Linear.Matrix:det33 from linear-1.19.1.3

Percentage Accurate: 73.2% → 81.6%

Time: 23.0s

Alternatives: 22

Speedup: 0.5×

• 57.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 73.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = ((x * ((y * z) - (t * a))) - (b * ((c * z) - (i * a)))) + (j * ((c * t) - (i * y)));
end

Wolfram

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

Alternative 1: 81.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 91.9%

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

   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 a around inf 62.0%

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

      1. distribute-lft-out-- 62.0%

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

      2. *-commutative 62.0%

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

      3. *-commutative 62.0%

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

   5. Simplified 62.0%

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

4. Final simplification 85.6%

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

Alternative 2: 57.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.4 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -8.8 \cdot 10^{-113}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-243}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-270}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-229}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z (- y (* b (/ c x)))) (* t a))))
        (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -3.4e+123)
     t_2
     (if (<= j -8.8e-113)
       t_1
       (if (<= j -6.2e-243)
         (* i (- (* a b) (* y j)))
         (if (<= j 4.5e-270)
           t_1
           (if (<= j 6.5e-229)
             (+ (* z (* x y)) (* i (* a b)))
             (if (<= j 2.5e+95) 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 * ((z * (y - (b * (c / x)))) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.4e+123) {
		tmp = t_2;
	} else if (j <= -8.8e-113) {
		tmp = t_1;
	} else if (j <= -6.2e-243) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 4.5e-270) {
		tmp = t_1;
	} else if (j <= 6.5e-229) {
		tmp = (z * (x * y)) + (i * (a * b));
	} else if (j <= 2.5e+95) {
		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 * ((z * (y - (b * (c / x)))) - (t * a))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-3.4d+123)) then
        tmp = t_2
    else if (j <= (-8.8d-113)) then
        tmp = t_1
    else if (j <= (-6.2d-243)) then
        tmp = i * ((a * b) - (y * j))
    else if (j <= 4.5d-270) then
        tmp = t_1
    else if (j <= 6.5d-229) then
        tmp = (z * (x * y)) + (i * (a * b))
    else if (j <= 2.5d+95) 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 * ((z * (y - (b * (c / x)))) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.4e+123) {
		tmp = t_2;
	} else if (j <= -8.8e-113) {
		tmp = t_1;
	} else if (j <= -6.2e-243) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 4.5e-270) {
		tmp = t_1;
	} else if (j <= 6.5e-229) {
		tmp = (z * (x * y)) + (i * (a * b));
	} else if (j <= 2.5e+95) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * (y - (b * (c / x)))) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -3.4e+123:
		tmp = t_2
	elif j <= -8.8e-113:
		tmp = t_1
	elif j <= -6.2e-243:
		tmp = i * ((a * b) - (y * j))
	elif j <= 4.5e-270:
		tmp = t_1
	elif j <= 6.5e-229:
		tmp = (z * (x * y)) + (i * (a * b))
	elif j <= 2.5e+95:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * Float64(y - Float64(b * Float64(c / x)))) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.4e+123)
		tmp = t_2;
	elseif (j <= -8.8e-113)
		tmp = t_1;
	elseif (j <= -6.2e-243)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (j <= 4.5e-270)
		tmp = t_1;
	elseif (j <= 6.5e-229)
		tmp = Float64(Float64(z * Float64(x * y)) + Float64(i * Float64(a * b)));
	elseif (j <= 2.5e+95)
		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 * ((z * (y - (b * (c / x)))) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.4e+123)
		tmp = t_2;
	elseif (j <= -8.8e-113)
		tmp = t_1;
	elseif (j <= -6.2e-243)
		tmp = i * ((a * b) - (y * j));
	elseif (j <= 4.5e-270)
		tmp = t_1;
	elseif (j <= 6.5e-229)
		tmp = (z * (x * y)) + (i * (a * b));
	elseif (j <= 2.5e+95)
		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[(x * N[(N[(z * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.4e+123], t$95$2, If[LessEqual[j, -8.8e-113], t$95$1, If[LessEqual[j, -6.2e-243], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e-270], t$95$1, If[LessEqual[j, 6.5e-229], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.5e+95], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -3.40000000000000001e123 or 2.50000000000000012e95 < j

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 81.6%

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

   if -3.40000000000000001e123 < j < -8.80000000000000016e-113 or -6.1999999999999999e-243 < j < 4.49999999999999998e-270 or 6.5e-229 < j < 2.50000000000000012e95

   1. Initial program 72.2%

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

   3. Taylor expanded in j around 0 69.6%

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

      1. *-commutative 69.6%

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

   5. Simplified 69.6%

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

   6. Taylor expanded in x around inf 67.0%

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

      1. +-commutative 67.0%

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

      2. mul-1-neg 67.0%

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

      3. unsub-neg 67.0%

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

      4. *-commutative 67.0%

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

      5. associate-/l* 68.5%

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

      6. *-commutative 68.5%

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

   8. Simplified 68.5%

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

   9. Taylor expanded in i around 0 57.8%

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

       1. +-commutative 57.8%

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

       2. associate--r+ 57.8%

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

   11. Simplified 66.7%

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

   if -8.80000000000000016e-113 < j < -6.1999999999999999e-243

   1. Initial program 67.6%

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

   3. Taylor expanded in i around inf 67.7%

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

      1. distribute-lft-out-- 67.7%

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

      2. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   if 4.49999999999999998e-270 < j < 6.5e-229

   1. Initial program 66.8%

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

   3. Taylor expanded in j around 0 82.9%

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

      1. *-commutative 82.9%

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

   5. Simplified 82.9%

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

   6. Taylor expanded in y around inf 91.3%

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

      1. *-commutative 91.3%

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

   8. Simplified 91.3%

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

   9. Taylor expanded in c around 0 73.8%

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

       1. associate-*r* 73.8%

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

       2. mul-1-neg 73.8%

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

       3. associate-*r* 91.3%

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

       4. *-commutative 91.3%

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

   11. Simplified 91.3%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.4 \cdot 10^{+123}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -8.8 \cdot 10^{-113}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ \mathbf{elif}\;j \leq -6.2 \cdot 10^{-243}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-270}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{-229}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 2.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.2 \cdot 10^{+126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z (- y (* b (/ c x)))) (* t a))))
        (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -2.2e+126)
     t_2
     (if (<= j -2.4e-112)
       t_1
       (if (<= j -2.1e-174)
         (* i (- (* a b) (* y j)))
         (if (<= j 2.3e-193)
           (+ (* x (- (* y z) (* t a))) (* i (* a b)))
           (if (<= j 3.1e-98) t_1 (- t_2 (* x (- (* t a) (* y z)))))))))))

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 * ((z * (y - (b * (c / x)))) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.2e+126) {
		tmp = t_2;
	} else if (j <= -2.4e-112) {
		tmp = t_1;
	} else if (j <= -2.1e-174) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 2.3e-193) {
		tmp = (x * ((y * z) - (t * a))) + (i * (a * b));
	} else if (j <= 3.1e-98) {
		tmp = t_1;
	} else {
		tmp = t_2 - (x * ((t * a) - (y * z)));
	}
	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 * ((z * (y - (b * (c / x)))) - (t * a))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-2.2d+126)) then
        tmp = t_2
    else if (j <= (-2.4d-112)) then
        tmp = t_1
    else if (j <= (-2.1d-174)) then
        tmp = i * ((a * b) - (y * j))
    else if (j <= 2.3d-193) then
        tmp = (x * ((y * z) - (t * a))) + (i * (a * b))
    else if (j <= 3.1d-98) then
        tmp = t_1
    else
        tmp = t_2 - (x * ((t * a) - (y * z)))
    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 * ((z * (y - (b * (c / x)))) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.2e+126) {
		tmp = t_2;
	} else if (j <= -2.4e-112) {
		tmp = t_1;
	} else if (j <= -2.1e-174) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 2.3e-193) {
		tmp = (x * ((y * z) - (t * a))) + (i * (a * b));
	} else if (j <= 3.1e-98) {
		tmp = t_1;
	} else {
		tmp = t_2 - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * (y - (b * (c / x)))) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -2.2e+126:
		tmp = t_2
	elif j <= -2.4e-112:
		tmp = t_1
	elif j <= -2.1e-174:
		tmp = i * ((a * b) - (y * j))
	elif j <= 2.3e-193:
		tmp = (x * ((y * z) - (t * a))) + (i * (a * b))
	elif j <= 3.1e-98:
		tmp = t_1
	else:
		tmp = t_2 - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * Float64(y - Float64(b * Float64(c / x)))) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.2e+126)
		tmp = t_2;
	elseif (j <= -2.4e-112)
		tmp = t_1;
	elseif (j <= -2.1e-174)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (j <= 2.3e-193)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(i * Float64(a * b)));
	elseif (j <= 3.1e-98)
		tmp = t_1;
	else
		tmp = Float64(t_2 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((z * (y - (b * (c / x)))) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.2e+126)
		tmp = t_2;
	elseif (j <= -2.4e-112)
		tmp = t_1;
	elseif (j <= -2.1e-174)
		tmp = i * ((a * b) - (y * j));
	elseif (j <= 2.3e-193)
		tmp = (x * ((y * z) - (t * a))) + (i * (a * b));
	elseif (j <= 3.1e-98)
		tmp = t_1;
	else
		tmp = t_2 - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(z * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.2e+126], t$95$2, If[LessEqual[j, -2.4e-112], t$95$1, If[LessEqual[j, -2.1e-174], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.3e-193], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.1e-98], t$95$1, N[(t$95$2 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -2.19999999999999999e126

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 79.1%

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

   if -2.19999999999999999e126 < j < -2.4000000000000001e-112 or 2.30000000000000009e-193 < j < 3.1e-98

   1. Initial program 70.9%

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

   3. Taylor expanded in j around 0 74.8%

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

      1. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in x around inf 73.6%

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

      1. +-commutative 73.6%

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

      2. mul-1-neg 73.6%

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

      3. unsub-neg 73.6%

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

      4. *-commutative 73.6%

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

      5. associate-/l* 74.9%

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

      6. *-commutative 74.9%

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

   8. Simplified 74.9%

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

   9. Taylor expanded in i around 0 64.6%

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

       1. +-commutative 64.6%

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

       2. associate--r+ 64.6%

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

   11. Simplified 72.5%

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

   if -2.4000000000000001e-112 < j < -2.1000000000000001e-174

   1. Initial program 63.7%

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

   3. Taylor expanded in i around inf 69.5%

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

      1. distribute-lft-out-- 69.5%

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

      2. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   if -2.1000000000000001e-174 < j < 2.30000000000000009e-193

   1. Initial program 74.7%

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

   3. Taylor expanded in j around 0 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%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in z around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. *-commutative 74.0%

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

      3. *-commutative 74.0%

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

      4. associate-*r* 74.4%

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

      5. *-commutative 74.4%

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

      6. distribute-rgt-neg-out 74.4%

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

      7. distribute-rgt-neg-in 74.4%

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

   8. Simplified 74.4%

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

   if 3.1e-98 < j

   1. Initial program 73.0%

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

   3. Taylor expanded in b around 0 72.9%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.2 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.4 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ \mathbf{elif}\;j \leq -2.1 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 2.3 \cdot 10^{-193}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 3.1 \cdot 10^{-98}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -6.4 \cdot 10^{+125}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z (- y (* b (/ c x)))) (* t a))))
        (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -6.4e+125)
     t_2
     (if (<= j -1.05e-112)
       t_1
       (if (<= j -8.6e-175)
         (* i (- (* a b) (* y j)))
         (if (<= j 1.2e-194)
           (+ (* x (- (* y z) (* t a))) (* i (* a b)))
           (if (<= j 6.5e+95) 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 * ((z * (y - (b * (c / x)))) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -6.4e+125) {
		tmp = t_2;
	} else if (j <= -1.05e-112) {
		tmp = t_1;
	} else if (j <= -8.6e-175) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 1.2e-194) {
		tmp = (x * ((y * z) - (t * a))) + (i * (a * b));
	} else if (j <= 6.5e+95) {
		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 * ((z * (y - (b * (c / x)))) - (t * a))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-6.4d+125)) then
        tmp = t_2
    else if (j <= (-1.05d-112)) then
        tmp = t_1
    else if (j <= (-8.6d-175)) then
        tmp = i * ((a * b) - (y * j))
    else if (j <= 1.2d-194) then
        tmp = (x * ((y * z) - (t * a))) + (i * (a * b))
    else if (j <= 6.5d+95) 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 * ((z * (y - (b * (c / x)))) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -6.4e+125) {
		tmp = t_2;
	} else if (j <= -1.05e-112) {
		tmp = t_1;
	} else if (j <= -8.6e-175) {
		tmp = i * ((a * b) - (y * j));
	} else if (j <= 1.2e-194) {
		tmp = (x * ((y * z) - (t * a))) + (i * (a * b));
	} else if (j <= 6.5e+95) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * (y - (b * (c / x)))) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -6.4e+125:
		tmp = t_2
	elif j <= -1.05e-112:
		tmp = t_1
	elif j <= -8.6e-175:
		tmp = i * ((a * b) - (y * j))
	elif j <= 1.2e-194:
		tmp = (x * ((y * z) - (t * a))) + (i * (a * b))
	elif j <= 6.5e+95:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * Float64(y - Float64(b * Float64(c / x)))) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -6.4e+125)
		tmp = t_2;
	elseif (j <= -1.05e-112)
		tmp = t_1;
	elseif (j <= -8.6e-175)
		tmp = Float64(i * Float64(Float64(a * b) - Float64(y * j)));
	elseif (j <= 1.2e-194)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(i * Float64(a * b)));
	elseif (j <= 6.5e+95)
		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 * ((z * (y - (b * (c / x)))) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -6.4e+125)
		tmp = t_2;
	elseif (j <= -1.05e-112)
		tmp = t_1;
	elseif (j <= -8.6e-175)
		tmp = i * ((a * b) - (y * j));
	elseif (j <= 1.2e-194)
		tmp = (x * ((y * z) - (t * a))) + (i * (a * b));
	elseif (j <= 6.5e+95)
		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[(x * N[(N[(z * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -6.4e+125], t$95$2, If[LessEqual[j, -1.05e-112], t$95$1, If[LessEqual[j, -8.6e-175], N[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.2e-194], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.5e+95], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -6.39999999999999967e125 or 6.5e95 < j

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 81.6%

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

   if -6.39999999999999967e125 < j < -1.05e-112 or 1.2e-194 < j < 6.5e95

   1. Initial program 70.9%

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

   3. Taylor expanded in j around 0 67.8%

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

      1. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in x around inf 66.2%

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

      1. +-commutative 66.2%

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

      2. mul-1-neg 66.2%

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

      3. unsub-neg 66.2%

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

      4. *-commutative 66.2%

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

      5. associate-/l* 68.1%

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

      6. *-commutative 68.1%

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

   8. Simplified 68.1%

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

   9. Taylor expanded in i around 0 57.5%

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

       1. +-commutative 57.5%

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

       2. associate--r+ 57.5%

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

   11. Simplified 68.3%

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

   if -1.05e-112 < j < -8.59999999999999996e-175

   1. Initial program 63.7%

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

   3. Taylor expanded in i around inf 69.5%

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

      1. distribute-lft-out-- 69.5%

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

      2. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   if -8.59999999999999996e-175 < j < 1.2e-194

   1. Initial program 74.7%

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

   3. Taylor expanded in j around 0 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%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in z around 0 74.0%

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

      1. mul-1-neg 74.0%

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

      2. *-commutative 74.0%

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

      3. *-commutative 74.0%

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

      4. associate-*r* 74.4%

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

      5. *-commutative 74.4%

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

      6. distribute-rgt-neg-out 74.4%

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

      7. distribute-rgt-neg-in 74.4%

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

   8. Simplified 74.4%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.4 \cdot 10^{+125}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ \mathbf{elif}\;j \leq -8.6 \cdot 10^{-175}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;j \leq 1.2 \cdot 10^{-194}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+95}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+124}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-37}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-184}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-291}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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_3 (* j (- (* t c) (* y i)))))
   (if (<= j -1.7e+124)
     t_3
     (if (<= j -5.8e-37)
       t_2
       (if (<= j -4.2e-184)
         t_1
         (if (<= j -1.9e-291)
           t_2
           (if (<= j 1.9e-98) t_1 (if (<= j 2.8e+101) 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));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.7e+124) {
		tmp = t_3;
	} else if (j <= -5.8e-37) {
		tmp = t_2;
	} else if (j <= -4.2e-184) {
		tmp = t_1;
	} else if (j <= -1.9e-291) {
		tmp = t_2;
	} else if (j <= 1.9e-98) {
		tmp = t_1;
	} else if (j <= 2.8e+101) {
		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) :: tmp
    t_1 = b * ((a * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = j * ((t * c) - (y * i))
    if (j <= (-1.7d+124)) then
        tmp = t_3
    else if (j <= (-5.8d-37)) then
        tmp = t_2
    else if (j <= (-4.2d-184)) then
        tmp = t_1
    else if (j <= (-1.9d-291)) then
        tmp = t_2
    else if (j <= 1.9d-98) then
        tmp = t_1
    else if (j <= 2.8d+101) 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));
	double t_3 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.7e+124) {
		tmp = t_3;
	} else if (j <= -5.8e-37) {
		tmp = t_2;
	} else if (j <= -4.2e-184) {
		tmp = t_1;
	} else if (j <= -1.9e-291) {
		tmp = t_2;
	} else if (j <= 1.9e-98) {
		tmp = t_1;
	} else if (j <= 2.8e+101) {
		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_3 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.7e+124:
		tmp = t_3
	elif j <= -5.8e-37:
		tmp = t_2
	elif j <= -4.2e-184:
		tmp = t_1
	elif j <= -1.9e-291:
		tmp = t_2
	elif j <= 1.9e-98:
		tmp = t_1
	elif j <= 2.8e+101:
		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(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.7e+124)
		tmp = t_3;
	elseif (j <= -5.8e-37)
		tmp = t_2;
	elseif (j <= -4.2e-184)
		tmp = t_1;
	elseif (j <= -1.9e-291)
		tmp = t_2;
	elseif (j <= 1.9e-98)
		tmp = t_1;
	elseif (j <= 2.8e+101)
		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_3 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.7e+124)
		tmp = t_3;
	elseif (j <= -5.8e-37)
		tmp = t_2;
	elseif (j <= -4.2e-184)
		tmp = t_1;
	elseif (j <= -1.9e-291)
		tmp = t_2;
	elseif (j <= 1.9e-98)
		tmp = t_1;
	elseif (j <= 2.8e+101)
		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[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e+124], t$95$3, If[LessEqual[j, -5.8e-37], t$95$2, If[LessEqual[j, -4.2e-184], t$95$1, If[LessEqual[j, -1.9e-291], t$95$2, If[LessEqual[j, 1.9e-98], t$95$1, If[LessEqual[j, 2.8e+101], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.7e124 or 2.79999999999999981e101 < j

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 81.6%

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

   if -1.7e124 < j < -5.80000000000000009e-37 or -4.1999999999999998e-184 < j < -1.8999999999999999e-291 or 1.9000000000000002e-98 < j < 2.79999999999999981e101

   1. Initial program 73.5%

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

   3. Taylor expanded in j around 0 67.7%

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

      1. *-commutative 67.7%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in x around inf 58.1%

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

      1. *-commutative 58.1%

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

      2. *-commutative 58.1%

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

   8. Simplified 58.1%

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

   if -5.80000000000000009e-37 < j < -4.1999999999999998e-184 or -1.8999999999999999e-291 < j < 1.9000000000000002e-98

   1. Initial program 68.5%

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

   3. Taylor expanded in b around inf 55.6%

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

      1. *-commutative 55.6%

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

   5. Simplified 55.6%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+124}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.8 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq -4.2 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq -1.9 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;j \leq 1.9 \cdot 10^{-98}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.8 \cdot 10^{+101}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-20}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-271}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-139}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-41}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -2.5e-20)
     t_3
     (if (<= t -3.2e-271)
       t_2
       (if (<= t 9.2e-177)
         t_1
         (if (<= t 4.8e-139)
           t_2
           (if (<= t 7e-41)
             t_1
             (if (<= t 2.3e+83) (* a (- (* b i) (* x t))) 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 = y * ((x * z) - (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.5e-20) {
		tmp = t_3;
	} else if (t <= -3.2e-271) {
		tmp = t_2;
	} else if (t <= 9.2e-177) {
		tmp = t_1;
	} else if (t <= 4.8e-139) {
		tmp = t_2;
	} else if (t <= 7e-41) {
		tmp = t_1;
	} else if (t <= 2.3e+83) {
		tmp = a * ((b * i) - (x * t));
	} 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 = y * ((x * z) - (i * j))
    t_2 = b * ((a * i) - (z * c))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-2.5d-20)) then
        tmp = t_3
    else if (t <= (-3.2d-271)) then
        tmp = t_2
    else if (t <= 9.2d-177) then
        tmp = t_1
    else if (t <= 4.8d-139) then
        tmp = t_2
    else if (t <= 7d-41) then
        tmp = t_1
    else if (t <= 2.3d+83) then
        tmp = a * ((b * i) - (x * t))
    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 = y * ((x * z) - (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -2.5e-20) {
		tmp = t_3;
	} else if (t <= -3.2e-271) {
		tmp = t_2;
	} else if (t <= 9.2e-177) {
		tmp = t_1;
	} else if (t <= 4.8e-139) {
		tmp = t_2;
	} else if (t <= 7e-41) {
		tmp = t_1;
	} else if (t <= 2.3e+83) {
		tmp = a * ((b * i) - (x * t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = b * ((a * i) - (z * c))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -2.5e-20:
		tmp = t_3
	elif t <= -3.2e-271:
		tmp = t_2
	elif t <= 9.2e-177:
		tmp = t_1
	elif t <= 4.8e-139:
		tmp = t_2
	elif t <= 7e-41:
		tmp = t_1
	elif t <= 2.3e+83:
		tmp = a * ((b * i) - (x * t))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.5e-20)
		tmp = t_3;
	elseif (t <= -3.2e-271)
		tmp = t_2;
	elseif (t <= 9.2e-177)
		tmp = t_1;
	elseif (t <= 4.8e-139)
		tmp = t_2;
	elseif (t <= 7e-41)
		tmp = t_1;
	elseif (t <= 2.3e+83)
		tmp = Float64(a * Float64(Float64(b * i) - Float64(x * t)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = b * ((a * i) - (z * c));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -2.5e-20)
		tmp = t_3;
	elseif (t <= -3.2e-271)
		tmp = t_2;
	elseif (t <= 9.2e-177)
		tmp = t_1;
	elseif (t <= 4.8e-139)
		tmp = t_2;
	elseif (t <= 7e-41)
		tmp = t_1;
	elseif (t <= 2.3e+83)
		tmp = a * ((b * i) - (x * t));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e-20], t$95$3, If[LessEqual[t, -3.2e-271], t$95$2, If[LessEqual[t, 9.2e-177], t$95$1, If[LessEqual[t, 4.8e-139], t$95$2, If[LessEqual[t, 7e-41], t$95$1, If[LessEqual[t, 2.3e+83], N[(a * N[(N[(b * i), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.4999999999999999e-20 or 2.29999999999999995e83 < t

   1. Initial program 64.1%

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

   3. Taylor expanded in t around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. *-commutative 71.0%

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

      5. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if -2.4999999999999999e-20 < t < -3.19999999999999978e-271 or 9.20000000000000087e-177 < t < 4.80000000000000029e-139

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf 60.8%

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

      1. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   if -3.19999999999999978e-271 < t < 9.20000000000000087e-177 or 4.80000000000000029e-139 < t < 6.9999999999999999e-41

   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 y around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

   5. Simplified 61.2%

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

   if 6.9999999999999999e-41 < t < 2.29999999999999995e83

   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 a around inf 59.4%

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

      1. distribute-lft-out-- 59.4%

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

      2. *-commutative 59.4%

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

      3. *-commutative 59.4%

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

   5. Simplified 59.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(x \cdot t - i \cdot b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{-20}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-271}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 9.2 \cdot 10^{-177}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-139}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.3 \cdot 10^{+83}:\\ \;\;\;\;a \cdot \left(b \cdot i - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 30.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;i \leq -0.00016:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-290}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-241}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -6e+214)
   (* y (- (* i j)))
   (if (<= i -0.00016)
     (* i (* a b))
     (if (<= i -1.4e-254)
       (* t (* x (- a)))
       (if (<= i 2.4e-290)
         (* c (* t j))
         (if (<= i 3.3e-241)
           (* c (* z (- b)))
           (if (<= i 3.1e+40) (* t (* c j)) (* a (* b i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -6e+214) {
		tmp = y * -(i * j);
	} else if (i <= -0.00016) {
		tmp = i * (a * b);
	} else if (i <= -1.4e-254) {
		tmp = t * (x * -a);
	} else if (i <= 2.4e-290) {
		tmp = c * (t * j);
	} else if (i <= 3.3e-241) {
		tmp = c * (z * -b);
	} else if (i <= 3.1e+40) {
		tmp = t * (c * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-6d+214)) then
        tmp = y * -(i * j)
    else if (i <= (-0.00016d0)) then
        tmp = i * (a * b)
    else if (i <= (-1.4d-254)) then
        tmp = t * (x * -a)
    else if (i <= 2.4d-290) then
        tmp = c * (t * j)
    else if (i <= 3.3d-241) then
        tmp = c * (z * -b)
    else if (i <= 3.1d+40) then
        tmp = t * (c * j)
    else
        tmp = a * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -6e+214) {
		tmp = y * -(i * j);
	} else if (i <= -0.00016) {
		tmp = i * (a * b);
	} else if (i <= -1.4e-254) {
		tmp = t * (x * -a);
	} else if (i <= 2.4e-290) {
		tmp = c * (t * j);
	} else if (i <= 3.3e-241) {
		tmp = c * (z * -b);
	} else if (i <= 3.1e+40) {
		tmp = t * (c * j);
	} else {
		tmp = a * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -6e+214:
		tmp = y * -(i * j)
	elif i <= -0.00016:
		tmp = i * (a * b)
	elif i <= -1.4e-254:
		tmp = t * (x * -a)
	elif i <= 2.4e-290:
		tmp = c * (t * j)
	elif i <= 3.3e-241:
		tmp = c * (z * -b)
	elif i <= 3.1e+40:
		tmp = t * (c * j)
	else:
		tmp = a * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -6e+214)
		tmp = Float64(y * Float64(-Float64(i * j)));
	elseif (i <= -0.00016)
		tmp = Float64(i * Float64(a * b));
	elseif (i <= -1.4e-254)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (i <= 2.4e-290)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 3.3e-241)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (i <= 3.1e+40)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = Float64(a * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -6e+214)
		tmp = y * -(i * j);
	elseif (i <= -0.00016)
		tmp = i * (a * b);
	elseif (i <= -1.4e-254)
		tmp = t * (x * -a);
	elseif (i <= 2.4e-290)
		tmp = c * (t * j);
	elseif (i <= 3.3e-241)
		tmp = c * (z * -b);
	elseif (i <= 3.1e+40)
		tmp = t * (c * j);
	else
		tmp = a * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -6e+214], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[i, -0.00016], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.4e-254], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.4e-290], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.3e-241], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.1e+40], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 7 regimes

2. if i < -6.0000000000000002e214

   1. Initial program 53.0%

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

   3. Taylor expanded in y around -inf 58.0%

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

   5. Simplified 58.0%

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

   6. Taylor expanded in y around inf 68.0%

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

      1. *-commutative 68.0%

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

   8. Simplified 68.0%

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

   9. Taylor expanded in x around 0 68.5%

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

       1. neg-mul-1 68.5%

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

       2. *-commutative 68.5%

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

       3. distribute-rgt-neg-in 68.5%

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

   11. Simplified 68.5%

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

   if -6.0000000000000002e214 < i < -1.60000000000000013e-4

   1. Initial program 70.3%

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

   3. Taylor expanded in j around 0 53.6%

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

      1. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in x around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

      4. *-commutative 51.2%

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

      5. associate-/l* 53.6%

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

      6. *-commutative 53.6%

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

   8. Simplified 53.6%

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

   9. Taylor expanded in i around inf 41.3%

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

       1. associate-*r* 41.3%

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

       2. *-commutative 41.3%

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

   11. Simplified 41.3%

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

   if -1.60000000000000013e-4 < i < -1.39999999999999992e-254

   1. Initial program 86.4%

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

   3. Taylor expanded in t around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

      4. *-commutative 49.2%

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

      5. *-commutative 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in j around 0 40.6%

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

      1. mul-1-neg 40.6%

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

      2. distribute-rgt-neg-in 40.6%

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

   8. Simplified 40.6%

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

   if -1.39999999999999992e-254 < i < 2.4000000000000001e-290

   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. Taylor expanded in t around inf 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

      4. *-commutative 54.1%

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

      5. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in j around inf 48.0%

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

   if 2.4000000000000001e-290 < i < 3.2999999999999999e-241

   1. Initial program 71.2%

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

   3. Taylor expanded in c around inf 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in t around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. associate-*r* 44.6%

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

      3. *-commutative 44.6%

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

      4. *-commutative 44.6%

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

      5. *-commutative 44.6%

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

      6. associate-*l* 51.5%

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

      7. *-commutative 51.5%

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

      8. distribute-rgt-neg-in 51.5%

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

      9. distribute-lft-neg-in 51.5%

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

      10. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   if 3.2999999999999999e-241 < i < 3.0999999999999998e40

   1. Initial program 77.0%

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

   3. Taylor expanded in t around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

      5. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in j around inf 38.6%

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

      1. associate-*r* 45.3%

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

   8. Simplified 45.3%

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

   if 3.0999999999999998e40 < i

   1. Initial program 65.6%

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

   3. Taylor expanded in b around inf 53.5%

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

      1. *-commutative 53.5%

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

   5. Simplified 53.5%

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

   6. Taylor expanded in a around inf 47.2%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{+214}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;i \leq -0.00016:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-254}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 2.4 \cdot 10^{-290}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 3.3 \cdot 10^{-241}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ t_2 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -3.8 \cdot 10^{+123}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{-112}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* z (- y (* b (/ c x)))) (* t a))))
        (t_2 (* j (- (* t c) (* y i)))))
   (if (<= j -3.8e+123)
     t_2
     (if (<= j -2.05e-112)
       t_1
       (if (<= j 4.5e-227)
         (+ (* x (* y z)) (* b (- (* a i) (* z c))))
         (if (<= j 1.35e+96) 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 * ((z * (y - (b * (c / x)))) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.8e+123) {
		tmp = t_2;
	} else if (j <= -2.05e-112) {
		tmp = t_1;
	} else if (j <= 4.5e-227) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (j <= 1.35e+96) {
		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 * ((z * (y - (b * (c / x)))) - (t * a))
    t_2 = j * ((t * c) - (y * i))
    if (j <= (-3.8d+123)) then
        tmp = t_2
    else if (j <= (-2.05d-112)) then
        tmp = t_1
    else if (j <= 4.5d-227) then
        tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
    else if (j <= 1.35d+96) 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 * ((z * (y - (b * (c / x)))) - (t * a));
	double t_2 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -3.8e+123) {
		tmp = t_2;
	} else if (j <= -2.05e-112) {
		tmp = t_1;
	} else if (j <= 4.5e-227) {
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	} else if (j <= 1.35e+96) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((z * (y - (b * (c / x)))) - (t * a))
	t_2 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -3.8e+123:
		tmp = t_2
	elif j <= -2.05e-112:
		tmp = t_1
	elif j <= 4.5e-227:
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)))
	elif j <= 1.35e+96:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(z * Float64(y - Float64(b * Float64(c / x)))) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -3.8e+123)
		tmp = t_2;
	elseif (j <= -2.05e-112)
		tmp = t_1;
	elseif (j <= 4.5e-227)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	elseif (j <= 1.35e+96)
		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 * ((z * (y - (b * (c / x)))) - (t * a));
	t_2 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -3.8e+123)
		tmp = t_2;
	elseif (j <= -2.05e-112)
		tmp = t_1;
	elseif (j <= 4.5e-227)
		tmp = (x * (y * z)) + (b * ((a * i) - (z * c)));
	elseif (j <= 1.35e+96)
		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[(x * N[(N[(z * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -3.8e+123], t$95$2, If[LessEqual[j, -2.05e-112], t$95$1, If[LessEqual[j, 4.5e-227], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.35e+96], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -3.79999999999999994e123 or 1.35000000000000011e96 < j

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 81.6%

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

   if -3.79999999999999994e123 < j < -2.04999999999999998e-112 or 4.49999999999999993e-227 < j < 1.35000000000000011e96

   1. Initial program 71.5%

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

   3. Taylor expanded in j around 0 67.8%

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

      1. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in x around inf 65.6%

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

      1. +-commutative 65.6%

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

      2. mul-1-neg 65.6%

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

      3. unsub-neg 65.6%

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

      4. *-commutative 65.6%

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

      5. associate-/l* 67.3%

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

      6. *-commutative 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in i around 0 56.8%

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

       1. +-commutative 56.8%

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

       2. associate--r+ 56.8%

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

   11. Simplified 66.8%

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

   if -2.04999999999999998e-112 < j < 4.49999999999999993e-227

   1. Initial program 70.5%

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

   3. Taylor expanded in j around 0 74.2%

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

      1. *-commutative 74.2%

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

   5. Simplified 74.2%

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

   6. Taylor expanded in y around inf 68.7%

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

      1. *-commutative 68.7%

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

   8. Simplified 68.7%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -3.8 \cdot 10^{+123}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.05 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-227}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.35 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(z \cdot \left(y - b \cdot \frac{c}{x}\right) - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right)\\ t_2 := b \cdot \left(a \cdot i - z \cdot c\right)\\ t_3 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-270}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-141}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (* i j))))
        (t_2 (* b (- (* a i) (* z c))))
        (t_3 (* t (- (* c j) (* x a)))))
   (if (<= t -4.5e-21)
     t_3
     (if (<= t -1e-270)
       t_2
       (if (<= t 5.2e-179)
         t_1
         (if (<= t 1.9e-141) t_2 (if (<= t 1.9e+80) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4.5e-21) {
		tmp = t_3;
	} else if (t <= -1e-270) {
		tmp = t_2;
	} else if (t <= 5.2e-179) {
		tmp = t_1;
	} else if (t <= 1.9e-141) {
		tmp = t_2;
	} else if (t <= 1.9e+80) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((x * z) - (i * j))
    t_2 = b * ((a * i) - (z * c))
    t_3 = t * ((c * j) - (x * a))
    if (t <= (-4.5d-21)) then
        tmp = t_3
    else if (t <= (-1d-270)) then
        tmp = t_2
    else if (t <= 5.2d-179) then
        tmp = t_1
    else if (t <= 1.9d-141) then
        tmp = t_2
    else if (t <= 1.9d+80) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * ((x * z) - (i * j));
	double t_2 = b * ((a * i) - (z * c));
	double t_3 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -4.5e-21) {
		tmp = t_3;
	} else if (t <= -1e-270) {
		tmp = t_2;
	} else if (t <= 5.2e-179) {
		tmp = t_1;
	} else if (t <= 1.9e-141) {
		tmp = t_2;
	} else if (t <= 1.9e+80) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - (i * j))
	t_2 = b * ((a * i) - (z * c))
	t_3 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -4.5e-21:
		tmp = t_3
	elif t <= -1e-270:
		tmp = t_2
	elif t <= 5.2e-179:
		tmp = t_1
	elif t <= 1.9e-141:
		tmp = t_2
	elif t <= 1.9e+80:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	t_2 = Float64(b * Float64(Float64(a * i) - Float64(z * c)))
	t_3 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -4.5e-21)
		tmp = t_3;
	elseif (t <= -1e-270)
		tmp = t_2;
	elseif (t <= 5.2e-179)
		tmp = t_1;
	elseif (t <= 1.9e-141)
		tmp = t_2;
	elseif (t <= 1.9e+80)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * ((x * z) - (i * j));
	t_2 = b * ((a * i) - (z * c));
	t_3 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -4.5e-21)
		tmp = t_3;
	elseif (t <= -1e-270)
		tmp = t_2;
	elseif (t <= 5.2e-179)
		tmp = t_1;
	elseif (t <= 1.9e-141)
		tmp = t_2;
	elseif (t <= 1.9e+80)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e-21], t$95$3, If[LessEqual[t, -1e-270], t$95$2, If[LessEqual[t, 5.2e-179], t$95$1, If[LessEqual[t, 1.9e-141], t$95$2, If[LessEqual[t, 1.9e+80], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.49999999999999968e-21 or 1.89999999999999999e80 < t

   1. Initial program 64.1%

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

   3. Taylor expanded in t around inf 71.0%

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

      1. +-commutative 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. *-commutative 71.0%

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

      5. *-commutative 71.0%

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

   5. Simplified 71.0%

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

   if -4.49999999999999968e-21 < t < -1e-270 or 5.20000000000000011e-179 < t < 1.89999999999999993e-141

   1. Initial program 84.1%

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

   3. Taylor expanded in b around inf 60.8%

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

      1. *-commutative 60.8%

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

   5. Simplified 60.8%

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

   if -1e-270 < t < 5.20000000000000011e-179 or 1.89999999999999993e-141 < t < 1.89999999999999999e80

   1. Initial program 77.7%

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

   3. Taylor expanded in y around inf 53.9%

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

      1. +-commutative 53.9%

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

      2. mul-1-neg 53.9%

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

      3. unsub-neg 53.9%

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

   5. Simplified 53.9%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{-21}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-270}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-141}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+80}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -3.45 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 8.4 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= i -3.45e-6)
     t_1
     (if (<= i -2.1e-256)
       (* t (* x (- a)))
       (if (<= i 1.7e-289)
         (* c (* t j))
         (if (<= i 8.5e-239)
           (* c (* z (- b)))
           (if (<= i 8.4e+40) (* t (* c j)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (i <= -3.45e-6) {
		tmp = t_1;
	} else if (i <= -2.1e-256) {
		tmp = t * (x * -a);
	} else if (i <= 1.7e-289) {
		tmp = c * (t * j);
	} else if (i <= 8.5e-239) {
		tmp = c * (z * -b);
	} else if (i <= 8.4e+40) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (i <= (-3.45d-6)) then
        tmp = t_1
    else if (i <= (-2.1d-256)) then
        tmp = t * (x * -a)
    else if (i <= 1.7d-289) then
        tmp = c * (t * j)
    else if (i <= 8.5d-239) then
        tmp = c * (z * -b)
    else if (i <= 8.4d+40) then
        tmp = t * (c * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (i <= -3.45e-6) {
		tmp = t_1;
	} else if (i <= -2.1e-256) {
		tmp = t * (x * -a);
	} else if (i <= 1.7e-289) {
		tmp = c * (t * j);
	} else if (i <= 8.5e-239) {
		tmp = c * (z * -b);
	} else if (i <= 8.4e+40) {
		tmp = t * (c * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if i <= -3.45e-6:
		tmp = t_1
	elif i <= -2.1e-256:
		tmp = t * (x * -a)
	elif i <= 1.7e-289:
		tmp = c * (t * j)
	elif i <= 8.5e-239:
		tmp = c * (z * -b)
	elif i <= 8.4e+40:
		tmp = t * (c * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -3.45e-6)
		tmp = t_1;
	elseif (i <= -2.1e-256)
		tmp = Float64(t * Float64(x * Float64(-a)));
	elseif (i <= 1.7e-289)
		tmp = Float64(c * Float64(t * j));
	elseif (i <= 8.5e-239)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (i <= 8.4e+40)
		tmp = Float64(t * Float64(c * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (i <= -3.45e-6)
		tmp = t_1;
	elseif (i <= -2.1e-256)
		tmp = t * (x * -a);
	elseif (i <= 1.7e-289)
		tmp = c * (t * j);
	elseif (i <= 8.5e-239)
		tmp = c * (z * -b);
	elseif (i <= 8.4e+40)
		tmp = t * (c * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.45e-6], t$95$1, If[LessEqual[i, -2.1e-256], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.7e-289], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.5e-239], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 8.4e+40], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.45e-6 or 8.4000000000000004e40 < i

   1. Initial program 65.0%

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

   3. Taylor expanded in b around inf 47.1%

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

      1. *-commutative 47.1%

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

   5. Simplified 47.1%

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

   6. Taylor expanded in a around inf 44.7%

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

   if -3.45e-6 < i < -2.10000000000000003e-256

   1. Initial program 86.4%

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

   3. Taylor expanded in t around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. mul-1-neg 49.2%

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

      3. unsub-neg 49.2%

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

      4. *-commutative 49.2%

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

      5. *-commutative 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in j around 0 40.6%

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

      1. mul-1-neg 40.6%

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

      2. distribute-rgt-neg-in 40.6%

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

   8. Simplified 40.6%

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

   if -2.10000000000000003e-256 < i < 1.70000000000000009e-289

   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. Taylor expanded in t around inf 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

      4. *-commutative 54.1%

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

      5. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in j around inf 48.0%

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

   if 1.70000000000000009e-289 < i < 8.49999999999999958e-239

   1. Initial program 71.2%

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

   3. Taylor expanded in c around inf 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in t around 0 51.2%

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

      1. mul-1-neg 51.2%

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

      2. associate-*r* 44.6%

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

      3. *-commutative 44.6%

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

      4. *-commutative 44.6%

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

      5. *-commutative 44.6%

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

      6. associate-*l* 51.5%

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

      7. *-commutative 51.5%

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

      8. distribute-rgt-neg-in 51.5%

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

      9. distribute-lft-neg-in 51.5%

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

      10. *-commutative 51.5%

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

   8. Simplified 51.5%

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

   if 8.49999999999999958e-239 < i < 8.4000000000000004e40

   1. Initial program 77.0%

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

   3. Taylor expanded in t around inf 59.2%

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

      1. +-commutative 59.2%

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

      2. mul-1-neg 59.2%

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

      3. unsub-neg 59.2%

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

      4. *-commutative 59.2%

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

      5. *-commutative 59.2%

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

   5. Simplified 59.2%

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

   6. Taylor expanded in j around inf 38.6%

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

      1. associate-*r* 45.3%

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

   8. Simplified 45.3%

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

4. Final simplification 44.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.45 \cdot 10^{-6}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -2.1 \cdot 10^{-256}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;i \leq 1.7 \cdot 10^{-289}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-239}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;i \leq 8.4 \cdot 10^{+40}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(a \cdot b - y \cdot j\right)\\ t_2 := t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* a b) (* y j)))) (t_2 (* t (- (* c j) (* x a)))))
   (if (<= t -9.2e+42)
     t_2
     (if (<= t -2.05e-170)
       t_1
       (if (<= t -2e-233)
         (* z (- (* x y) (* b c)))
         (if (<= t 1.05e+81) 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 = i * ((a * b) - (y * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -9.2e+42) {
		tmp = t_2;
	} else if (t <= -2.05e-170) {
		tmp = t_1;
	} else if (t <= -2e-233) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.05e+81) {
		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 = i * ((a * b) - (y * j))
    t_2 = t * ((c * j) - (x * a))
    if (t <= (-9.2d+42)) then
        tmp = t_2
    else if (t <= (-2.05d-170)) then
        tmp = t_1
    else if (t <= (-2d-233)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1.05d+81) 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 = i * ((a * b) - (y * j));
	double t_2 = t * ((c * j) - (x * a));
	double tmp;
	if (t <= -9.2e+42) {
		tmp = t_2;
	} else if (t <= -2.05e-170) {
		tmp = t_1;
	} else if (t <= -2e-233) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1.05e+81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((a * b) - (y * j))
	t_2 = t * ((c * j) - (x * a))
	tmp = 0
	if t <= -9.2e+42:
		tmp = t_2
	elif t <= -2.05e-170:
		tmp = t_1
	elif t <= -2e-233:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1.05e+81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(a * b) - Float64(y * j)))
	t_2 = Float64(t * Float64(Float64(c * j) - Float64(x * a)))
	tmp = 0.0
	if (t <= -9.2e+42)
		tmp = t_2;
	elseif (t <= -2.05e-170)
		tmp = t_1;
	elseif (t <= -2e-233)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1.05e+81)
		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 = i * ((a * b) - (y * j));
	t_2 = t * ((c * j) - (x * a));
	tmp = 0.0;
	if (t <= -9.2e+42)
		tmp = t_2;
	elseif (t <= -2.05e-170)
		tmp = t_1;
	elseif (t <= -2e-233)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1.05e+81)
		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[(i * N[(N[(a * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9.2e+42], t$95$2, If[LessEqual[t, -2.05e-170], t$95$1, If[LessEqual[t, -2e-233], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.05e+81], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.2e42 or 1.0499999999999999e81 < t

   1. Initial program 63.1%

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

   3. Taylor expanded in t around inf 73.0%

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

      1. +-commutative 73.0%

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

      2. mul-1-neg 73.0%

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

      3. unsub-neg 73.0%

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

      4. *-commutative 73.0%

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

      5. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -9.2e42 < t < -2.04999999999999983e-170 or -1.99999999999999992e-233 < t < 1.0499999999999999e81

   1. Initial program 79.6%

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

   3. Taylor expanded in i around inf 60.0%

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

      1. distribute-lft-out-- 60.0%

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

      2. *-commutative 60.0%

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

   5. Simplified 60.0%

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

   if -2.04999999999999983e-170 < t < -1.99999999999999992e-233

   1. Initial program 83.7%

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

   3. Taylor expanded in z around inf 75.4%

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

      1. *-commutative 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.2 \cdot 10^{+42}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{-170}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{+81}:\\ \;\;\;\;i \cdot \left(a \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 67.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -1.7e+101)
     t_1
     (if (<= j 1.65e-41)
       (+ (* x (- (* y z) (* t a))) (* b (- (* a i) (* z c))))
       (- t_1 (* x (- (* t a) (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.7e+101) {
		tmp = t_1;
	} else if (j <= 1.65e-41) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((t * c) - (y * i))
    if (j <= (-1.7d+101)) then
        tmp = t_1
    else if (j <= 1.65d-41) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
    else
        tmp = t_1 - (x * ((t * a) - (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -1.7e+101) {
		tmp = t_1;
	} else if (j <= 1.65e-41) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	} else {
		tmp = t_1 - (x * ((t * a) - (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -1.7e+101:
		tmp = t_1
	elif j <= 1.65e-41:
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)))
	else:
		tmp = t_1 - (x * ((t * a) - (y * z)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.7e+101)
		tmp = t_1;
	elseif (j <= 1.65e-41)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(a * i) - Float64(z * c))));
	else
		tmp = Float64(t_1 - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.7e+101)
		tmp = t_1;
	elseif (j <= 1.65e-41)
		tmp = (x * ((y * z) - (t * a))) + (b * ((a * i) - (z * c)));
	else
		tmp = t_1 - (x * ((t * a) - (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e+101], t$95$1, If[LessEqual[j, 1.65e-41], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.70000000000000009e101

   1. Initial program 74.9%

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

   3. Taylor expanded in j around inf 78.2%

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

   if -1.70000000000000009e101 < j < 1.65000000000000012e-41

   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 j around 0 73.1%

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

      1. *-commutative 73.1%

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

   5. Simplified 73.1%

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

   if 1.65000000000000012e-41 < j

   1. Initial program 71.1%

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

   3. Taylor expanded in b around 0 75.9%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+101}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 1.65 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(c \cdot j\right)\\ \mathbf{if}\;j \leq -1.32 \cdot 10^{+74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-111}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 2.75 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (* c j))))
   (if (<= j -1.32e+74)
     t_1
     (if (<= j -1.2e-112)
       (* x (* t (- a)))
       (if (<= j 4.5e-111)
         (* i (* a b))
         (if (<= j 2.75e+100) (* t (* x (- a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (j <= -1.32e+74) {
		tmp = t_1;
	} else if (j <= -1.2e-112) {
		tmp = x * (t * -a);
	} else if (j <= 4.5e-111) {
		tmp = i * (a * b);
	} else if (j <= 2.75e+100) {
		tmp = t * (x * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (c * j)
    if (j <= (-1.32d+74)) then
        tmp = t_1
    else if (j <= (-1.2d-112)) then
        tmp = x * (t * -a)
    else if (j <= 4.5d-111) then
        tmp = i * (a * b)
    else if (j <= 2.75d+100) then
        tmp = t * (x * -a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * (c * j);
	double tmp;
	if (j <= -1.32e+74) {
		tmp = t_1;
	} else if (j <= -1.2e-112) {
		tmp = x * (t * -a);
	} else if (j <= 4.5e-111) {
		tmp = i * (a * b);
	} else if (j <= 2.75e+100) {
		tmp = t * (x * -a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * (c * j)
	tmp = 0
	if j <= -1.32e+74:
		tmp = t_1
	elif j <= -1.2e-112:
		tmp = x * (t * -a)
	elif j <= 4.5e-111:
		tmp = i * (a * b)
	elif j <= 2.75e+100:
		tmp = t * (x * -a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(c * j))
	tmp = 0.0
	if (j <= -1.32e+74)
		tmp = t_1;
	elseif (j <= -1.2e-112)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (j <= 4.5e-111)
		tmp = Float64(i * Float64(a * b));
	elseif (j <= 2.75e+100)
		tmp = Float64(t * Float64(x * Float64(-a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = t * (c * j);
	tmp = 0.0;
	if (j <= -1.32e+74)
		tmp = t_1;
	elseif (j <= -1.2e-112)
		tmp = x * (t * -a);
	elseif (j <= 4.5e-111)
		tmp = i * (a * b);
	elseif (j <= 2.75e+100)
		tmp = t * (x * -a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.32e+74], t$95$1, If[LessEqual[j, -1.2e-112], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.5e-111], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.75e+100], N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.32000000000000012e74 or 2.7500000000000001e100 < j

   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 t around inf 55.8%

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

      1. +-commutative 55.8%

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

      2. mul-1-neg 55.8%

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

      3. unsub-neg 55.8%

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

      4. *-commutative 55.8%

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

      5. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   6. Taylor expanded in j around inf 43.2%

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

      1. associate-*r* 51.0%

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

   8. Simplified 51.0%

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

   if -1.32000000000000012e74 < j < -1.2e-112

   1. Initial program 73.1%

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

   3. Taylor expanded in j around 0 77.3%

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

      1. *-commutative 77.3%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in x around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

      4. *-commutative 75.3%

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

      5. associate-/l* 75.3%

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

      6. *-commutative 75.3%

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

   8. Simplified 75.3%

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

   9. Taylor expanded in t around inf 41.1%

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

       1. neg-mul-1 41.1%

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

       2. distribute-rgt-neg-in 41.1%

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

   11. Simplified 41.1%

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

   if -1.2e-112 < j < 4.49999999999999994e-111

   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 j around 0 72.3%

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

      1. *-commutative 72.3%

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

   5. Simplified 72.3%

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

   6. Taylor expanded in x around inf 67.4%

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

      1. +-commutative 67.4%

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

      2. mul-1-neg 67.4%

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

      3. unsub-neg 67.4%

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

      4. *-commutative 67.4%

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

      5. associate-/l* 67.4%

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

      6. *-commutative 67.4%

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

   8. Simplified 67.4%

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

   9. Taylor expanded in i around inf 38.4%

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

       1. associate-*r* 40.0%

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

       2. *-commutative 40.0%

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

   11. Simplified 40.0%

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

   if 4.49999999999999994e-111 < j < 2.7500000000000001e100

   1. Initial program 68.6%

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

   3. Taylor expanded in t around inf 44.0%

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

      1. +-commutative 44.0%

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

      2. mul-1-neg 44.0%

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

      3. unsub-neg 44.0%

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

      4. *-commutative 44.0%

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

      5. *-commutative 44.0%

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

   5. Simplified 44.0%

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

   6. Taylor expanded in j around 0 38.8%

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

      1. mul-1-neg 38.8%

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

      2. distribute-rgt-neg-in 38.8%

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

   8. Simplified 38.8%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.32 \cdot 10^{+74}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq -1.2 \cdot 10^{-112}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{-111}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \mathbf{elif}\;j \leq 2.75 \cdot 10^{+100}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(b \cdot i\right)\\ \mathbf{if}\;i \leq -52000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-165} \lor \neg \left(i \leq 9.2 \cdot 10^{-63}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* b i))))
   (if (<= i -52000000.0)
     t_1
     (if (<= i -8e-142)
       (* x (* y z))
       (if (or (<= i -1.05e-165) (not (<= i 9.2e-63))) t_1 (* c (* t j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (i <= -52000000.0) {
		tmp = t_1;
	} else if (i <= -8e-142) {
		tmp = x * (y * z);
	} else if ((i <= -1.05e-165) || !(i <= 9.2e-63)) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (b * i)
    if (i <= (-52000000.0d0)) then
        tmp = t_1
    else if (i <= (-8d-142)) then
        tmp = x * (y * z)
    else if ((i <= (-1.05d-165)) .or. (.not. (i <= 9.2d-63))) then
        tmp = t_1
    else
        tmp = c * (t * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (b * i);
	double tmp;
	if (i <= -52000000.0) {
		tmp = t_1;
	} else if (i <= -8e-142) {
		tmp = x * (y * z);
	} else if ((i <= -1.05e-165) || !(i <= 9.2e-63)) {
		tmp = t_1;
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (b * i)
	tmp = 0
	if i <= -52000000.0:
		tmp = t_1
	elif i <= -8e-142:
		tmp = x * (y * z)
	elif (i <= -1.05e-165) or not (i <= 9.2e-63):
		tmp = t_1
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(b * i))
	tmp = 0.0
	if (i <= -52000000.0)
		tmp = t_1;
	elseif (i <= -8e-142)
		tmp = Float64(x * Float64(y * z));
	elseif ((i <= -1.05e-165) || !(i <= 9.2e-63))
		tmp = t_1;
	else
		tmp = Float64(c * Float64(t * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (b * i);
	tmp = 0.0;
	if (i <= -52000000.0)
		tmp = t_1;
	elseif (i <= -8e-142)
		tmp = x * (y * z);
	elseif ((i <= -1.05e-165) || ~((i <= 9.2e-63)))
		tmp = t_1;
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -52000000.0], t$95$1, If[LessEqual[i, -8e-142], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, -1.05e-165], N[Not[LessEqual[i, 9.2e-63]], $MachinePrecision]], t$95$1, N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -5.2e7 or -8.0000000000000003e-142 < i < -1.04999999999999997e-165 or 9.2e-63 < i

   1. Initial program 66.4%

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

   3. Taylor expanded in b around inf 46.7%

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

      1. *-commutative 46.7%

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

   5. Simplified 46.7%

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

   6. Taylor expanded in a around inf 42.6%

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

   if -5.2e7 < i < -8.0000000000000003e-142

   1. Initial program 75.8%

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

   3. Taylor expanded in j around 0 64.1%

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

      1. *-commutative 64.1%

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

   5. Simplified 64.1%

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

   6. Taylor expanded in x around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

      5. associate-/l* 72.1%

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

      6. *-commutative 72.1%

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

   8. Simplified 72.1%

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

   9. Taylor expanded in y around inf 37.2%

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

       1. *-commutative 37.2%

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

   11. Simplified 37.2%

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

   if -1.04999999999999997e-165 < i < 9.2e-63

   1. Initial program 82.2%

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

   3. Taylor expanded in t around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

      5. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in j around inf 34.2%

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

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -52000000:\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-142}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-165} \lor \neg \left(i \leq 9.2 \cdot 10^{-63}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 52.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -5.4 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* t c) (* y i)))))
   (if (<= j -2.5e+101)
     t_1
     (if (<= j -5.4e-39)
       (* t (- (* c j) (* x a)))
       (if (<= j 2.2e+60) (* 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.5e+101) {
		tmp = t_1;
	} else if (j <= -5.4e-39) {
		tmp = t * ((c * j) - (x * a));
	} else if (j <= 2.2e+60) {
		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 = j * ((t * c) - (y * i))
    if (j <= (-2.5d+101)) then
        tmp = t_1
    else if (j <= (-5.4d-39)) then
        tmp = t * ((c * j) - (x * a))
    else if (j <= 2.2d+60) 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 = j * ((t * c) - (y * i));
	double tmp;
	if (j <= -2.5e+101) {
		tmp = t_1;
	} else if (j <= -5.4e-39) {
		tmp = t * ((c * j) - (x * a));
	} else if (j <= 2.2e+60) {
		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 = j * ((t * c) - (y * i))
	tmp = 0
	if j <= -2.5e+101:
		tmp = t_1
	elif j <= -5.4e-39:
		tmp = t * ((c * j) - (x * a))
	elif j <= 2.2e+60:
		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(j * Float64(Float64(t * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -2.5e+101)
		tmp = t_1;
	elseif (j <= -5.4e-39)
		tmp = Float64(t * Float64(Float64(c * j) - Float64(x * a)));
	elseif (j <= 2.2e+60)
		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 = j * ((t * c) - (y * i));
	tmp = 0.0;
	if (j <= -2.5e+101)
		tmp = t_1;
	elseif (j <= -5.4e-39)
		tmp = t * ((c * j) - (x * a));
	elseif (j <= 2.2e+60)
		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[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e+101], t$95$1, If[LessEqual[j, -5.4e-39], N[(t * N[(N[(c * j), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.2e+60], 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 j < -2.49999999999999994e101 or 2.19999999999999996e60 < j

   1. Initial program 76.4%

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

   3. Taylor expanded in j around inf 78.4%

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

   if -2.49999999999999994e101 < j < -5.4000000000000001e-39

   1. Initial program 73.6%

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

   3. Taylor expanded in t around inf 56.3%

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

      1. +-commutative 56.3%

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

      2. mul-1-neg 56.3%

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

      3. unsub-neg 56.3%

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

      4. *-commutative 56.3%

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

      5. *-commutative 56.3%

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

   5. Simplified 56.3%

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

   if -5.4000000000000001e-39 < j < 2.19999999999999996e60

   1. Initial program 69.9%

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

   3. Taylor expanded in b around inf 48.6%

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

      1. *-commutative 48.6%

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

   5. Simplified 48.6%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{+101}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -5.4 \cdot 10^{-39}:\\ \;\;\;\;t \cdot \left(c \cdot j - x \cdot a\right)\\ \mathbf{elif}\;j \leq 2.2 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 42.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+264}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -1.25e+80)
   (* t (* c j))
   (if (<= j 2.85e+57)
     (* b (- (* a i) (* z c)))
     (if (<= j 4e+264) (* y (- (* i j))) (* 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 (j <= -1.25e+80) {
		tmp = t * (c * j);
	} else if (j <= 2.85e+57) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 4e+264) {
		tmp = y * -(i * j);
	} 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 (j <= (-1.25d+80)) then
        tmp = t * (c * j)
    else if (j <= 2.85d+57) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 4d+264) then
        tmp = y * -(i * j)
    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 (j <= -1.25e+80) {
		tmp = t * (c * j);
	} else if (j <= 2.85e+57) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 4e+264) {
		tmp = y * -(i * j);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -1.25e+80:
		tmp = t * (c * j)
	elif j <= 2.85e+57:
		tmp = b * ((a * i) - (z * c))
	elif j <= 4e+264:
		tmp = y * -(i * j)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -1.25e+80)
		tmp = Float64(t * Float64(c * j));
	elseif (j <= 2.85e+57)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 4e+264)
		tmp = Float64(y * Float64(-Float64(i * j)));
	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 (j <= -1.25e+80)
		tmp = t * (c * j);
	elseif (j <= 2.85e+57)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 4e+264)
		tmp = y * -(i * j);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -1.25e+80], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.85e+57], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4e+264], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.2499999999999999e80

   1. Initial program 74.9%

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

   3. Taylor expanded in t around inf 57.3%

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

      1. +-commutative 57.3%

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

      2. mul-1-neg 57.3%

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

      3. unsub-neg 57.3%

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

      4. *-commutative 57.3%

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

      5. *-commutative 57.3%

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

   5. Simplified 57.3%

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

   6. Taylor expanded in j around inf 45.0%

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

      1. associate-*r* 55.3%

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

   8. Simplified 55.3%

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

   if -1.2499999999999999e80 < j < 2.8499999999999999e57

   1. Initial program 71.2%

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

   3. Taylor expanded in b around inf 46.4%

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

      1. *-commutative 46.4%

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

   5. Simplified 46.4%

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

   if 2.8499999999999999e57 < j < 4.00000000000000018e264

   1. Initial program 78.3%

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

   3. Taylor expanded in y around -inf 58.1%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in y around inf 51.1%

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

      1. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   9. Taylor expanded in x around 0 45.8%

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

       1. neg-mul-1 45.8%

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

       2. *-commutative 45.8%

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

       3. distribute-rgt-neg-in 45.8%

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

   11. Simplified 45.8%

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

   if 4.00000000000000018e264 < j

   1. Initial program 57.1%

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

   3. Taylor expanded in t around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. *-commutative 72.2%

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

      5. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in j around inf 85.7%

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

4. Final simplification 48.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{+80}:\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.85 \cdot 10^{+57}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4 \cdot 10^{+264}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 44.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -26000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+265}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -26000.0)
   (* c (- (* t j) (* z b)))
   (if (<= j 6.3e+56)
     (* b (- (* a i) (* z c)))
     (if (<= j 1.05e+265) (* y (- (* i j))) (* 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 (j <= -26000.0) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= 6.3e+56) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 1.05e+265) {
		tmp = y * -(i * j);
	} 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 (j <= (-26000.0d0)) then
        tmp = c * ((t * j) - (z * b))
    else if (j <= 6.3d+56) then
        tmp = b * ((a * i) - (z * c))
    else if (j <= 1.05d+265) then
        tmp = y * -(i * j)
    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 (j <= -26000.0) {
		tmp = c * ((t * j) - (z * b));
	} else if (j <= 6.3e+56) {
		tmp = b * ((a * i) - (z * c));
	} else if (j <= 1.05e+265) {
		tmp = y * -(i * j);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -26000.0:
		tmp = c * ((t * j) - (z * b))
	elif j <= 6.3e+56:
		tmp = b * ((a * i) - (z * c))
	elif j <= 1.05e+265:
		tmp = y * -(i * j)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -26000.0)
		tmp = Float64(c * Float64(Float64(t * j) - Float64(z * b)));
	elseif (j <= 6.3e+56)
		tmp = Float64(b * Float64(Float64(a * i) - Float64(z * c)));
	elseif (j <= 1.05e+265)
		tmp = Float64(y * Float64(-Float64(i * j)));
	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 (j <= -26000.0)
		tmp = c * ((t * j) - (z * b));
	elseif (j <= 6.3e+56)
		tmp = b * ((a * i) - (z * c));
	elseif (j <= 1.05e+265)
		tmp = y * -(i * j);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -26000.0], N[(c * N[(N[(t * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.3e+56], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.05e+265], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -26000

   1. Initial program 75.0%

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

   3. Taylor expanded in c around inf 49.7%

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

      1. *-commutative 49.7%

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

      2. *-commutative 49.7%

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

   5. Simplified 49.7%

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

   if -26000 < j < 6.3000000000000001e56

   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 b around inf 48.4%

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

      1. *-commutative 48.4%

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

   5. Simplified 48.4%

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

   if 6.3000000000000001e56 < j < 1.0499999999999999e265

   1. Initial program 78.3%

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

   3. Taylor expanded in y around -inf 58.1%

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

   5. Simplified 65.9%

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

   6. Taylor expanded in y around inf 51.1%

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

      1. *-commutative 51.1%

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

   8. Simplified 51.1%

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

   9. Taylor expanded in x around 0 45.8%

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

       1. neg-mul-1 45.8%

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

       2. *-commutative 45.8%

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

       3. distribute-rgt-neg-in 45.8%

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

   11. Simplified 45.8%

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

   if 1.0499999999999999e265 < j

   1. Initial program 57.1%

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

   3. Taylor expanded in t around inf 72.2%

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

      1. +-commutative 72.2%

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

      2. mul-1-neg 72.2%

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

      3. unsub-neg 72.2%

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

      4. *-commutative 72.2%

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

      5. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in j around inf 85.7%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -26000:\\ \;\;\;\;c \cdot \left(t \cdot j - z \cdot b\right)\\ \mathbf{elif}\;j \leq 6.3 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.05 \cdot 10^{+265}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -20000 \lor \neg \left(j \leq 1.3 \cdot 10^{+64}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -20000.0) (not (<= j 1.3e+64)))
   (* j (- (* t c) (* y i)))
   (* 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 ((j <= -20000.0) || !(j <= 1.3e+64)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = 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 ((j <= (-20000.0d0)) .or. (.not. (j <= 1.3d+64))) then
        tmp = j * ((t * c) - (y * i))
    else
        tmp = 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 ((j <= -20000.0) || !(j <= 1.3e+64)) {
		tmp = j * ((t * c) - (y * i));
	} else {
		tmp = b * ((a * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -20000.0) or not (j <= 1.3e+64):
		tmp = j * ((t * c) - (y * i))
	else:
		tmp = b * ((a * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -20000.0) || !(j <= 1.3e+64))
		tmp = Float64(j * Float64(Float64(t * c) - Float64(y * i)));
	else
		tmp = 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 ((j <= -20000.0) || ~((j <= 1.3e+64)))
		tmp = j * ((t * c) - (y * i));
	else
		tmp = b * ((a * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -20000.0], N[Not[LessEqual[j, 1.3e+64]], $MachinePrecision]], N[(j * N[(N[(t * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(a * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -2e4 or 1.29999999999999998e64 < j

   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 j around inf 70.6%

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

   if -2e4 < j < 1.29999999999999998e64

   1. Initial program 70.4%

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

   3. Taylor expanded in b around inf 47.8%

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

      1. *-commutative 47.8%

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

   5. Simplified 47.8%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -20000 \lor \neg \left(j \leq 1.3 \cdot 10^{+64}\right):\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(a \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.35 \cdot 10^{-165} \lor \neg \left(i \leq 1.7 \cdot 10^{-62}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.35e-165) (not (<= i 1.7e-62))) (* a (* b i)) (* 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 ((i <= -1.35e-165) || !(i <= 1.7e-62)) {
		tmp = a * (b * i);
	} 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 ((i <= (-1.35d-165)) .or. (.not. (i <= 1.7d-62))) then
        tmp = a * (b * i)
    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 ((i <= -1.35e-165) || !(i <= 1.7e-62)) {
		tmp = a * (b * i);
	} else {
		tmp = c * (t * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.35e-165) or not (i <= 1.7e-62):
		tmp = a * (b * i)
	else:
		tmp = c * (t * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.35e-165) || !(i <= 1.7e-62))
		tmp = Float64(a * Float64(b * i));
	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 ((i <= -1.35e-165) || ~((i <= 1.7e-62)))
		tmp = a * (b * i);
	else
		tmp = c * (t * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.35e-165], N[Not[LessEqual[i, 1.7e-62]], $MachinePrecision]], N[(a * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.3499999999999999e-165 or 1.69999999999999994e-62 < i

   1. Initial program 67.8%

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

   3. Taylor expanded in b around inf 44.2%

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

      1. *-commutative 44.2%

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

   5. Simplified 44.2%

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

   6. Taylor expanded in a around inf 38.9%

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

   if -1.3499999999999999e-165 < i < 1.69999999999999994e-62

   1. Initial program 82.2%

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

   3. Taylor expanded in t around inf 54.4%

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

      1. +-commutative 54.4%

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

      2. mul-1-neg 54.4%

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

      3. unsub-neg 54.4%

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

      4. *-commutative 54.4%

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

      5. *-commutative 54.4%

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

   5. Simplified 54.4%

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

   6. Taylor expanded in j around inf 34.2%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.35 \cdot 10^{-165} \lor \neg \left(i \leq 1.7 \cdot 10^{-62}\right):\\ \;\;\;\;a \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 31.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.22 \cdot 10^{+16} \lor \neg \left(j \leq 6.2 \cdot 10^{+63}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.22e+16) (not (<= j 6.2e+63))) (* 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 ((j <= -1.22e+16) || !(j <= 6.2e+63)) {
		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 ((j <= (-1.22d+16)) .or. (.not. (j <= 6.2d+63))) 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 ((j <= -1.22e+16) || !(j <= 6.2e+63)) {
		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 (j <= -1.22e+16) or not (j <= 6.2e+63):
		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 ((j <= -1.22e+16) || !(j <= 6.2e+63))
		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 ((j <= -1.22e+16) || ~((j <= 6.2e+63)))
		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[j, -1.22e+16], N[Not[LessEqual[j, 6.2e+63]], $MachinePrecision]], N[(c * N[(t * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.22e16 or 6.2000000000000001e63 < j

   1. Initial program 75.0%

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

   3. Taylor expanded in t around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

      4. *-commutative 54.8%

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

      5. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in j around inf 39.3%

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

   if -1.22e16 < j < 6.2000000000000001e63

   1. Initial program 70.8%

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

   3. Taylor expanded in j around 0 69.5%

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

      1. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in x around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

      5. associate-/l* 66.6%

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

      6. *-commutative 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in i around inf 33.6%

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

       1. associate-*r* 34.4%

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

       2. *-commutative 34.4%

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

   11. Simplified 34.4%

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

4. Final simplification 36.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.22 \cdot 10^{+16} \lor \neg \left(j \leq 6.2 \cdot 10^{+63}\right):\\ \;\;\;\;c \cdot \left(t \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 31.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -6.6 \cdot 10^{+25} \lor \neg \left(j \leq 1.6 \cdot 10^{+65}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -6.6e+25) (not (<= j 1.6e+65))) (* t (* c 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 ((j <= -6.6e+25) || !(j <= 1.6e+65)) {
		tmp = t * (c * 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 ((j <= (-6.6d+25)) .or. (.not. (j <= 1.6d+65))) then
        tmp = t * (c * 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 ((j <= -6.6e+25) || !(j <= 1.6e+65)) {
		tmp = t * (c * j);
	} else {
		tmp = i * (a * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -6.6e+25) or not (j <= 1.6e+65):
		tmp = t * (c * j)
	else:
		tmp = i * (a * b)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -6.6e+25) || !(j <= 1.6e+65))
		tmp = Float64(t * Float64(c * 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 ((j <= -6.6e+25) || ~((j <= 1.6e+65)))
		tmp = t * (c * 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[j, -6.6e+25], N[Not[LessEqual[j, 1.6e+65]], $MachinePrecision]], N[(t * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(i * N[(a * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -6.6000000000000002e25 or 1.60000000000000003e65 < j

   1. Initial program 75.0%

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

   3. Taylor expanded in t around inf 54.8%

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

      1. +-commutative 54.8%

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

      2. mul-1-neg 54.8%

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

      3. unsub-neg 54.8%

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

      4. *-commutative 54.8%

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

      5. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in j around inf 39.3%

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

      1. associate-*r* 45.4%

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

   8. Simplified 45.4%

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

   if -6.6000000000000002e25 < j < 1.60000000000000003e65

   1. Initial program 70.8%

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

   3. Taylor expanded in j around 0 69.5%

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

      1. *-commutative 69.5%

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

   5. Simplified 69.5%

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

   6. Taylor expanded in x around inf 66.4%

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

      1. +-commutative 66.4%

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

      2. mul-1-neg 66.4%

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

      3. unsub-neg 66.4%

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

      4. *-commutative 66.4%

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

      5. associate-/l* 66.6%

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

      6. *-commutative 66.6%

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

   8. Simplified 66.6%

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

   9. Taylor expanded in i around inf 33.6%

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

       1. associate-*r* 34.4%

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

       2. *-commutative 34.4%

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

   11. Simplified 34.4%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -6.6 \cdot 10^{+25} \lor \neg \left(j \leq 1.6 \cdot 10^{+65}\right):\\ \;\;\;\;t \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(a \cdot b\right)\\ \end{array} \]
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 72.5%

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

3. Taylor expanded in b around inf 38.0%

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

   1. *-commutative 38.0%

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

5. Simplified 38.0%

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

6. Taylor expanded in a around inf 28.7%

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

7. Final simplification 28.7%

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

Developer target: 68.4% 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 2024077 
(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)))))