9%

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

   if -2.49999999999999979e28 < t < -1.34999999999999994e-30 or 1.3e-287 < t < 1.40000000000000008e-96 or 5.50000000000000001e35 < t < 1.05e175

   1. Initial program 79.8%

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

   3. Taylor expanded in b around inf 53.4%

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

   4. Taylor expanded in a around 0 39.0%

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

      1. mul-1-neg 39.0%

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

      2. *-commutative 39.0%

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

      3. distribute-rgt-neg-in 39.0%

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

   6. Simplified 39.0%

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

   if -1.34999999999999994e-30 < t < -1.9499999999999999e-221 or -5.6000000000000002e-279 < t < 1.3e-287

   1. Initial program 79.2%

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

   3. Taylor expanded in b around inf 57.5%

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

   4. Taylor expanded in a around inf 44.7%

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

      1. *-commutative 44.7%

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

   6. Simplified 44.7%

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

   if -1.9499999999999999e-221 < t < -5.6000000000000002e-279

   1. Initial program 91.2%

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

   3. Taylor expanded in y around inf 51.0%

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

      1. +-commutative 51.0%

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

      2. mul-1-neg 51.0%

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

      3. unsub-neg 51.0%

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

      4. *-commutative 51.0%

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

   5. Simplified 51.0%

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

   6. Taylor expanded in z around inf 51.4%

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

      1. *-commutative 51.4%

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

   8. Simplified 51.4%

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

   if 1.40000000000000008e-96 < t < 5.50000000000000001e35

   1. Initial program 77.1%

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

   3. Taylor expanded in b around inf 56.5%

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

   4. Taylor expanded in a around inf 38.1%

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

      1. associate-*r* 42.4%

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

      2. *-commutative 42.4%

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

      3. *-commutative 42.4%

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

   6. Simplified 42.4%

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

   if 1.05e175 < t < 3.20000000000000016e243

   1. Initial program 58.7%

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

   3. Taylor expanded in x around inf 53.9%

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

      1. *-commutative 53.9%

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

   5. Simplified 53.9%

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

   6. Taylor expanded in z around 0 54.1%

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

      1. associate-*r* 54.1%

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

      2. neg-mul-1 54.1%

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

      3. *-commutative 54.1%

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

   8. Simplified 54.1%

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

   if 3.20000000000000016e243 < t

   1. Initial program 89.6%

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

   3. Taylor expanded in x around inf 68.6%

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

      1. *-commutative 68.6%

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

   5. Simplified 68.6%

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

   6. Taylor expanded in z around 0 67.9%

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

      1. mul-1-neg 67.9%

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

      2. distribute-rgt-neg-out 67.9%

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

   8. Simplified 67.9%

      \[\leadsto x \cdot \color{blue}{\left(a \cdot \left(-t\right)\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+28}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-30}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{-221}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-279}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-287}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-96}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{+35}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+175}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+243}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-97}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+198}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* z (* x y)) (* b (- (* a i) (* z c)))))
        (t_2 (+ (* j (- (* t c) (* y i))) (* x (- (* y z) (* t a))))))
   (if (<= b -6.8e-38)
     t_1
     (if (<= b -8.5e-97)
       t_2
       (if (<= b -4.2e-150)
         t_1
         (if (<= b 1.02e-85)
           t_2
           (if (<= b 2e-71)
             (* c (- (* t j) (* z b)))
             (if (<= b 1.5e+198) t_2 t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * (x * y)) + (b * ((a * i) - (z * c)));
	double t_2 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double tmp;
	if (b <= -6.8e-38) {
		tmp = t_1;
	} else if (b <= -8.5e-97) {
		tmp = t_2;
	} else if (b <= -4.2e-150) {
		tmp = t_1;
	} else if (b <= 1.02e-85) {
		tmp = t_2;
	} else if (b <= 2e-71) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.5e+198) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * (x * y)) + (b * ((a * i) - (z * c)))
    t_2 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
    if (b <= (-6.8d-38)) then
        tmp = t_1
    else if (b <= (-8.5d-97)) then
        tmp = t_2
    else if (b <= (-4.2d-150)) then
        tmp = t_1
    else if (b <= 1.02d-85) then
        tmp = t_2
    else if (b <= 2d-71) then
        tmp = c * ((t * j) - (z * b))
    else if (b <= 1.5d+198) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (z * (x * y)) + (b * ((a * i) - (z * c)));
	double t_2 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	double tmp;
	if (b <= -6.8e-38) {
		tmp = t_1;
	} else if (b <= -8.5e-97) {
		tmp = t_2;
	} else if (b <= -4.2e-150) {
		tmp = t_1;
	} else if (b <= 1.02e-85) {
		tmp = t_2;
	} else if (b <= 2e-71) {
		tmp = c * ((t * j) - (z * b));
	} else if (b <= 1.5e+198) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (z * (x * y)) + (b * ((a * i) - (z * c)))
	t_2 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)))
	tmp = 0
	if b <= -6.8e-38:
		tmp = t_1
	elif b <= -8.5e-97:
		tmp = t_2
	elif b <= -4.2e-150:
		tmp = t_1
	elif b <= 1.02e-85:
		tmp = t_2
	elif b <= 2e-71:
		tmp = c * ((t * j) - (z * b))
	elif b <= 1.5e+198:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))))
	t_2 = Float64(Float64(j * Float64(Float64(t * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))))
	tmp = 0.0
	if (b <= -6.8e-38)
		tmp = t_1;
	elseif (b <= -8.5e-97)
		tmp = t_2;
	elseif (b <= -4.2e-150)
		tmp = t_1;
	elseif (b <= 1.02e-85)
		tmp = t_2;
	elseif (b <= 2e-71)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (b <= 1.5e+198)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (z * (x * y)) + (b * ((a * i) - (z * c)));
	t_2 = (j * ((t * c) - (y * i))) + (x * ((y * z) - (t * a)));
	tmp = 0.0;
	if (b <= -6.8e-38)
		tmp = t_1;
	elseif (b <= -8.5e-97)
		tmp = t_2;
	elseif (b <= -4.2e-150)
		tmp = t_1;
	elseif (b <= 1.02e-85)
		tmp = t_2;
	elseif (b <= 2e-71)
		tmp = c * ((t * j) - (z * b));
	elseif (b <= 1.5e+198)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6.8e-38], t$95$1, If[LessEqual[b, -8.5e-97], t$95$2, If[LessEqual[b, -4.2e-150], t$95$1, If[LessEqual[b, 1.02e-85], t$95$2, If[LessEqual[b, 2e-71], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e+198], t$95$2, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -6.8000000000000004e-38 or -8.5000000000000002e-97 < b < -4.2000000000000002e-150 or 1.50000000000000009e198 < b

   1. Initial program 75.5%

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

   3. Taylor expanded in j around 0 76.5%

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

      1. *-commutative 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in z around inf 71.5%

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

      1. associate-*r* 72.4%

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

      2. *-commutative 72.4%

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

   8. Simplified 72.4%

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

   if -6.8000000000000004e-38 < b < -8.5000000000000002e-97 or -4.2000000000000002e-150 < b < 1.02000000000000001e-85 or 1.9999999999999998e-71 < b < 1.50000000000000009e198

   1. Initial program 80.2%

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

   3. Taylor expanded in b around 0 76.2%

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

   if 1.02000000000000001e-85 < b < 1.9999999999999998e-71

   1. Initial program 75.4%

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

   3. Taylor expanded in c around inf 99.6%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-38}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -8.5 \cdot 10^{-97}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-150}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.02 \cdot 10^{-85}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-71}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{+198}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + t\_1\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_4 := t\_3 + t\_1\\ \mathbf{if}\;j \leq -8.5 \cdot 10^{-33}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+163}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+169}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (+ (* x (- (* y z) (* t a))) t_1))
        (t_3 (* j (- (* t c) (* y i))))
        (t_4 (+ t_3 t_1)))
   (if (<= j -8.5e-33)
     t_4
     (if (<= j 3.7e+121)
       t_2
       (if (<= j 5e+163) t_4 (if (<= j 3.8e+169) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = t_3 + t_1;
	double tmp;
	if (j <= -8.5e-33) {
		tmp = t_4;
	} else if (j <= 3.7e+121) {
		tmp = t_2;
	} else if (j <= 5e+163) {
		tmp = t_4;
	} else if (j <= 3.8e+169) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = (x * ((y * z) - (t * a))) + t_1
    t_3 = j * ((t * c) - (y * i))
    t_4 = t_3 + t_1
    if (j <= (-8.5d-33)) then
        tmp = t_4
    else if (j <= 3.7d+121) then
        tmp = t_2
    else if (j <= 5d+163) then
        tmp = t_4
    else if (j <= 3.8d+169) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = (x * ((y * z) - (t * a))) + t_1;
	double t_3 = j * ((t * c) - (y * i));
	double t_4 = t_3 + t_1;
	double tmp;
	if (j <= -8.5e-33) {
		tmp = t_4;
	} else if (j <= 3.7e+121) {
		tmp = t_2;
	} else if (j <= 5e+163) {
		tmp = t_4;
	} else if (j <= 3.8e+169) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = (x * ((y * z) - (t * a))) + t_1
	t_3 = j * ((t * c) - (y * i))
	t_4 = t_3 + t_1
	tmp = 0
	if j <= -8.5e-33:
		tmp = t_4
	elif j <= 3.7e+121:
		tmp = t_2
	elif j <= 5e+163:
		tmp = t_4
	elif j <= 3.8e+169:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + t_1)
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_4 = Float64(t_3 + t_1)
	tmp = 0.0
	if (j <= -8.5e-33)
		tmp = t_4;
	elseif (j <= 3.7e+121)
		tmp = t_2;
	elseif (j <= 5e+163)
		tmp = t_4;
	elseif (j <= 3.8e+169)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = (x * ((y * z) - (t * a))) + t_1;
	t_3 = j * ((t * c) - (y * i));
	t_4 = t_3 + t_1;
	tmp = 0.0;
	if (j <= -8.5e-33)
		tmp = t_4;
	elseif (j <= 3.7e+121)
		tmp = t_2;
	elseif (j <= 5e+163)
		tmp = t_4;
	elseif (j <= 3.8e+169)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 + t$95$1), $MachinePrecision]}, If[LessEqual[j, -8.5e-33], t$95$4, If[LessEqual[j, 3.7e+121], t$95$2, If[LessEqual[j, 5e+163], t$95$4, If[LessEqual[j, 3.8e+169], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -8.49999999999999945e-33 or 3.70000000000000013e121 < j < 5e163

   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 x around 0 76.3%

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

   if -8.49999999999999945e-33 < j < 3.70000000000000013e121 or 5e163 < j < 3.79999999999999992e169

   1. Initial program 78.5%

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

   3. Taylor expanded in j around 0 77.2%

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

      1. *-commutative 77.2%

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

   5. Simplified 77.2%

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

   if 3.79999999999999992e169 < j

   1. Initial program 62.8%

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

      1. *-commutative 62.8%

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

      2. *-commutative 62.8%

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

      3. add-cube-cbrt 62.6%

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

      4. pow3 62.8%

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

      5. *-commutative 62.8%

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

      6. *-commutative 62.8%

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

   4. Applied egg-rr 62.8%

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

   5. Taylor expanded in j around inf 74.9%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{-33}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.7 \cdot 10^{+121}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+163}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{+169}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ t_3 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;j \leq -5.6 \cdot 10^{+112}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{c \cdot \left(t \cdot j - z \cdot b\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-66}:\\ \;\;\;\;t\_2 + t\_3\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+133}:\\ \;\;\;\;t\_3 + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c))))
        (t_2 (* j (- (* t c) (* y i))))
        (t_3 (* x (- (* y z) (* t a)))))
   (if (<= j -5.6e+112)
     (+ t_2 t_1)
     (if (<= j -1.65e-5)
       (* y (+ (* x z) (- (/ (* c (- (* t j) (* z b))) y) (* i j))))
       (if (<= j -8.5e-66)
         (+ t_2 t_3)
         (if (<= j 9.2e+133) (+ t_3 t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -5.6e+112) {
		tmp = t_2 + t_1;
	} else if (j <= -1.65e-5) {
		tmp = y * ((x * z) + (((c * ((t * j) - (z * b))) / y) - (i * j)));
	} else if (j <= -8.5e-66) {
		tmp = t_2 + t_3;
	} else if (j <= 9.2e+133) {
		tmp = t_3 + 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) :: t_3
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = j * ((t * c) - (y * i))
    t_3 = x * ((y * z) - (t * a))
    if (j <= (-5.6d+112)) then
        tmp = t_2 + t_1
    else if (j <= (-1.65d-5)) then
        tmp = y * ((x * z) + (((c * ((t * j) - (z * b))) / y) - (i * j)))
    else if (j <= (-8.5d-66)) then
        tmp = t_2 + t_3
    else if (j <= 9.2d+133) then
        tmp = t_3 + t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = j * ((t * c) - (y * i));
	double t_3 = x * ((y * z) - (t * a));
	double tmp;
	if (j <= -5.6e+112) {
		tmp = t_2 + t_1;
	} else if (j <= -1.65e-5) {
		tmp = y * ((x * z) + (((c * ((t * j) - (z * b))) / y) - (i * j)));
	} else if (j <= -8.5e-66) {
		tmp = t_2 + t_3;
	} else if (j <= 9.2e+133) {
		tmp = t_3 + t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = j * ((t * c) - (y * i))
	t_3 = x * ((y * z) - (t * a))
	tmp = 0
	if j <= -5.6e+112:
		tmp = t_2 + t_1
	elif j <= -1.65e-5:
		tmp = y * ((x * z) + (((c * ((t * j) - (z * b))) / y) - (i * j)))
	elif j <= -8.5e-66:
		tmp = t_2 + t_3
	elif j <= 9.2e+133:
		tmp = t_3 + t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	t_3 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (j <= -5.6e+112)
		tmp = Float64(t_2 + t_1);
	elseif (j <= -1.65e-5)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(c * Float64(Float64(t * j) - Float64(z * b))) / y) - Float64(i * j))));
	elseif (j <= -8.5e-66)
		tmp = Float64(t_2 + t_3);
	elseif (j <= 9.2e+133)
		tmp = Float64(t_3 + t_1);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = j * ((t * c) - (y * i));
	t_3 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (j <= -5.6e+112)
		tmp = t_2 + t_1;
	elseif (j <= -1.65e-5)
		tmp = y * ((x * z) + (((c * ((t * j) - (z * b))) / y) - (i * j)));
	elseif (j <= -8.5e-66)
		tmp = t_2 + t_3;
	elseif (j <= 9.2e+133)
		tmp = t_3 + t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -5.6e+112], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[j, -1.65e-5], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -8.5e-66], N[(t$95$2 + t$95$3), $MachinePrecision], If[LessEqual[j, 9.2e+133], N[(t$95$3 + t$95$1), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -5.6000000000000003e112

   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. Taylor expanded in x around 0 72.5%

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

   if -5.6000000000000003e112 < j < -1.6500000000000001e-5

   1. Initial program 77.1%

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

   3. Taylor expanded in y around -inf 77.2%

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

   5. Simplified 74.3%

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

   6. Taylor expanded in c around inf 82.9%

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

   if -1.6500000000000001e-5 < j < -8.49999999999999966e-66

   1. Initial program 88.4%

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

   3. Taylor expanded in b around 0 71.5%

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

   if -8.49999999999999966e-66 < j < 9.1999999999999996e133

   1. Initial program 79.5%

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

   3. Taylor expanded in j around 0 78.8%

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

      1. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   if 9.1999999999999996e133 < j

   1. Initial program 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

      3. add-cube-cbrt 66.3%

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

      4. pow3 66.4%

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

      5. *-commutative 66.4%

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

      6. *-commutative 66.4%

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

   4. Applied egg-rr 66.4%

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

   5. Taylor expanded in j around inf 70.9%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -5.6 \cdot 10^{+112}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.65 \cdot 10^{-5}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{c \cdot \left(t \cdot j - z \cdot b\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;j \leq -8.5 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 9.2 \cdot 10^{+133}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;j \leq -3100000000:\\ \;\;\;\;j \cdot \left(c \cdot \left(t - i \cdot \frac{y}{c}\right)\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-128}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 10^{+127}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c)))))
   (if (<= j -3100000000.0)
     (* j (* c (- t (* i (/ y c)))))
     (if (<= j -5e-31)
       t_1
       (if (<= j -1.15e-84)
         (* t (- (* c j) (* x a)))
         (if (<= j 1.7e-128)
           t_1
           (if (<= j 1e+127)
             (* 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 t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (j <= -3100000000.0) {
		tmp = j * (c * (t - (i * (y / c))));
	} else if (j <= -5e-31) {
		tmp = t_1;
	} else if (j <= -1.15e-84) {
		tmp = t * ((c * j) - (x * a));
	} else if (j <= 1.7e-128) {
		tmp = t_1;
	} else if (j <= 1e+127) {
		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) :: t_1
    real(8) :: tmp
    t_1 = z * ((x * y) - (b * c))
    if (j <= (-3100000000.0d0)) then
        tmp = j * (c * (t - (i * (y / c))))
    else if (j <= (-5d-31)) then
        tmp = t_1
    else if (j <= (-1.15d-84)) then
        tmp = t * ((c * j) - (x * a))
    else if (j <= 1.7d-128) then
        tmp = t_1
    else if (j <= 1d+127) 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 t_1 = z * ((x * y) - (b * c));
	double tmp;
	if (j <= -3100000000.0) {
		tmp = j * (c * (t - (i * (y / c))));
	} else if (j <= -5e-31) {
		tmp = t_1;
	} else if (j <= -1.15e-84) {
		tmp = t * ((c * j) - (x * a));
	} else if (j <= 1.7e-128) {
		tmp = t_1;
	} else if (j <= 1e+127) {
		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):
	t_1 = z * ((x * y) - (b * c))
	tmp = 0
	if j <= -3100000000.0:
		tmp = j * (c * (t - (i * (y / c))))
	elif j <= -5e-31:
		tmp = t_1
	elif j <= -1.15e-84:
		tmp = t * ((c * j) - (x * a))
	elif j <= 1.7e-128:
		tmp = t_1
	elif j <= 1e+127:
		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)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (j <= -3100000000.0)
		tmp = Float64(j * Float64(c * Float64(t - Float64(i * Float64(y / c)))));
	elseif (j <= -5e-31)
		tmp = t_1;
	elseif (j <= -1.15e-84)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (j <= 1.7e-128)
		tmp = t_1;
	elseif (j <= 1e+127)
		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)
	t_1 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (j <= -3100000000.0)
		tmp = j * (c * (t - (i * (y / c))));
	elseif (j <= -5e-31)
		tmp = t_1;
	elseif (j <= -1.15e-84)
		tmp = t * ((c * j) - (x * a));
	elseif (j <= 1.7e-128)
		tmp = t_1;
	elseif (j <= 1e+127)
		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_] := Block[{t$95$1 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3100000000.0], N[(j * N[(c * N[(t - N[(i * N[(y / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -5e-31], t$95$1, If[LessEqual[j, -1.15e-84], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.7e-128], t$95$1, If[LessEqual[j, 1e+127], 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 5 regimes

2. if j < -3.1e9

   1. Initial program 79.3%

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

      1. *-commutative 79.3%

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

      2. *-commutative 79.3%

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

      3. add-cube-cbrt 79.1%

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

      4. pow3 79.1%

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

      5. *-commutative 79.1%

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

      6. *-commutative 79.1%

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

   4. Applied egg-rr 79.1%

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

   5. Taylor expanded in j around inf 58.4%

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

   6. Taylor expanded in c around inf 59.9%

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

      1. mul-1-neg 59.9%

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

      2. unsub-neg 59.9%

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

      3. associate-/l* 61.3%

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

   8. Simplified 61.3%

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

   if -3.1e9 < j < -5e-31 or -1.1499999999999999e-84 < j < 1.69999999999999987e-128

   1. Initial program 78.9%

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

   3. Taylor expanded in z around inf 63.0%

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

      1. *-commutative 63.0%

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

   5. Simplified 63.0%

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

   if -5e-31 < j < -1.1499999999999999e-84

   1. Initial program 79.7%

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

   3. Taylor expanded in t around inf 53.0%

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

      1. +-commutative 53.0%

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

      2. mul-1-neg 53.0%

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

      3. unsub-neg 53.0%

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

   5. Simplified 53.0%

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

   if 1.69999999999999987e-128 < j < 9.99999999999999955e126

   1. Initial program 83.5%

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

   3. Taylor expanded in a around inf 63.8%

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

      1. distribute-lft-out-- 63.8%

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

   5. Simplified 63.8%

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

   if 9.99999999999999955e126 < j

   1. Initial program 66.5%

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

      1. *-commutative 66.5%

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

      2. *-commutative 66.5%

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

      3. add-cube-cbrt 66.3%

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

      4. pow3 66.4%

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

      5. *-commutative 66.4%

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

      6. *-commutative 66.4%

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

   4. Applied egg-rr 66.4%

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

   5. Taylor expanded in j around inf 70.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3100000000:\\ \;\;\;\;j \cdot \left(c \cdot \left(t - i \cdot \frac{y}{c}\right)\right)\\ \mathbf{elif}\;j \leq -5 \cdot 10^{-31}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq -1.15 \cdot 10^{-84}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.7 \cdot 10^{-128}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 10^{+127}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.95 \cdot 10^{+134}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{c \cdot \left(t \cdot j\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+196}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -1.95e+134)
     t_1
     (if (<= t -4e+30)
       (* y (+ (* x z) (- (/ (* c (* t j)) y) (* i j))))
       (if (<= t 3.1e+196) (+ (* z (* x y)) (* b (- (* a i) (* z c)))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.95e+134) {
		tmp = t_1;
	} else if (t <= -4e+30) {
		tmp = y * ((x * z) + (((c * (t * j)) / y) - (i * j)));
	} else if (t <= 3.1e+196) {
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (t <= (-1.95d+134)) then
        tmp = t_1
    else if (t <= (-4d+30)) then
        tmp = y * ((x * z) + (((c * (t * j)) / y) - (i * j)))
    else if (t <= 3.1d+196) then
        tmp = (z * (x * y)) + (b * ((a * i) - (z * c)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.95e+134) {
		tmp = t_1;
	} else if (t <= -4e+30) {
		tmp = y * ((x * z) + (((c * (t * j)) / y) - (i * j)));
	} else if (t <= 3.1e+196) {
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.95e+134:
		tmp = t_1
	elif t <= -4e+30:
		tmp = y * ((x * z) + (((c * (t * j)) / y) - (i * j)))
	elif t <= 3.1e+196:
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.95e+134)
		tmp = t_1;
	elseif (t <= -4e+30)
		tmp = Float64(y * Float64(Float64(x * z) + Float64(Float64(Float64(c * Float64(t * j)) / y) - Float64(i * j))));
	elseif (t <= 3.1e+196)
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.95e+134)
		tmp = t_1;
	elseif (t <= -4e+30)
		tmp = y * ((x * z) + (((c * (t * j)) / y) - (i * j)));
	elseif (t <= 3.1e+196)
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.95e+134], t$95$1, If[LessEqual[t, -4e+30], N[(y * N[(N[(x * z), $MachinePrecision] + N[(N[(N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e+196], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.94999999999999992e134 or 3.1000000000000001e196 < t

   1. Initial program 72.9%

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

   3. Taylor expanded in t around inf 81.3%

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

      1. +-commutative 81.3%

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

      2. mul-1-neg 81.3%

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

      3. unsub-neg 81.3%

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

   5. Simplified 81.3%

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

   if -1.94999999999999992e134 < t < -4.0000000000000001e30

   1. Initial program 71.3%

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

   3. Taylor expanded in y around -inf 63.4%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in j around inf 63.2%

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

   if -4.0000000000000001e30 < t < 3.1000000000000001e196

   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. Taylor expanded in j around 0 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in z around inf 64.0%

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

      1. associate-*r* 65.2%

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

      2. *-commutative 65.2%

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

   8. Simplified 65.2%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.95 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{+30}:\\ \;\;\;\;y \cdot \left(x \cdot z + \left(\frac{c \cdot \left(t \cdot j\right)}{y} - i \cdot j\right)\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+196}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.92 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+114}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -1.92e+30)
     t_2
     (if (<= t -1e-30)
       t_1
       (if (<= t -1.4e-78)
         (* j (- (* t c) (* y i)))
         (if (<= t 4.5e+114) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.92e+30) {
		tmp = t_2;
	} else if (t <= -1e-30) {
		tmp = t_1;
	} else if (t <= -1.4e-78) {
		tmp = j * ((t * c) - (y * i));
	} else if (t <= 4.5e+114) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-1.92d+30)) then
        tmp = t_2
    else if (t <= (-1d-30)) then
        tmp = t_1
    else if (t <= (-1.4d-78)) then
        tmp = j * ((t * c) - (y * i))
    else if (t <= 4.5d+114) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.92e+30) {
		tmp = t_2;
	} else if (t <= -1e-30) {
		tmp = t_1;
	} else if (t <= -1.4e-78) {
		tmp = j * ((t * c) - (y * i));
	} else if (t <= 4.5e+114) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.92e+30:
		tmp = t_2
	elif t <= -1e-30:
		tmp = t_1
	elif t <= -1.4e-78:
		tmp = j * ((t * c) - (y * i))
	elif t <= 4.5e+114:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.92e+30)
		tmp = t_2;
	elseif (t <= -1e-30)
		tmp = t_1;
	elseif (t <= -1.4e-78)
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	elseif (t <= 4.5e+114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.92e+30)
		tmp = t_2;
	elseif (t <= -1e-30)
		tmp = t_1;
	elseif (t <= -1.4e-78)
		tmp = j * ((t * c) - (y * i));
	elseif (t <= 4.5e+114)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.92e+30], t$95$2, If[LessEqual[t, -1e-30], t$95$1, If[LessEqual[t, -1.4e-78], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+114], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.9200000000000001e30 or 4.5000000000000001e114 < t

   1. Initial program 74.3%

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

   3. Taylor expanded in t around inf 66.6%

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

      1. +-commutative 66.6%

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

      2. mul-1-neg 66.6%

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

      3. unsub-neg 66.6%

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

   5. Simplified 66.6%

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

   if -1.9200000000000001e30 < t < -1e-30 or -1.40000000000000012e-78 < t < 4.5000000000000001e114

   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. Taylor expanded in b around inf 60.2%

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

   if -1e-30 < t < -1.40000000000000012e-78

   1. Initial program 75.2%

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

      1. *-commutative 75.2%

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

      2. *-commutative 75.2%

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

      3. add-cube-cbrt 75.0%

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

      4. pow3 75.1%

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

      5. *-commutative 75.1%

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

      6. *-commutative 75.1%

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

   4. Applied egg-rr 75.1%

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

   5. Taylor expanded in j around inf 46.3%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.92 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-30}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-78}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+115}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -1.25e+30)
     t_2
     (if (<= t -4.1e-29)
       t_1
       (if (<= t -1.1e-61)
         (* x (- (* y z) (* t a)))
         (if (<= t 5.8e+115) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.25e+30) {
		tmp = t_2;
	} else if (t <= -4.1e-29) {
		tmp = t_1;
	} else if (t <= -1.1e-61) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 5.8e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-1.25d+30)) then
        tmp = t_2
    else if (t <= (-4.1d-29)) then
        tmp = t_1
    else if (t <= (-1.1d-61)) then
        tmp = x * ((y * z) - (t * a))
    else if (t <= 5.8d+115) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.25e+30) {
		tmp = t_2;
	} else if (t <= -4.1e-29) {
		tmp = t_1;
	} else if (t <= -1.1e-61) {
		tmp = x * ((y * z) - (t * a));
	} else if (t <= 5.8e+115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.25e+30:
		tmp = t_2
	elif t <= -4.1e-29:
		tmp = t_1
	elif t <= -1.1e-61:
		tmp = x * ((y * z) - (t * a))
	elif t <= 5.8e+115:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.25e+30)
		tmp = t_2;
	elseif (t <= -4.1e-29)
		tmp = t_1;
	elseif (t <= -1.1e-61)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (t <= 5.8e+115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.25e+30)
		tmp = t_2;
	elseif (t <= -4.1e-29)
		tmp = t_1;
	elseif (t <= -1.1e-61)
		tmp = x * ((y * z) - (t * a));
	elseif (t <= 5.8e+115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+30], t$95$2, If[LessEqual[t, -4.1e-29], t$95$1, If[LessEqual[t, -1.1e-61], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.8e+115], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25e30 or 5.80000000000000009e115 < t

   1. Initial program 74.3%

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

   3. Taylor expanded in t around inf 66.6%

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

      1. +-commutative 66.6%

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

      2. mul-1-neg 66.6%

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

      3. unsub-neg 66.6%

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

   5. Simplified 66.6%

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

   if -1.25e30 < t < -4.0999999999999998e-29 or -1.10000000000000004e-61 < t < 5.80000000000000009e115

   1. Initial program 80.8%

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

   3. Taylor expanded in b around inf 60.0%

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

   if -4.0999999999999998e-29 < t < -1.10000000000000004e-61

   1. Initial program 70.7%

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

   3. Taylor expanded in x around inf 48.9%

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

      1. *-commutative 48.9%

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

   5. Simplified 48.9%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+115}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 51.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.5 \cdot 10^{+30}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+113}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* a i) (* z c)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -1.5e+30)
     t_2
     (if (<= t -9.5e-29)
       t_1
       (if (<= t -1.4e-74)
         (* y (- (* x z) (* i j)))
         (if (<= t 2.4e+113) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.5e+30) {
		tmp = t_2;
	} else if (t <= -9.5e-29) {
		tmp = t_1;
	} else if (t <= -1.4e-74) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 2.4e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-1.5d+30)) then
        tmp = t_2
    else if (t <= (-9.5d-29)) then
        tmp = t_1
    else if (t <= (-1.4d-74)) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 2.4d+113) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((a * i) - (z * c));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -1.5e+30) {
		tmp = t_2;
	} else if (t <= -9.5e-29) {
		tmp = t_1;
	} else if (t <= -1.4e-74) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 2.4e+113) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((a * i) - (z * c))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -1.5e+30:
		tmp = t_2
	elif t <= -9.5e-29:
		tmp = t_1
	elif t <= -1.4e-74:
		tmp = y * ((x * z) - (i * j))
	elif t <= 2.4e+113:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.5e+30)
		tmp = t_2;
	elseif (t <= -9.5e-29)
		tmp = t_1;
	elseif (t <= -1.4e-74)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 2.4e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((a * i) - (z * c));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -1.5e+30)
		tmp = t_2;
	elseif (t <= -9.5e-29)
		tmp = t_1;
	elseif (t <= -1.4e-74)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 2.4e+113)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5e+30], t$95$2, If[LessEqual[t, -9.5e-29], t$95$1, If[LessEqual[t, -1.4e-74], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.4e+113], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.49999999999999989e30 or 2.39999999999999983e113 < t

   1. Initial program 74.3%

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

   3. Taylor expanded in t around inf 66.6%

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

      1. +-commutative 66.6%

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

      2. mul-1-neg 66.6%

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

      3. unsub-neg 66.6%

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

   5. Simplified 66.6%

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

   if -1.49999999999999989e30 < t < -9.50000000000000023e-29 or -1.39999999999999994e-74 < t < 2.39999999999999983e113

   1. Initial program 81.1%

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

   3. Taylor expanded in b around inf 60.5%

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

   if -9.50000000000000023e-29 < t < -1.39999999999999994e-74

   1. Initial program 69.8%

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

   3. Taylor expanded in y around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

   5. Simplified 55.9%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -9.5 \cdot 10^{-29}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{+113}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+153} \lor \neg \left(x \leq 1.85 \cdot 10^{-40}\right):\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (or (<= x -2.4e+153) (not (<= x 1.85e-40)))
     (+ t_1 (* x (- (* y z) (* t a))))
     (+ t_1 (* b (- (* a i) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if ((x <= -2.4e+153) || !(x <= 1.85e-40)) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if ((x <= (-2.4d+153)) .or. (.not. (x <= 1.85d-40))) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else
        tmp = t_1 + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if ((x <= -2.4e+153) || !(x <= 1.85e-40)) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1 + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if (x <= -2.4e+153) or not (x <= 1.85e-40):
		tmp = t_1 + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1 + (b * ((a * i) - (z * c)))
	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 ((x <= -2.4e+153) || !(x <= 1.85e-40))
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(t_1 + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	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 ((x <= -2.4e+153) || ~((x <= 1.85e-40)))
		tmp = t_1 + (x * ((y * z) - (t * a)));
	else
		tmp = t_1 + (b * ((a * i) - (z * c)));
	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[Or[LessEqual[x, -2.4e+153], N[Not[LessEqual[x, 1.85e-40]], $MachinePrecision]], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.39999999999999992e153 or 1.84999999999999999e-40 < x

   1. Initial program 81.0%

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

   3. Taylor expanded in 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 -2.39999999999999992e153 < x < 1.84999999999999999e-40

   1. Initial program 76.0%

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

   3. Taylor expanded in x around 0 72.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+153} \lor \neg \left(x \leq 1.85 \cdot 10^{-40}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 58.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.85 \cdot 10^{+30} \lor \neg \left(t \leq 1.22 \cdot 10^{+196}\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -4.85e+30) (not (<= t 1.22e+196)))
   (* t (- (* c j) (* x a)))
   (+ (* z (* x y)) (* b (- (* a i) (* z 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 ((t <= -4.85e+30) || !(t <= 1.22e+196)) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-4.85d+30)) .or. (.not. (t <= 1.22d+196))) then
        tmp = t * ((c * j) - (x * a))
    else
        tmp = (z * (x * y)) + (b * ((a * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -4.85e+30) || !(t <= 1.22e+196)) {
		tmp = t * ((c * j) - (x * a));
	} else {
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -4.85e+30) or not (t <= 1.22e+196):
		tmp = t * ((c * j) - (x * a))
	else:
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -4.85e+30) || !(t <= 1.22e+196))
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	else
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -4.85e+30) || ~((t <= 1.22e+196)))
		tmp = t * ((c * j) - (x * a));
	else
		tmp = (z * (x * y)) + (b * ((a * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -4.85e+30], N[Not[LessEqual[t, 1.22e+196]], $MachinePrecision]], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.85000000000000014e30 or 1.21999999999999995e196 < t

   1. Initial program 72.4%

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

   3. Taylor expanded in t around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

   5. Simplified 70.4%

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

   if -4.85000000000000014e30 < t < 1.21999999999999995e196

   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. Taylor expanded in j around 0 70.2%

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

      1. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   6. Taylor expanded in z around inf 64.0%

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

      1. associate-*r* 65.2%

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

      2. *-commutative 65.2%

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

   8. Simplified 65.2%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.85 \cdot 10^{+30} \lor \neg \left(t \leq 1.22 \cdot 10^{+196}\right):\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 51.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -12500000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-63}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* c j) (* x a)))))
   (if (<= t -12500000000.0)
     t_1
     (if (<= t -6.5e-63)
       (* z (- (* x y) (* b c)))
       (if (<= t 7.6e+114) (* b (- (* a i) (* z c))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -12500000000.0) {
		tmp = t_1;
	} else if (t <= -6.5e-63) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 7.6e+114) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * ((c * j) - (x * a))
    if (t <= (-12500000000.0d0)) then
        tmp = t_1
    else if (t <= (-6.5d-63)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 7.6d+114) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -12500000000.0) {
		tmp = t_1;
	} else if (t <= -6.5e-63) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 7.6e+114) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -12500000000.0:
		tmp = t_1
	elif t <= -6.5e-63:
		tmp = z * ((x * y) - (b * c))
	elif t <= 7.6e+114:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -12500000000.0)
		tmp = t_1;
	elseif (t <= -6.5e-63)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 7.6e+114)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -12500000000.0)
		tmp = t_1;
	elseif (t <= -6.5e-63)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 7.6e+114)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -12500000000.0], t$95$1, If[LessEqual[t, -6.5e-63], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e+114], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.25e10 or 7.6000000000000001e114 < t

   1. Initial program 75.1%

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

   3. Taylor expanded in t around inf 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

   5. Simplified 65.7%

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

   if -1.25e10 < t < -6.4999999999999998e-63

   1. Initial program 82.4%

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

   3. Taylor expanded in z around inf 64.8%

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

      1. *-commutative 64.8%

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

   5. Simplified 64.8%

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

   if -6.4999999999999998e-63 < t < 7.6000000000000001e114

   1. Initial program 79.3%

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

   3. Taylor expanded in b around inf 59.1%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -12500000000:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-63}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+114}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 41.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -5.8e+31)
   (* j (* t c))
   (if (<= t 1.15e+175) (* b (- (* a i) (* z c))) (* x (* t (- a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -5.8e+31) {
		tmp = j * (t * c);
	} else if (t <= 1.15e+175) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = x * (t * -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) :: tmp
    if (t <= (-5.8d+31)) then
        tmp = j * (t * c)
    else if (t <= 1.15d+175) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = x * (t * -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 tmp;
	if (t <= -5.8e+31) {
		tmp = j * (t * c);
	} else if (t <= 1.15e+175) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -5.8e+31:
		tmp = j * (t * c)
	elif t <= 1.15e+175:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -5.8e+31)
		tmp = Float64(j * Float64(t * c));
	elseif (t <= 1.15e+175)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -5.8e+31)
		tmp = j * (t * c);
	elseif (t <= 1.15e+175)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -5.8e+31], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.15e+175], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.8000000000000001e31

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. add-cube-cbrt 75.4%

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

      4. pow3 75.4%

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

      5. *-commutative 75.4%

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

      6. *-commutative 75.4%

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

   4. Applied egg-rr 75.4%

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

   5. Taylor expanded in j around inf 53.7%

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

   6. Taylor expanded in c around inf 40.9%

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

      1. *-commutative 40.9%

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

      2. associate-*l* 47.3%

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

      3. *-commutative 47.3%

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

   8. Simplified 47.3%

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

   if -5.8000000000000001e31 < t < 1.15e175

   1. Initial program 80.3%

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

   3. Taylor expanded in b around inf 55.2%

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

   if 1.15e175 < t

   1. Initial program 68.7%

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

   3. Taylor expanded in x around inf 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in z around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. distribute-rgt-neg-out 55.1%

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

   8. Simplified 55.1%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+31}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 43.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -2.5e+30)
   (* c (- (* t j) (* z b)))
   (if (<= t 4.7e+175) (* b (- (* a i) (* z c))) (* x (* t (- a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -2.5e+30) {
		tmp = c * ((t * j) - (z * b));
	} else if (t <= 4.7e+175) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = x * (t * -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) :: tmp
    if (t <= (-2.5d+30)) then
        tmp = c * ((t * j) - (z * b))
    else if (t <= 4.7d+175) then
        tmp = b * ((a * i) - (z * c))
    else
        tmp = x * (t * -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 tmp;
	if (t <= -2.5e+30) {
		tmp = c * ((t * j) - (z * b));
	} else if (t <= 4.7e+175) {
		tmp = b * ((a * i) - (z * c));
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -2.5e+30:
		tmp = c * ((t * j) - (z * b))
	elif t <= 4.7e+175:
		tmp = b * ((a * i) - (z * c))
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -2.5e+30)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (t <= 4.7e+175)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -2.5e+30)
		tmp = c * ((t * j) - (z * b));
	elseif (t <= 4.7e+175)
		tmp = b * ((a * i) - (z * c));
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -2.5e+30], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.7e+175], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4999999999999999e30

   1. Initial program 76.1%

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

   3. Taylor expanded in c around inf 53.6%

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

   if -2.4999999999999999e30 < t < 4.69999999999999995e175

   1. Initial program 80.1%

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

   3. Taylor expanded in b around inf 55.5%

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

   if 4.69999999999999995e175 < t

   1. Initial program 68.7%

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

   3. Taylor expanded in x around inf 58.6%

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

      1. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in z around 0 55.1%

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

      1. mul-1-neg 55.1%

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

      2. distribute-rgt-neg-out 55.1%

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

   8. Simplified 55.1%

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

4. Final simplification 55.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+30}:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 4.7 \cdot 10^{+175}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+30}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+46}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.4e+30)
   (* j (* t c))
   (if (<= t 4.5e+46) (* i (* a b)) (* x (* t (- a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.4e+30) {
		tmp = j * (t * c);
	} else if (t <= 4.5e+46) {
		tmp = i * (a * b);
	} else {
		tmp = x * (t * -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) :: tmp
    if (t <= (-4.4d+30)) then
        tmp = j * (t * c)
    else if (t <= 4.5d+46) then
        tmp = i * (a * b)
    else
        tmp = x * (t * -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 tmp;
	if (t <= -4.4e+30) {
		tmp = j * (t * c);
	} else if (t <= 4.5e+46) {
		tmp = i * (a * b);
	} else {
		tmp = x * (t * -a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.4e+30:
		tmp = j * (t * c)
	elif t <= 4.5e+46:
		tmp = i * (a * b)
	else:
		tmp = x * (t * -a)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.4e+30)
		tmp = Float64(j * Float64(t * c));
	elseif (t <= 4.5e+46)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(x * Float64(t * Float64(-a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.4e+30)
		tmp = j * (t * c);
	elseif (t <= 4.5e+46)
		tmp = i * (a * b);
	else
		tmp = x * (t * -a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.4e+30], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+46], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.4e30

   1. Initial program 76.1%

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

      1. *-commutative 76.1%

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

      2. *-commutative 76.1%

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

      3. add-cube-cbrt 75.8%

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

      4. pow3 75.9%

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

      5. *-commutative 75.9%

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

      6. *-commutative 75.9%

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

   4. Applied egg-rr 75.9%

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

   5. Taylor expanded in j around inf 52.9%

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

   6. Taylor expanded in c around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. associate-*l* 46.6%

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

      3. *-commutative 46.6%

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

   8. Simplified 46.6%

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

   if -4.4e30 < t < 4.5000000000000001e46

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 56.1%

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

   4. Taylor expanded in a around inf 32.5%

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

      1. associate-*r* 32.7%

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

      2. *-commutative 32.7%

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

      3. *-commutative 32.7%

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

   6. Simplified 32.7%

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

   if 4.5000000000000001e46 < t

   1. Initial program 73.4%

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

   3. Taylor expanded in x around inf 51.5%

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

      1. *-commutative 51.5%

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

   5. Simplified 51.5%

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

   6. Taylor expanded in z around 0 41.4%

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

      1. mul-1-neg 41.4%

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

      2. distribute-rgt-neg-out 41.4%

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

   8. Simplified 41.4%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.4 \cdot 10^{+30}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+46}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+30} \lor \neg \left(t \leq 1.15 \cdot 10^{+118}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.85e+30) (not (<= t 1.15e+118))) (* 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 ((t <= -1.85e+30) || !(t <= 1.15e+118)) {
		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 ((t <= (-1.85d+30)) .or. (.not. (t <= 1.15d+118))) 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 ((t <= -1.85e+30) || !(t <= 1.15e+118)) {
		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 (t <= -1.85e+30) or not (t <= 1.15e+118):
		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 ((t <= -1.85e+30) || !(t <= 1.15e+118))
		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 ((t <= -1.85e+30) || ~((t <= 1.15e+118)))
		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[t, -1.85e+30], N[Not[LessEqual[t, 1.15e+118]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(a * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.85000000000000008e30 or 1.15000000000000008e118 < t

   1. Initial program 74.3%

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

   3. Taylor expanded in b around 0 70.4%

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

   4. Taylor expanded in c around inf 39.6%

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

   if -1.85000000000000008e30 < t < 1.15000000000000008e118

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 56.4%

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

   4. Taylor expanded in a around inf 31.9%

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

      1. *-commutative 31.9%

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

   6. Simplified 31.9%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+30} \lor \neg \left(t \leq 1.15 \cdot 10^{+118}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+30} \lor \neg \left(t \leq 1.15 \cdot 10^{+118}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -1.5e+30) (not (<= t 1.15e+118))) (* c (* t j)) (* i (* a b))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.5e+30) || !(t <= 1.15e+118)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((t <= (-1.5d+30)) .or. (.not. (t <= 1.15d+118))) then
        tmp = c * (t * j)
    else
        tmp = i * (a * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -1.5e+30) || !(t <= 1.15e+118)) {
		tmp = c * (t * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -1.5e+30) or not (t <= 1.15e+118):
		tmp = c * (t * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -1.5e+30) || !(t <= 1.15e+118))
		tmp = Float64(c * Float64(t * j));
	else
		tmp = Float64(i * Float64(a * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -1.5e+30) || ~((t <= 1.15e+118)))
		tmp = c * (t * j);
	else
		tmp = i * (a * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -1.5e+30], N[Not[LessEqual[t, 1.15e+118]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.49999999999999989e30 or 1.15000000000000008e118 < t

   1. Initial program 74.3%

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

   3. Taylor expanded in b around 0 70.4%

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

   4. Taylor expanded in c around inf 39.6%

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

   if -1.49999999999999989e30 < t < 1.15000000000000008e118

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 56.4%

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

   4. Taylor expanded in a around inf 31.8%

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

      1. associate-*r* 32.0%

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

      2. *-commutative 32.0%

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

      3. *-commutative 32.0%

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

   6. Simplified 32.0%

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

4. Final simplification 34.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+30} \lor \neg \left(t \leq 1.15 \cdot 10^{+118}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+30}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -4.5e+30)
   (* j (* t c))
   (if (<= t 2.5e+120) (* i (* a b)) (* c (* t j)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.5e+30) {
		tmp = j * (t * c);
	} else if (t <= 2.5e+120) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-4.5d+30)) then
        tmp = j * (t * c)
    else if (t <= 2.5d+120) then
        tmp = i * (a * b)
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -4.5e+30) {
		tmp = j * (t * c);
	} else if (t <= 2.5e+120) {
		tmp = i * (a * b);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -4.5e+30:
		tmp = j * (t * c)
	elif t <= 2.5e+120:
		tmp = i * (a * b)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -4.5e+30)
		tmp = Float64(j * Float64(t * c));
	elseif (t <= 2.5e+120)
		tmp = Float64(i * Float64(a * b));
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (t <= -4.5e+30)
		tmp = j * (t * c);
	elseif (t <= 2.5e+120)
		tmp = i * (a * b);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -4.5e+30], N[(j * N[(t * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e+120], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.49999999999999995e30

   1. Initial program 76.1%

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

      1. *-commutative 76.1%

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

      2. *-commutative 76.1%

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

      3. add-cube-cbrt 75.8%

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

      4. pow3 75.9%

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

      5. *-commutative 75.9%

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

      6. *-commutative 75.9%

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

   4. Applied egg-rr 75.9%

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

   5. Taylor expanded in j around inf 52.9%

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

   6. Taylor expanded in c around inf 40.3%

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

      1. *-commutative 40.3%

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

      2. associate-*l* 46.6%

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

      3. *-commutative 46.6%

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

   8. Simplified 46.6%

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

   if -4.49999999999999995e30 < t < 2.50000000000000009e120

   1. Initial program 80.2%

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

   3. Taylor expanded in b around inf 56.4%

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

   4. Taylor expanded in a around inf 31.8%

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

      1. associate-*r* 32.0%

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

      2. *-commutative 32.0%

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

      3. *-commutative 32.0%

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

   6. Simplified 32.0%

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

   if 2.50000000000000009e120 < t

   1. Initial program 71.6%

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

   3. Taylor expanded in b around 0 69.4%

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

   4. Taylor expanded in c around inf 38.4%

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

4. Final simplification 36.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+30}:\\ \;\;\;\;j \cdot \left(t \cdot c\right)\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{+120}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 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 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 42.9%

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

4. Taylor expanded in a around inf 24.8%

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

5. Final simplification 24.8%

   \[\leadsto a \cdot \left(b \cdot i\right) \]
6. Add Preprocessing

Developer target: 68.7% 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 2024095 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64

  :alt
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2.0) (pow (* i y) 2.0))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))