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

Percentage Accurate: 73.3% → 82.7%

Time: 26.4s

Alternatives: 28

Speedup: 0.5×

• 58.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 82.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 89.3%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around -inf 32.5%

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

   5. Simplified 36.5%

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

   6. Taylor expanded in j around inf 60.1%

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

      1. associate-*r* 60.4%

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

      2. *-commutative 60.4%

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

   8. Simplified 60.4%

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

4. Final simplification 83.7%

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

Alternative 2: 57.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-284}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-295}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-10}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+73} \lor \neg \left(t \leq 2.7 \cdot 10^{+166}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* y (- (* x z) (* i j))) (* b (* z c))))
        (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -2.1e+113)
     t_2
     (if (<= t -6e-10)
       t_1
       (if (<= t -6.2e-64)
         t_2
         (if (<= t -3.5e-284)
           t_1
           (if (<= t 3.5e-295)
             (* c (- (* a j) (* z b)))
             (if (<= t 1.2e-10)
               t_1
               (if (or (<= t 5.1e+73) (not (<= t 2.7e+166)))
                 t_2
                 (* i (* y (- (* b (/ t y)) 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 = (y * ((x * z) - (i * j))) - (b * (z * c));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.1e+113) {
		tmp = t_2;
	} else if (t <= -6e-10) {
		tmp = t_1;
	} else if (t <= -6.2e-64) {
		tmp = t_2;
	} else if (t <= -3.5e-284) {
		tmp = t_1;
	} else if (t <= 3.5e-295) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.2e-10) {
		tmp = t_1;
	} else if ((t <= 5.1e+73) || !(t <= 2.7e+166)) {
		tmp = t_2;
	} else {
		tmp = i * (y * ((b * (t / y)) - j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y * ((x * z) - (i * j))) - (b * (z * c))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-2.1d+113)) then
        tmp = t_2
    else if (t <= (-6d-10)) then
        tmp = t_1
    else if (t <= (-6.2d-64)) then
        tmp = t_2
    else if (t <= (-3.5d-284)) then
        tmp = t_1
    else if (t <= 3.5d-295) then
        tmp = c * ((a * j) - (z * b))
    else if (t <= 1.2d-10) then
        tmp = t_1
    else if ((t <= 5.1d+73) .or. (.not. (t <= 2.7d+166))) then
        tmp = t_2
    else
        tmp = i * (y * ((b * (t / y)) - 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 = (y * ((x * z) - (i * j))) - (b * (z * c));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.1e+113) {
		tmp = t_2;
	} else if (t <= -6e-10) {
		tmp = t_1;
	} else if (t <= -6.2e-64) {
		tmp = t_2;
	} else if (t <= -3.5e-284) {
		tmp = t_1;
	} else if (t <= 3.5e-295) {
		tmp = c * ((a * j) - (z * b));
	} else if (t <= 1.2e-10) {
		tmp = t_1;
	} else if ((t <= 5.1e+73) || !(t <= 2.7e+166)) {
		tmp = t_2;
	} else {
		tmp = i * (y * ((b * (t / y)) - j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (y * ((x * z) - (i * j))) - (b * (z * c))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2.1e+113:
		tmp = t_2
	elif t <= -6e-10:
		tmp = t_1
	elif t <= -6.2e-64:
		tmp = t_2
	elif t <= -3.5e-284:
		tmp = t_1
	elif t <= 3.5e-295:
		tmp = c * ((a * j) - (z * b))
	elif t <= 1.2e-10:
		tmp = t_1
	elif (t <= 5.1e+73) or not (t <= 2.7e+166):
		tmp = t_2
	else:
		tmp = i * (y * ((b * (t / y)) - j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(z * c)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.1e+113)
		tmp = t_2;
	elseif (t <= -6e-10)
		tmp = t_1;
	elseif (t <= -6.2e-64)
		tmp = t_2;
	elseif (t <= -3.5e-284)
		tmp = t_1;
	elseif (t <= 3.5e-295)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (t <= 1.2e-10)
		tmp = t_1;
	elseif ((t <= 5.1e+73) || !(t <= 2.7e+166))
		tmp = t_2;
	else
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(t / y)) - j)));
	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))) - (b * (z * c));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2.1e+113)
		tmp = t_2;
	elseif (t <= -6e-10)
		tmp = t_1;
	elseif (t <= -6.2e-64)
		tmp = t_2;
	elseif (t <= -3.5e-284)
		tmp = t_1;
	elseif (t <= 3.5e-295)
		tmp = c * ((a * j) - (z * b));
	elseif (t <= 1.2e-10)
		tmp = t_1;
	elseif ((t <= 5.1e+73) || ~((t <= 2.7e+166)))
		tmp = t_2;
	else
		tmp = i * (y * ((b * (t / y)) - j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+113], t$95$2, If[LessEqual[t, -6e-10], t$95$1, If[LessEqual[t, -6.2e-64], t$95$2, If[LessEqual[t, -3.5e-284], t$95$1, If[LessEqual[t, 3.5e-295], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.2e-10], t$95$1, If[Or[LessEqual[t, 5.1e+73], N[Not[LessEqual[t, 2.7e+166]], $MachinePrecision]], t$95$2, N[(i * N[(y * N[(N[(b * N[(t / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.0999999999999999e113 or -6e-10 < t < -6.20000000000000049e-64 or 1.2e-10 < t < 5.10000000000000024e73 or 2.70000000000000012e166 < t

   1. Initial program 64.6%

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

   3. Taylor expanded in t around inf 74.8%

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

      1. distribute-lft-out-- 74.8%

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

      2. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   if -2.0999999999999999e113 < t < -6e-10 or -6.20000000000000049e-64 < t < -3.49999999999999975e-284 or 3.49999999999999988e-295 < t < 1.2e-10

   1. Initial program 78.7%

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

   3. Taylor expanded in a around 0 69.7%

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

   5. Simplified 70.6%

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

   6. Taylor expanded in t around 0 64.6%

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

      1. +-commutative 64.6%

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

      2. sub-neg 64.6%

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

      3. *-commutative 64.6%

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

      4. sub-neg 64.6%

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

      5. mul-1-neg 64.6%

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

      6. unsub-neg 64.6%

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

      7. *-commutative 64.6%

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

      8. *-commutative 64.6%

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

   8. Simplified 64.6%

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

   if -3.49999999999999975e-284 < t < 3.49999999999999988e-295

   1. Initial program 64.0%

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

   3. Taylor expanded in c around inf 88.4%

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

      1. *-commutative 88.4%

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

   5. Simplified 88.4%

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

   if 5.10000000000000024e73 < t < 2.70000000000000012e166

   1. Initial program 69.9%

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

   3. Taylor expanded in y around -inf 80.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in i around inf 70.6%

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

      1. associate-*r* 70.6%

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

      2. mul-1-neg 70.6%

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

      3. associate-/l* 70.6%

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

   8. Simplified 70.6%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+113}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-64}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-284}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-295}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{+73} \lor \neg \left(t \leq 2.7 \cdot 10^{+166}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 52.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;i \leq -1.75 \cdot 10^{-23}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-75}:\\ \;\;\;\;b \cdot \left(x \cdot \frac{y \cdot z}{b} - z \cdot c\right)\\ \mathbf{elif}\;i \leq -3.1 \cdot 10^{-151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-194}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -4.7 \cdot 10^{-295}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 6.7 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)\\ \mathbf{elif}\;i \leq 2900000000 \lor \neg \left(i \leq 1.95 \cdot 10^{+37}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= i -1.75e-23)
     (* i (* y (- (* b (/ t y)) j)))
     (if (<= i -8.2e-75)
       (* b (- (* x (/ (* y z) b)) (* z c)))
       (if (<= i -3.1e-151)
         t_1
         (if (<= i -2.2e-194)
           t_2
           (if (<= i -4.7e-295)
             t_1
             (if (<= i 6.7e-53)
               (* z (* x (- y (* b (/ c x)))))
               (if (or (<= i 2900000000.0) (not (<= i 1.95e+37)))
                 (* i (- (* t b) (* y j)))
                 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (i <= -1.75e-23) {
		tmp = i * (y * ((b * (t / y)) - j));
	} else if (i <= -8.2e-75) {
		tmp = b * ((x * ((y * z) / b)) - (z * c));
	} else if (i <= -3.1e-151) {
		tmp = t_1;
	} else if (i <= -2.2e-194) {
		tmp = t_2;
	} else if (i <= -4.7e-295) {
		tmp = t_1;
	} else if (i <= 6.7e-53) {
		tmp = z * (x * (y - (b * (c / x))));
	} else if ((i <= 2900000000.0) || !(i <= 1.95e+37)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = z * ((x * y) - (b * c))
    if (i <= (-1.75d-23)) then
        tmp = i * (y * ((b * (t / y)) - j))
    else if (i <= (-8.2d-75)) then
        tmp = b * ((x * ((y * z) / b)) - (z * c))
    else if (i <= (-3.1d-151)) then
        tmp = t_1
    else if (i <= (-2.2d-194)) then
        tmp = t_2
    else if (i <= (-4.7d-295)) then
        tmp = t_1
    else if (i <= 6.7d-53) then
        tmp = z * (x * (y - (b * (c / x))))
    else if ((i <= 2900000000.0d0) .or. (.not. (i <= 1.95d+37))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (i <= -1.75e-23) {
		tmp = i * (y * ((b * (t / y)) - j));
	} else if (i <= -8.2e-75) {
		tmp = b * ((x * ((y * z) / b)) - (z * c));
	} else if (i <= -3.1e-151) {
		tmp = t_1;
	} else if (i <= -2.2e-194) {
		tmp = t_2;
	} else if (i <= -4.7e-295) {
		tmp = t_1;
	} else if (i <= 6.7e-53) {
		tmp = z * (x * (y - (b * (c / x))));
	} else if ((i <= 2900000000.0) || !(i <= 1.95e+37)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if i <= -1.75e-23:
		tmp = i * (y * ((b * (t / y)) - j))
	elif i <= -8.2e-75:
		tmp = b * ((x * ((y * z) / b)) - (z * c))
	elif i <= -3.1e-151:
		tmp = t_1
	elif i <= -2.2e-194:
		tmp = t_2
	elif i <= -4.7e-295:
		tmp = t_1
	elif i <= 6.7e-53:
		tmp = z * (x * (y - (b * (c / x))))
	elif (i <= 2900000000.0) or not (i <= 1.95e+37):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (i <= -1.75e-23)
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(t / y)) - j)));
	elseif (i <= -8.2e-75)
		tmp = Float64(b * Float64(Float64(x * Float64(Float64(y * z) / b)) - Float64(z * c)));
	elseif (i <= -3.1e-151)
		tmp = t_1;
	elseif (i <= -2.2e-194)
		tmp = t_2;
	elseif (i <= -4.7e-295)
		tmp = t_1;
	elseif (i <= 6.7e-53)
		tmp = Float64(z * Float64(x * Float64(y - Float64(b * Float64(c / x)))));
	elseif ((i <= 2900000000.0) || !(i <= 1.95e+37))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (i <= -1.75e-23)
		tmp = i * (y * ((b * (t / y)) - j));
	elseif (i <= -8.2e-75)
		tmp = b * ((x * ((y * z) / b)) - (z * c));
	elseif (i <= -3.1e-151)
		tmp = t_1;
	elseif (i <= -2.2e-194)
		tmp = t_2;
	elseif (i <= -4.7e-295)
		tmp = t_1;
	elseif (i <= 6.7e-53)
		tmp = z * (x * (y - (b * (c / x))));
	elseif ((i <= 2900000000.0) || ~((i <= 1.95e+37)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.75e-23], N[(i * N[(y * N[(N[(b * N[(t / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.2e-75], N[(b * N[(N[(x * N[(N[(y * z), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.1e-151], t$95$1, If[LessEqual[i, -2.2e-194], t$95$2, If[LessEqual[i, -4.7e-295], t$95$1, If[LessEqual[i, 6.7e-53], N[(z * N[(x * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[i, 2900000000.0], N[Not[LessEqual[i, 1.95e+37]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.74999999999999997e-23

   1. Initial program 60.7%

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

   3. Taylor expanded in y around -inf 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in i around inf 69.0%

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

      1. associate-*r* 69.0%

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

      2. mul-1-neg 69.0%

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

      3. associate-/l* 69.1%

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

   8. Simplified 69.1%

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

   if -1.74999999999999997e-23 < i < -8.20000000000000005e-75

   1. Initial program 92.9%

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

   3. Taylor expanded in z around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. *-commutative 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in b around inf 74.3%

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

      1. neg-mul-1 74.3%

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

      2. +-commutative 74.3%

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

      3. unsub-neg 74.3%

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

      4. associate-/l* 74.2%

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

      5. *-commutative 74.2%

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

   8. Simplified 74.2%

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

   if -8.20000000000000005e-75 < i < -3.09999999999999984e-151 or -2.2000000000000001e-194 < i < -4.6999999999999998e-295

   1. Initial program 83.7%

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

   3. Taylor expanded in a around inf 76.9%

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

      1. +-commutative 76.9%

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

      2. mul-1-neg 76.9%

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

      3. unsub-neg 76.9%

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

      4. *-commutative 76.9%

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

   5. Simplified 76.9%

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

   if -3.09999999999999984e-151 < i < -2.2000000000000001e-194 or 2.9e9 < i < 1.9499999999999999e37

   1. Initial program 69.5%

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

   3. Taylor expanded in z around inf 79.1%

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

      1. *-commutative 79.1%

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

      2. *-commutative 79.1%

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

   5. Simplified 79.1%

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

   if -4.6999999999999998e-295 < i < 6.69999999999999957e-53

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. *-commutative 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in x around inf 52.4%

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

      1. mul-1-neg 52.4%

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

      2. unsub-neg 52.4%

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

      3. associate-/l* 55.8%

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

   8. Simplified 55.8%

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

   if 6.69999999999999957e-53 < i < 2.9e9 or 1.9499999999999999e37 < i

   1. Initial program 69.5%

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

   3. Taylor expanded in a around 0 66.1%

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

   5. Simplified 61.9%

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

   6. Taylor expanded in i around inf 64.6%

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

      1. +-commutative 64.6%

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

      2. mul-1-neg 64.6%

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

      3. unsub-neg 64.6%

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

      4. *-commutative 64.6%

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

   8. Simplified 64.6%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.75 \cdot 10^{-23}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq -8.2 \cdot 10^{-75}:\\ \;\;\;\;b \cdot \left(x \cdot \frac{y \cdot z}{b} - z \cdot c\right)\\ \mathbf{elif}\;i \leq -3.1 \cdot 10^{-151}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -2.2 \cdot 10^{-194}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -4.7 \cdot 10^{-295}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 6.7 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)\\ \mathbf{elif}\;i \leq 2900000000 \lor \neg \left(i \leq 1.95 \cdot 10^{+37}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.8 \cdot 10^{+125}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-136}:\\ \;\;\;\;b \cdot \left(\left(x \cdot z - i \cdot j\right) \cdot \frac{y}{b} - z \cdot c\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \mathbf{elif}\;t \leq 0.029:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+165}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* t (- (* b i) (* x a)))))
   (if (<= t -2.8e+125)
     t_1
     (if (<= t 2.7e-209)
       (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))
       (if (<= t 2.8e-136)
         (* b (- (* (- (* x z) (* i j)) (/ y b)) (* z c)))
         (if (<= t 5e-97)
           (* y (- (* x z) (- (* i j) (/ (* j (* a c)) y))))
           (if (<= t 0.029)
             (+ (* b (- (* t i) (* z c))) (* x (* y z)))
             (if (<= t 4.5e+165)
               (* y (- (* x z) (+ (* i j) (/ (* a (* x t)) y))))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.8e+125) {
		tmp = t_1;
	} else if (t <= 2.7e-209) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (t <= 2.8e-136) {
		tmp = b * ((((x * z) - (i * j)) * (y / b)) - (z * c));
	} else if (t <= 5e-97) {
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	} else if (t <= 0.029) {
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	} else if (t <= 4.5e+165) {
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	} 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 * ((b * i) - (x * a))
    if (t <= (-2.8d+125)) then
        tmp = t_1
    else if (t <= 2.7d-209) then
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    else if (t <= 2.8d-136) then
        tmp = b * ((((x * z) - (i * j)) * (y / b)) - (z * c))
    else if (t <= 5d-97) then
        tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)))
    else if (t <= 0.029d0) then
        tmp = (b * ((t * i) - (z * c))) + (x * (y * z))
    else if (t <= 4.5d+165) then
        tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
    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 * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.8e+125) {
		tmp = t_1;
	} else if (t <= 2.7e-209) {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	} else if (t <= 2.8e-136) {
		tmp = b * ((((x * z) - (i * j)) * (y / b)) - (z * c));
	} else if (t <= 5e-97) {
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	} else if (t <= 0.029) {
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	} else if (t <= 4.5e+165) {
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2.8e+125:
		tmp = t_1
	elif t <= 2.7e-209:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	elif t <= 2.8e-136:
		tmp = b * ((((x * z) - (i * j)) * (y / b)) - (z * c))
	elif t <= 5e-97:
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)))
	elif t <= 0.029:
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z))
	elif t <= 4.5e+165:
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.8e+125)
		tmp = t_1;
	elseif (t <= 2.7e-209)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	elseif (t <= 2.8e-136)
		tmp = Float64(b * Float64(Float64(Float64(Float64(x * z) - Float64(i * j)) * Float64(y / b)) - Float64(z * c)));
	elseif (t <= 5e-97)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) - Float64(Float64(j * Float64(a * c)) / y))));
	elseif (t <= 0.029)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(x * Float64(y * z)));
	elseif (t <= 4.5e+165)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) + Float64(Float64(a * Float64(x * t)) / y))));
	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 * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2.8e+125)
		tmp = t_1;
	elseif (t <= 2.7e-209)
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	elseif (t <= 2.8e-136)
		tmp = b * ((((x * z) - (i * j)) * (y / b)) - (z * c));
	elseif (t <= 5e-97)
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	elseif (t <= 0.029)
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	elseif (t <= 4.5e+165)
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.8e+125], t$95$1, If[LessEqual[t, 2.7e-209], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.8e-136], N[(b * N[(N[(N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision] * N[(y / b), $MachinePrecision]), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5e-97], N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] - N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.029], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.5e+165], N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] + N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.8000000000000001e125 or 4.4999999999999996e165 < t

   1. Initial program 57.6%

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

   3. Taylor expanded in t around inf 77.6%

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

      1. distribute-lft-out-- 77.6%

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

      2. *-commutative 77.6%

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

   5. Simplified 77.6%

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

   if -2.8000000000000001e125 < t < 2.69999999999999998e-209

   1. Initial program 82.9%

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

   3. Taylor expanded in b around 0 70.1%

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

   if 2.69999999999999998e-209 < t < 2.8000000000000001e-136

   1. Initial program 83.2%

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

   3. Taylor expanded in a around 0 83.9%

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

   5. Simplified 92.4%

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

   6. Taylor expanded in t around 0 84.3%

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

      1. +-commutative 84.3%

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

      2. sub-neg 84.3%

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

      3. *-commutative 84.3%

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

      4. sub-neg 84.3%

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

      5. mul-1-neg 84.3%

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

      6. unsub-neg 84.3%

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

      7. *-commutative 84.3%

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

      8. *-commutative 84.3%

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

   8. Simplified 84.3%

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

   9. Taylor expanded in b around inf 84.4%

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

       1. *-commutative 84.4%

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

       2. *-commutative 84.4%

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

       3. *-commutative 84.4%

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

       4. associate-/l* 84.4%

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

       5. *-commutative 84.4%

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

   11. Simplified 84.4%

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

   if 2.8000000000000001e-136 < t < 4.9999999999999995e-97

   1. Initial program 50.9%

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

   3. Taylor expanded in y around -inf 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around inf 84.0%

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

      1. associate-*r* 84.0%

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

      2. *-commutative 84.0%

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

   8. Simplified 84.0%

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

   if 4.9999999999999995e-97 < t < 0.0290000000000000015

   1. Initial program 72.6%

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

   3. Taylor expanded in a around 0 69.6%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in j around 0 66.3%

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

   if 0.0290000000000000015 < t < 4.4999999999999996e165

   1. Initial program 67.9%

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

   3. Taylor expanded in y around -inf 76.4%

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

   5. Simplified 79.4%

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

   6. Taylor expanded in x around inf 65.9%

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

      1. associate-*r/ 65.9%

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

      2. associate-*r* 65.9%

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

      3. mul-1-neg 65.9%

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

   8. Simplified 65.9%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{+125}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-209}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-136}:\\ \;\;\;\;b \cdot \left(\left(x \cdot z - i \cdot j\right) \cdot \frac{y}{b} - z \cdot c\right)\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-97}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \mathbf{elif}\;t \leq 0.029:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+165}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 29.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+201}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+33}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-247}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))))
   (if (<= t -2.5e+201)
     (* x (* t (- a)))
     (if (<= t -8.5e+115)
       (* t (* b i))
       (if (<= t -1.5e+33)
         t_1
         (if (<= t -1.9e-28)
           (* j (* a c))
           (if (<= t -5.2e-60)
             (* a (* t (- x)))
             (if (<= t -2.6e-137)
               (* y (* x z))
               (if (<= t -1.5e-247)
                 t_1
                 (if (<= t 2.05e-10) (* x (* y z)) (* b (* t i))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double tmp;
	if (t <= -2.5e+201) {
		tmp = x * (t * -a);
	} else if (t <= -8.5e+115) {
		tmp = t * (b * i);
	} else if (t <= -1.5e+33) {
		tmp = t_1;
	} else if (t <= -1.9e-28) {
		tmp = j * (a * c);
	} else if (t <= -5.2e-60) {
		tmp = a * (t * -x);
	} else if (t <= -2.6e-137) {
		tmp = y * (x * z);
	} else if (t <= -1.5e-247) {
		tmp = t_1;
	} else if (t <= 2.05e-10) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * (y * -j)
    if (t <= (-2.5d+201)) then
        tmp = x * (t * -a)
    else if (t <= (-8.5d+115)) then
        tmp = t * (b * i)
    else if (t <= (-1.5d+33)) then
        tmp = t_1
    else if (t <= (-1.9d-28)) then
        tmp = j * (a * c)
    else if (t <= (-5.2d-60)) then
        tmp = a * (t * -x)
    else if (t <= (-2.6d-137)) then
        tmp = y * (x * z)
    else if (t <= (-1.5d-247)) then
        tmp = t_1
    else if (t <= 2.05d-10) then
        tmp = x * (y * z)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double tmp;
	if (t <= -2.5e+201) {
		tmp = x * (t * -a);
	} else if (t <= -8.5e+115) {
		tmp = t * (b * i);
	} else if (t <= -1.5e+33) {
		tmp = t_1;
	} else if (t <= -1.9e-28) {
		tmp = j * (a * c);
	} else if (t <= -5.2e-60) {
		tmp = a * (t * -x);
	} else if (t <= -2.6e-137) {
		tmp = y * (x * z);
	} else if (t <= -1.5e-247) {
		tmp = t_1;
	} else if (t <= 2.05e-10) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	tmp = 0
	if t <= -2.5e+201:
		tmp = x * (t * -a)
	elif t <= -8.5e+115:
		tmp = t * (b * i)
	elif t <= -1.5e+33:
		tmp = t_1
	elif t <= -1.9e-28:
		tmp = j * (a * c)
	elif t <= -5.2e-60:
		tmp = a * (t * -x)
	elif t <= -2.6e-137:
		tmp = y * (x * z)
	elif t <= -1.5e-247:
		tmp = t_1
	elif t <= 2.05e-10:
		tmp = x * (y * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (t <= -2.5e+201)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (t <= -8.5e+115)
		tmp = Float64(t * Float64(b * i));
	elseif (t <= -1.5e+33)
		tmp = t_1;
	elseif (t <= -1.9e-28)
		tmp = Float64(j * Float64(a * c));
	elseif (t <= -5.2e-60)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (t <= -2.6e-137)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= -1.5e-247)
		tmp = t_1;
	elseif (t <= 2.05e-10)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	tmp = 0.0;
	if (t <= -2.5e+201)
		tmp = x * (t * -a);
	elseif (t <= -8.5e+115)
		tmp = t * (b * i);
	elseif (t <= -1.5e+33)
		tmp = t_1;
	elseif (t <= -1.9e-28)
		tmp = j * (a * c);
	elseif (t <= -5.2e-60)
		tmp = a * (t * -x);
	elseif (t <= -2.6e-137)
		tmp = y * (x * z);
	elseif (t <= -1.5e-247)
		tmp = t_1;
	elseif (t <= 2.05e-10)
		tmp = x * (y * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+201], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.5e+115], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e+33], t$95$1, If[LessEqual[t, -1.9e-28], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.2e-60], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.6e-137], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.5e-247], t$95$1, If[LessEqual[t, 2.05e-10], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if t < -2.4999999999999998e201

   1. Initial program 67.1%

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

   3. Taylor expanded in a around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in j around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. associate-*r* 64.2%

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

      3. distribute-lft-neg-in 64.2%

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

      4. *-commutative 64.2%

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

      5. distribute-rgt-neg-in 64.2%

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

   8. Simplified 64.2%

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

   if -2.4999999999999998e201 < t < -8.50000000000000057e115

   1. Initial program 67.2%

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

   3. Taylor expanded in t around inf 74.1%

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

      1. distribute-lft-out-- 74.1%

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

      2. *-commutative 74.1%

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

   5. Simplified 74.1%

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

   6. Taylor expanded in a around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. distribute-rgt-neg-in 54.8%

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

   8. Simplified 54.8%

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

   if -8.50000000000000057e115 < t < -1.49999999999999992e33 or -2.6e-137 < t < -1.4999999999999999e-247

   1. Initial program 82.9%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

      5. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in z around 0 54.5%

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

      1. associate-*r* 54.5%

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

      2. mul-1-neg 54.5%

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

      3. *-commutative 54.5%

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

   8. Simplified 54.5%

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

   if -1.49999999999999992e33 < t < -1.90000000000000005e-28

   1. Initial program 75.3%

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

   3. Taylor expanded in a around inf 42.3%

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

      1. +-commutative 42.3%

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

      2. mul-1-neg 42.3%

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

      3. unsub-neg 42.3%

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

      4. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in j around inf 35.1%

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

      1. associate-*r* 42.4%

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

      2. *-commutative 42.4%

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

   8. Simplified 42.4%

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

   if -1.90000000000000005e-28 < t < -5.1999999999999995e-60

   1. Initial program 99.6%

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

   3. Taylor expanded in a around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. unsub-neg 63.5%

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

      4. *-commutative 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in j around 0 55.9%

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

      1. associate-*r* 55.9%

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

      2. mul-1-neg 55.9%

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

   8. Simplified 55.9%

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

   if -5.1999999999999995e-60 < t < -2.6e-137

   1. Initial program 77.1%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

      5. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -1.4999999999999999e-247 < t < 2.0499999999999999e-10

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in y around inf 36.6%

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

   if 2.0499999999999999e-10 < t

   1. Initial program 57.6%

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

   3. Taylor expanded in t around inf 59.4%

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

      1. distribute-lft-out-- 59.4%

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

      2. *-commutative 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in a around 0 41.3%

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

      1. *-commutative 41.3%

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

   8. Simplified 41.3%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+201}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+115}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+33}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-137}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-247}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 2.05 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+201}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-244}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* i (* y (- j)))))
   (if (<= t -2.5e+201)
     (* x (* t (- a)))
     (if (<= t -2.05e+120)
       t_1
       (if (<= t -1.6e+29)
         t_2
         (if (<= t -2.5e-28)
           (* j (* a c))
           (if (<= t -1.12e-60)
             (* a (* t (- x)))
             (if (<= t -6.6e-136)
               (* y (* x z))
               (if (<= t -5.4e-244)
                 t_2
                 (if (<= t 3e-11) (* x (* y z)) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = i * (y * -j);
	double tmp;
	if (t <= -2.5e+201) {
		tmp = x * (t * -a);
	} else if (t <= -2.05e+120) {
		tmp = t_1;
	} else if (t <= -1.6e+29) {
		tmp = t_2;
	} else if (t <= -2.5e-28) {
		tmp = j * (a * c);
	} else if (t <= -1.12e-60) {
		tmp = a * (t * -x);
	} else if (t <= -6.6e-136) {
		tmp = y * (x * z);
	} else if (t <= -5.4e-244) {
		tmp = t_2;
	} else if (t <= 3e-11) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = i * (y * -j)
    if (t <= (-2.5d+201)) then
        tmp = x * (t * -a)
    else if (t <= (-2.05d+120)) then
        tmp = t_1
    else if (t <= (-1.6d+29)) then
        tmp = t_2
    else if (t <= (-2.5d-28)) then
        tmp = j * (a * c)
    else if (t <= (-1.12d-60)) then
        tmp = a * (t * -x)
    else if (t <= (-6.6d-136)) then
        tmp = y * (x * z)
    else if (t <= (-5.4d-244)) then
        tmp = t_2
    else if (t <= 3d-11) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = i * (y * -j);
	double tmp;
	if (t <= -2.5e+201) {
		tmp = x * (t * -a);
	} else if (t <= -2.05e+120) {
		tmp = t_1;
	} else if (t <= -1.6e+29) {
		tmp = t_2;
	} else if (t <= -2.5e-28) {
		tmp = j * (a * c);
	} else if (t <= -1.12e-60) {
		tmp = a * (t * -x);
	} else if (t <= -6.6e-136) {
		tmp = y * (x * z);
	} else if (t <= -5.4e-244) {
		tmp = t_2;
	} else if (t <= 3e-11) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = i * (y * -j)
	tmp = 0
	if t <= -2.5e+201:
		tmp = x * (t * -a)
	elif t <= -2.05e+120:
		tmp = t_1
	elif t <= -1.6e+29:
		tmp = t_2
	elif t <= -2.5e-28:
		tmp = j * (a * c)
	elif t <= -1.12e-60:
		tmp = a * (t * -x)
	elif t <= -6.6e-136:
		tmp = y * (x * z)
	elif t <= -5.4e-244:
		tmp = t_2
	elif t <= 3e-11:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (t <= -2.5e+201)
		tmp = Float64(x * Float64(t * Float64(-a)));
	elseif (t <= -2.05e+120)
		tmp = t_1;
	elseif (t <= -1.6e+29)
		tmp = t_2;
	elseif (t <= -2.5e-28)
		tmp = Float64(j * Float64(a * c));
	elseif (t <= -1.12e-60)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (t <= -6.6e-136)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= -5.4e-244)
		tmp = t_2;
	elseif (t <= 3e-11)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = i * (y * -j);
	tmp = 0.0;
	if (t <= -2.5e+201)
		tmp = x * (t * -a);
	elseif (t <= -2.05e+120)
		tmp = t_1;
	elseif (t <= -1.6e+29)
		tmp = t_2;
	elseif (t <= -2.5e-28)
		tmp = j * (a * c);
	elseif (t <= -1.12e-60)
		tmp = a * (t * -x);
	elseif (t <= -6.6e-136)
		tmp = y * (x * z);
	elseif (t <= -5.4e-244)
		tmp = t_2;
	elseif (t <= 3e-11)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+201], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.05e+120], t$95$1, If[LessEqual[t, -1.6e+29], t$95$2, If[LessEqual[t, -2.5e-28], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.12e-60], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.6e-136], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.4e-244], t$95$2, If[LessEqual[t, 3e-11], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -2.4999999999999998e201

   1. Initial program 67.1%

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

   3. Taylor expanded in a around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in j around 0 61.2%

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

      1. mul-1-neg 61.2%

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

      2. associate-*r* 64.2%

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

      3. distribute-lft-neg-in 64.2%

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

      4. *-commutative 64.2%

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

      5. distribute-rgt-neg-in 64.2%

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

   8. Simplified 64.2%

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

   if -2.4999999999999998e201 < t < -2.05e120 or 3e-11 < t

   1. Initial program 59.5%

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

   3. Taylor expanded in t around inf 62.2%

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

      1. distribute-lft-out-- 62.2%

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

      2. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in a around 0 43.8%

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

      1. *-commutative 43.8%

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

   8. Simplified 43.8%

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

   if -2.05e120 < t < -1.59999999999999993e29 or -6.60000000000000035e-136 < t < -5.3999999999999999e-244

   1. Initial program 82.9%

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

   3. Taylor expanded in y around inf 63.1%

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

      1. +-commutative 63.1%

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

      2. mul-1-neg 63.1%

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

      3. unsub-neg 63.1%

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

      4. *-commutative 63.1%

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

      5. *-commutative 63.1%

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

   5. Simplified 63.1%

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

   6. Taylor expanded in z around 0 54.5%

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

      1. associate-*r* 54.5%

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

      2. mul-1-neg 54.5%

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

      3. *-commutative 54.5%

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

   8. Simplified 54.5%

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

   if -1.59999999999999993e29 < t < -2.5000000000000001e-28

   1. Initial program 75.3%

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

   3. Taylor expanded in a around inf 42.3%

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

      1. +-commutative 42.3%

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

      2. mul-1-neg 42.3%

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

      3. unsub-neg 42.3%

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

      4. *-commutative 42.3%

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

   5. Simplified 42.3%

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

   6. Taylor expanded in j around inf 35.1%

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

      1. associate-*r* 42.4%

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

      2. *-commutative 42.4%

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

   8. Simplified 42.4%

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

   if -2.5000000000000001e-28 < t < -1.12e-60

   1. Initial program 99.6%

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

   3. Taylor expanded in a around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. unsub-neg 63.5%

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

      4. *-commutative 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in j around 0 55.9%

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

      1. associate-*r* 55.9%

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

      2. mul-1-neg 55.9%

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

   8. Simplified 55.9%

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

   if -1.12e-60 < t < -6.60000000000000035e-136

   1. Initial program 77.1%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

      5. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -5.3999999999999999e-244 < t < 3e-11

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in y around inf 36.6%

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

4. Final simplification 46.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+201}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{elif}\;t \leq -2.05 \cdot 10^{+120}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+29}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-28}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-244}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;i \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-75}:\\ \;\;\;\;b \cdot \left(x \cdot \frac{y \cdot z}{b} - z \cdot c\right)\\ \mathbf{elif}\;i \leq -7.6 \cdot 10^{-148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-295}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= i -1.85e-22)
     (* i (* y (- (* b (/ t y)) j)))
     (if (<= i -3.8e-75)
       (* b (- (* x (/ (* y z) b)) (* z c)))
       (if (<= i -7.6e-148)
         t_1
         (if (<= i -4.6e-193)
           (* z (- (* x y) (* b c)))
           (if (<= i -1.95e-295)
             t_1
             (if (<= i 1.8e+43)
               (+ (* b (- (* t i) (* z c))) (* x (* y z)))
               (* i (- (* t b) (* y 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 * ((c * j) - (x * t));
	double tmp;
	if (i <= -1.85e-22) {
		tmp = i * (y * ((b * (t / y)) - j));
	} else if (i <= -3.8e-75) {
		tmp = b * ((x * ((y * z) / b)) - (z * c));
	} else if (i <= -7.6e-148) {
		tmp = t_1;
	} else if (i <= -4.6e-193) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= -1.95e-295) {
		tmp = t_1;
	} else if (i <= 1.8e+43) {
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	} else {
		tmp = i * ((t * b) - (y * 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 * ((c * j) - (x * t))
    if (i <= (-1.85d-22)) then
        tmp = i * (y * ((b * (t / y)) - j))
    else if (i <= (-3.8d-75)) then
        tmp = b * ((x * ((y * z) / b)) - (z * c))
    else if (i <= (-7.6d-148)) then
        tmp = t_1
    else if (i <= (-4.6d-193)) then
        tmp = z * ((x * y) - (b * c))
    else if (i <= (-1.95d-295)) then
        tmp = t_1
    else if (i <= 1.8d+43) then
        tmp = (b * ((t * i) - (z * c))) + (x * (y * z))
    else
        tmp = i * ((t * b) - (y * 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 * ((c * j) - (x * t));
	double tmp;
	if (i <= -1.85e-22) {
		tmp = i * (y * ((b * (t / y)) - j));
	} else if (i <= -3.8e-75) {
		tmp = b * ((x * ((y * z) / b)) - (z * c));
	} else if (i <= -7.6e-148) {
		tmp = t_1;
	} else if (i <= -4.6e-193) {
		tmp = z * ((x * y) - (b * c));
	} else if (i <= -1.95e-295) {
		tmp = t_1;
	} else if (i <= 1.8e+43) {
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if i <= -1.85e-22:
		tmp = i * (y * ((b * (t / y)) - j))
	elif i <= -3.8e-75:
		tmp = b * ((x * ((y * z) / b)) - (z * c))
	elif i <= -7.6e-148:
		tmp = t_1
	elif i <= -4.6e-193:
		tmp = z * ((x * y) - (b * c))
	elif i <= -1.95e-295:
		tmp = t_1
	elif i <= 1.8e+43:
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z))
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (i <= -1.85e-22)
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(t / y)) - j)));
	elseif (i <= -3.8e-75)
		tmp = Float64(b * Float64(Float64(x * Float64(Float64(y * z) / b)) - Float64(z * c)));
	elseif (i <= -7.6e-148)
		tmp = t_1;
	elseif (i <= -4.6e-193)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (i <= -1.95e-295)
		tmp = t_1;
	elseif (i <= 1.8e+43)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(x * Float64(y * z)));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (i <= -1.85e-22)
		tmp = i * (y * ((b * (t / y)) - j));
	elseif (i <= -3.8e-75)
		tmp = b * ((x * ((y * z) / b)) - (z * c));
	elseif (i <= -7.6e-148)
		tmp = t_1;
	elseif (i <= -4.6e-193)
		tmp = z * ((x * y) - (b * c));
	elseif (i <= -1.95e-295)
		tmp = t_1;
	elseif (i <= 1.8e+43)
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.85e-22], N[(i * N[(y * N[(N[(b * N[(t / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.8e-75], N[(b * N[(N[(x * N[(N[(y * z), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.6e-148], t$95$1, If[LessEqual[i, -4.6e-193], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.95e-295], t$95$1, If[LessEqual[i, 1.8e+43], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.85e-22

   1. Initial program 60.7%

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

   3. Taylor expanded in y around -inf 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in i around inf 69.0%

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

      1. associate-*r* 69.0%

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

      2. mul-1-neg 69.0%

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

      3. associate-/l* 69.1%

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

   8. Simplified 69.1%

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

   if -1.85e-22 < i < -3.79999999999999994e-75

   1. Initial program 92.9%

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

   3. Taylor expanded in z around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. *-commutative 56.0%

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

   5. Simplified 56.0%

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

   6. Taylor expanded in b around inf 74.3%

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

      1. neg-mul-1 74.3%

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

      2. +-commutative 74.3%

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

      3. unsub-neg 74.3%

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

      4. associate-/l* 74.2%

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

      5. *-commutative 74.2%

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

   8. Simplified 74.2%

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

   if -3.79999999999999994e-75 < i < -7.60000000000000028e-148 or -4.60000000000000017e-193 < i < -1.95e-295

   1. Initial program 81.8%

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

   3. Taylor expanded in a around inf 75.1%

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

      1. +-commutative 75.1%

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

      2. mul-1-neg 75.1%

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

      3. unsub-neg 75.1%

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

      4. *-commutative 75.1%

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

   5. Simplified 75.1%

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

   if -7.60000000000000028e-148 < i < -4.60000000000000017e-193

   1. Initial program 67.3%

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

   3. Taylor expanded in z around inf 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if -1.95e-295 < i < 1.80000000000000005e43

   1. Initial program 76.9%

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

   3. Taylor expanded in a around 0 65.1%

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

   5. Simplified 63.8%

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

   6. Taylor expanded in j around 0 57.3%

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

   if 1.80000000000000005e43 < i

   1. Initial program 64.3%

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

   3. Taylor expanded in a around 0 62.0%

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

   5. Simplified 58.6%

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

   6. Taylor expanded in i around inf 63.8%

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

      1. +-commutative 63.8%

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

      2. mul-1-neg 63.8%

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

      3. unsub-neg 63.8%

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

      4. *-commutative 63.8%

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

   8. Simplified 63.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq -3.8 \cdot 10^{-75}:\\ \;\;\;\;b \cdot \left(x \cdot \frac{y \cdot z}{b} - z \cdot c\right)\\ \mathbf{elif}\;i \leq -7.6 \cdot 10^{-148}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -1.95 \cdot 10^{-295}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+108}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \mathbf{elif}\;t \leq 0.025:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+166}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (- (* x z) (+ (* i j) (/ (* a (* x t)) y)))))
        (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -9e+108)
     t_2
     (if (<= t -6.2e-87)
       t_1
       (if (<= t 1.52e-89)
         (* y (- (* x z) (- (* i j) (/ (* j (* a c)) y))))
         (if (<= t 0.025)
           (+ (* b (- (* t i) (* z c))) (* x (* y z)))
           (if (<= t 1.02e+166) 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 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -9e+108) {
		tmp = t_2;
	} else if (t <= -6.2e-87) {
		tmp = t_1;
	} else if (t <= 1.52e-89) {
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	} else if (t <= 0.025) {
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	} else if (t <= 1.02e+166) {
		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 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-9d+108)) then
        tmp = t_2
    else if (t <= (-6.2d-87)) then
        tmp = t_1
    else if (t <= 1.52d-89) then
        tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)))
    else if (t <= 0.025d0) then
        tmp = (b * ((t * i) - (z * c))) + (x * (y * z))
    else if (t <= 1.02d+166) 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 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -9e+108) {
		tmp = t_2;
	} else if (t <= -6.2e-87) {
		tmp = t_1;
	} else if (t <= 1.52e-89) {
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	} else if (t <= 0.025) {
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	} else if (t <= 1.02e+166) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -9e+108:
		tmp = t_2
	elif t <= -6.2e-87:
		tmp = t_1
	elif t <= 1.52e-89:
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)))
	elif t <= 0.025:
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z))
	elif t <= 1.02e+166:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) + Float64(Float64(a * Float64(x * t)) / y))))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -9e+108)
		tmp = t_2;
	elseif (t <= -6.2e-87)
		tmp = t_1;
	elseif (t <= 1.52e-89)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) - Float64(Float64(j * Float64(a * c)) / y))));
	elseif (t <= 0.025)
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(x * Float64(y * z)));
	elseif (t <= 1.02e+166)
		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 = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -9e+108)
		tmp = t_2;
	elseif (t <= -6.2e-87)
		tmp = t_1;
	elseif (t <= 1.52e-89)
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	elseif (t <= 0.025)
		tmp = (b * ((t * i) - (z * c))) + (x * (y * z));
	elseif (t <= 1.02e+166)
		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[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] + N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -9e+108], t$95$2, If[LessEqual[t, -6.2e-87], t$95$1, If[LessEqual[t, 1.52e-89], N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] - N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 0.025], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+166], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -9e108 or 1.0200000000000001e166 < t

   1. Initial program 58.1%

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

   3. Taylor expanded in t around inf 76.5%

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

      1. distribute-lft-out-- 76.5%

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

      2. *-commutative 76.5%

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

   5. Simplified 76.5%

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

   if -9e108 < t < -6.19999999999999995e-87 or 0.025000000000000001 < t < 1.0200000000000001e166

   1. Initial program 74.6%

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

   3. Taylor expanded in y around -inf 81.6%

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

   5. Simplified 83.0%

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

   6. Taylor expanded in x around inf 67.6%

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

      1. associate-*r/ 67.6%

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

      2. associate-*r* 67.6%

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

      3. mul-1-neg 67.6%

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

   8. Simplified 67.6%

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

   if -6.19999999999999995e-87 < t < 1.52e-89

   1. Initial program 78.9%

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

   3. Taylor expanded in y around -inf 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in j around inf 67.1%

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

      1. associate-*r* 66.0%

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

      2. *-commutative 66.0%

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

   8. Simplified 66.0%

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

   if 1.52e-89 < t < 0.025000000000000001

   1. Initial program 79.7%

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

   3. Taylor expanded in a around 0 64.8%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in j around 0 64.9%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9 \cdot 10^{+108}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-87}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{elif}\;t \leq 1.52 \cdot 10^{-89}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \mathbf{elif}\;t \leq 0.025:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+166}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-271}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-131}:\\ \;\;\;\;\left(t\_1 - c \cdot \left(z \cdot b\right)\right) - c \cdot \left(j \cdot \left(\frac{y \cdot i}{c} - a\right)\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+67}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* b (- (* t i) (* z c))))))
   (if (<= y -2.5e-16)
     (* y (- (* x z) (+ (* i j) (/ (* a (* x t)) y))))
     (if (<= y 1.5e-271)
       t_2
       (if (<= y 1.12e-131)
         (- (- t_1 (* c (* z b))) (* c (* j (- (/ (* y i) c) a))))
         (if (<= y 5.6e+67)
           t_2
           (* y (- (* x z) (- (* i j) (/ (* j (* a c)) y))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double tmp;
	if (y <= -2.5e-16) {
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	} else if (y <= 1.5e-271) {
		tmp = t_2;
	} else if (y <= 1.12e-131) {
		tmp = (t_1 - (c * (z * b))) - (c * (j * (((y * i) / c) - a)));
	} else if (y <= 5.6e+67) {
		tmp = t_2;
	} else {
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * ((t * i) - (z * c)))
    if (y <= (-2.5d-16)) then
        tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
    else if (y <= 1.5d-271) then
        tmp = t_2
    else if (y <= 1.12d-131) then
        tmp = (t_1 - (c * (z * b))) - (c * (j * (((y * i) / c) - a)))
    else if (y <= 5.6d+67) then
        tmp = t_2
    else
        tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * ((t * i) - (z * c)));
	double tmp;
	if (y <= -2.5e-16) {
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	} else if (y <= 1.5e-271) {
		tmp = t_2;
	} else if (y <= 1.12e-131) {
		tmp = (t_1 - (c * (z * b))) - (c * (j * (((y * i) / c) - a)));
	} else if (y <= 5.6e+67) {
		tmp = t_2;
	} else {
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 + (b * ((t * i) - (z * c)))
	tmp = 0
	if y <= -2.5e-16:
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
	elif y <= 1.5e-271:
		tmp = t_2
	elif y <= 1.12e-131:
		tmp = (t_1 - (c * (z * b))) - (c * (j * (((y * i) / c) - a)))
	elif y <= 5.6e+67:
		tmp = t_2
	else:
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))))
	tmp = 0.0
	if (y <= -2.5e-16)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) + Float64(Float64(a * Float64(x * t)) / y))));
	elseif (y <= 1.5e-271)
		tmp = t_2;
	elseif (y <= 1.12e-131)
		tmp = Float64(Float64(t_1 - Float64(c * Float64(z * b))) - Float64(c * Float64(j * Float64(Float64(Float64(y * i) / c) - a))));
	elseif (y <= 5.6e+67)
		tmp = t_2;
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) - Float64(Float64(j * Float64(a * c)) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 + (b * ((t * i) - (z * c)));
	tmp = 0.0;
	if (y <= -2.5e-16)
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	elseif (y <= 1.5e-271)
		tmp = t_2;
	elseif (y <= 1.12e-131)
		tmp = (t_1 - (c * (z * b))) - (c * (j * (((y * i) / c) - a)));
	elseif (y <= 5.6e+67)
		tmp = t_2;
	else
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-16], N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] + N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-271], t$95$2, If[LessEqual[y, 1.12e-131], N[(N[(t$95$1 - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(j * N[(N[(N[(y * i), $MachinePrecision] / c), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.6e+67], t$95$2, N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] - N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.5000000000000002e-16

   1. Initial program 60.8%

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

   3. Taylor expanded in y around -inf 84.2%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in x around inf 73.9%

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

      1. associate-*r/ 73.9%

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

      2. associate-*r* 73.9%

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

      3. mul-1-neg 73.9%

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

   8. Simplified 73.9%

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

   if -2.5000000000000002e-16 < y < 1.50000000000000001e-271 or 1.12000000000000001e-131 < y < 5.5999999999999995e67

   1. Initial program 78.9%

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

   3. Taylor expanded in j around 0 72.2%

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

   if 1.50000000000000001e-271 < y < 1.12000000000000001e-131

   1. Initial program 87.3%

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

   3. Taylor expanded in c around inf 90.6%

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

      1. +-commutative 90.6%

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

      2. mul-1-neg 90.6%

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

      3. unsub-neg 90.6%

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

      4. *-commutative 90.6%

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

      5. associate-/l* 90.6%

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

   5. Simplified 90.6%

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

   6. Taylor expanded in c around inf 78.1%

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

      1. *-commutative 78.1%

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

      2. associate-*l* 84.3%

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

      3. *-commutative 84.3%

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

   8. Simplified 84.3%

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

   9. Taylor expanded in j around 0 84.2%

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

   if 5.5999999999999995e67 < y

   1. Initial program 63.9%

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

   3. Taylor expanded in y around -inf 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in j around inf 73.3%

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

      1. associate-*r* 79.6%

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

      2. *-commutative 79.6%

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

   8. Simplified 79.6%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-271}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{-131}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\right) - c \cdot \left(j \cdot \left(\frac{y \cdot i}{c} - a\right)\right)\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{+67}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 56.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot z - i \cdot j\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -2.1 \cdot 10^{+109}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-5}:\\ \;\;\;\;b \cdot \left(t\_1 \cdot \frac{y}{b} - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-63}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;y \cdot t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+73} \lor \neg \left(t \leq 2.7 \cdot 10^{+166}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* x z) (* i j))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -2.1e+109)
     t_2
     (if (<= t -1.9e-5)
       (* b (- (* t_1 (/ y b)) (* z c)))
       (if (<= t -1.2e-63)
         t_2
         (if (<= t 3.7e-10)
           (- (* y t_1) (* b (* z c)))
           (if (or (<= t 7e+73) (not (<= t 2.7e+166)))
             t_2
             (* i (* y (- (* b (/ t y)) j))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * z) - (i * j);
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.1e+109) {
		tmp = t_2;
	} else if (t <= -1.9e-5) {
		tmp = b * ((t_1 * (y / b)) - (z * c));
	} else if (t <= -1.2e-63) {
		tmp = t_2;
	} else if (t <= 3.7e-10) {
		tmp = (y * t_1) - (b * (z * c));
	} else if ((t <= 7e+73) || !(t <= 2.7e+166)) {
		tmp = t_2;
	} else {
		tmp = i * (y * ((b * (t / y)) - j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x * z) - (i * j)
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-2.1d+109)) then
        tmp = t_2
    else if (t <= (-1.9d-5)) then
        tmp = b * ((t_1 * (y / b)) - (z * c))
    else if (t <= (-1.2d-63)) then
        tmp = t_2
    else if (t <= 3.7d-10) then
        tmp = (y * t_1) - (b * (z * c))
    else if ((t <= 7d+73) .or. (.not. (t <= 2.7d+166))) then
        tmp = t_2
    else
        tmp = i * (y * ((b * (t / y)) - j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (x * z) - (i * j);
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -2.1e+109) {
		tmp = t_2;
	} else if (t <= -1.9e-5) {
		tmp = b * ((t_1 * (y / b)) - (z * c));
	} else if (t <= -1.2e-63) {
		tmp = t_2;
	} else if (t <= 3.7e-10) {
		tmp = (y * t_1) - (b * (z * c));
	} else if ((t <= 7e+73) || !(t <= 2.7e+166)) {
		tmp = t_2;
	} else {
		tmp = i * (y * ((b * (t / y)) - j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (x * z) - (i * j)
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -2.1e+109:
		tmp = t_2
	elif t <= -1.9e-5:
		tmp = b * ((t_1 * (y / b)) - (z * c))
	elif t <= -1.2e-63:
		tmp = t_2
	elif t <= 3.7e-10:
		tmp = (y * t_1) - (b * (z * c))
	elif (t <= 7e+73) or not (t <= 2.7e+166):
		tmp = t_2
	else:
		tmp = i * (y * ((b * (t / y)) - j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(x * z) - Float64(i * j))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -2.1e+109)
		tmp = t_2;
	elseif (t <= -1.9e-5)
		tmp = Float64(b * Float64(Float64(t_1 * Float64(y / b)) - Float64(z * c)));
	elseif (t <= -1.2e-63)
		tmp = t_2;
	elseif (t <= 3.7e-10)
		tmp = Float64(Float64(y * t_1) - Float64(b * Float64(z * c)));
	elseif ((t <= 7e+73) || !(t <= 2.7e+166))
		tmp = t_2;
	else
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(t / y)) - j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (x * z) - (i * j);
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -2.1e+109)
		tmp = t_2;
	elseif (t <= -1.9e-5)
		tmp = b * ((t_1 * (y / b)) - (z * c));
	elseif (t <= -1.2e-63)
		tmp = t_2;
	elseif (t <= 3.7e-10)
		tmp = (y * t_1) - (b * (z * c));
	elseif ((t <= 7e+73) || ~((t <= 2.7e+166)))
		tmp = t_2;
	else
		tmp = i * (y * ((b * (t / y)) - j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.1e+109], t$95$2, If[LessEqual[t, -1.9e-5], N[(b * N[(N[(t$95$1 * N[(y / b), $MachinePrecision]), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.2e-63], t$95$2, If[LessEqual[t, 3.7e-10], N[(N[(y * t$95$1), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 7e+73], N[Not[LessEqual[t, 2.7e+166]], $MachinePrecision]], t$95$2, N[(i * N[(y * N[(N[(b * N[(t / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.1000000000000001e109 or -1.9000000000000001e-5 < t < -1.2e-63 or 3.70000000000000015e-10 < t < 7.00000000000000004e73 or 2.70000000000000012e166 < t

   1. Initial program 64.6%

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

   3. Taylor expanded in t around inf 74.8%

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

      1. distribute-lft-out-- 74.8%

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

      2. *-commutative 74.8%

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

   5. Simplified 74.8%

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

   if -2.1000000000000001e109 < t < -1.9000000000000001e-5

   1. Initial program 73.2%

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

   3. Taylor expanded in a around 0 62.3%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around 0 62.2%

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

      1. +-commutative 62.2%

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

      2. sub-neg 62.2%

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

      3. *-commutative 62.2%

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

      4. sub-neg 62.2%

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

      5. mul-1-neg 62.2%

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

      6. unsub-neg 62.2%

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

      7. *-commutative 62.2%

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

      8. *-commutative 62.2%

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

   8. Simplified 62.2%

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

   9. Taylor expanded in b around inf 67.4%

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

       1. *-commutative 67.4%

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

       2. *-commutative 67.4%

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

       3. *-commutative 67.4%

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

       4. associate-/l* 67.1%

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

       5. *-commutative 67.1%

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

   11. Simplified 67.1%

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

   if -1.2e-63 < t < 3.70000000000000015e-10

   1. Initial program 78.6%

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

   3. Taylor expanded in a around 0 67.5%

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

   5. Simplified 67.7%

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

   6. Taylor expanded in t around 0 62.0%

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

      1. +-commutative 62.0%

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

      2. sub-neg 62.0%

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

      3. *-commutative 62.0%

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

      4. sub-neg 62.0%

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

      5. mul-1-neg 62.0%

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

      6. unsub-neg 62.0%

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

      7. *-commutative 62.0%

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

      8. *-commutative 62.0%

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

   8. Simplified 62.0%

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

   if 7.00000000000000004e73 < t < 2.70000000000000012e166

   1. Initial program 69.9%

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

   3. Taylor expanded in y around -inf 80.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in i around inf 70.6%

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

      1. associate-*r* 70.6%

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

      2. mul-1-neg 70.6%

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

      3. associate-/l* 70.6%

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

   8. Simplified 70.6%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.1 \cdot 10^{+109}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-5}:\\ \;\;\;\;b \cdot \left(\left(x \cdot z - i \cdot j\right) \cdot \frac{y}{b} - z \cdot c\right)\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-63}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq 3.7 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+73} \lor \neg \left(t \leq 2.7 \cdot 10^{+166}\right):\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 51.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{-18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-120}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{-90}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+69} \lor \neg \left(b \leq 4.6 \cdot 10^{+102}\right):\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -4.7e-18)
     t_2
     (if (<= b 9e-120)
       t_1
       (if (<= b 1.46e-90)
         (* z (* x y))
         (if (<= b 6.8e+16)
           t_1
           (if (or (<= b 6.2e+69) (not (<= b 4.6e+102)))
             t_2
             (* x (* 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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.7e-18) {
		tmp = t_2;
	} else if (b <= 9e-120) {
		tmp = t_1;
	} else if (b <= 1.46e-90) {
		tmp = z * (x * y);
	} else if (b <= 6.8e+16) {
		tmp = t_1;
	} else if ((b <= 6.2e+69) || !(b <= 4.6e+102)) {
		tmp = t_2;
	} else {
		tmp = x * (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 = a * ((c * j) - (x * t))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-4.7d-18)) then
        tmp = t_2
    else if (b <= 9d-120) then
        tmp = t_1
    else if (b <= 1.46d-90) then
        tmp = z * (x * y)
    else if (b <= 6.8d+16) then
        tmp = t_1
    else if ((b <= 6.2d+69) .or. (.not. (b <= 4.6d+102))) then
        tmp = t_2
    else
        tmp = x * (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 = a * ((c * j) - (x * t));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -4.7e-18) {
		tmp = t_2;
	} else if (b <= 9e-120) {
		tmp = t_1;
	} else if (b <= 1.46e-90) {
		tmp = z * (x * y);
	} else if (b <= 6.8e+16) {
		tmp = t_1;
	} else if ((b <= 6.2e+69) || !(b <= 4.6e+102)) {
		tmp = t_2;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -4.7e-18:
		tmp = t_2
	elif b <= 9e-120:
		tmp = t_1
	elif b <= 1.46e-90:
		tmp = z * (x * y)
	elif b <= 6.8e+16:
		tmp = t_1
	elif (b <= 6.2e+69) or not (b <= 4.6e+102):
		tmp = t_2
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -4.7e-18)
		tmp = t_2;
	elseif (b <= 9e-120)
		tmp = t_1;
	elseif (b <= 1.46e-90)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 6.8e+16)
		tmp = t_1;
	elseif ((b <= 6.2e+69) || !(b <= 4.6e+102))
		tmp = t_2;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -4.7e-18)
		tmp = t_2;
	elseif (b <= 9e-120)
		tmp = t_1;
	elseif (b <= 1.46e-90)
		tmp = z * (x * y);
	elseif (b <= 6.8e+16)
		tmp = t_1;
	elseif ((b <= 6.2e+69) || ~((b <= 4.6e+102)))
		tmp = t_2;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.7e-18], t$95$2, If[LessEqual[b, 9e-120], t$95$1, If[LessEqual[b, 1.46e-90], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.8e+16], t$95$1, If[Or[LessEqual[b, 6.2e+69], N[Not[LessEqual[b, 4.6e+102]], $MachinePrecision]], t$95$2, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -4.6999999999999996e-18 or 6.8e16 < b < 6.1999999999999997e69 or 4.5999999999999998e102 < b

   1. Initial program 76.8%

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

   3. Taylor expanded in b around inf 62.5%

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

   if -4.6999999999999996e-18 < b < 9e-120 or 1.46000000000000004e-90 < b < 6.8e16

   1. Initial program 67.4%

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

   3. Taylor expanded in a around inf 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

      4. *-commutative 49.3%

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

   5. Simplified 49.3%

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

   if 9e-120 < b < 1.46000000000000004e-90

   1. Initial program 60.1%

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

   3. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

      2. *-commutative 99.7%

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

   5. Simplified 99.7%

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

   6. Taylor expanded in y around inf 81.2%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   if 6.1999999999999997e69 < b < 4.5999999999999998e102

   1. Initial program 77.6%

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

   3. Taylor expanded in z around inf 89.4%

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

      1. *-commutative 89.4%

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

      2. *-commutative 89.4%

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

   5. Simplified 89.4%

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

   6. Taylor expanded in y around inf 89.4%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{-18}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-120}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.46 \cdot 10^{-90}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 6.8 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+69} \lor \neg \left(b \leq 4.6 \cdot 10^{+102}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-204} \lor \neg \left(a \leq 4.2 \cdot 10^{-103}\right) \land a \leq 1.25 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -5.6e+110)
   (* a (- (* c j) (* x t)))
   (if (or (<= a 5.5e-204) (and (not (<= a 4.2e-103)) (<= a 1.25e-26)))
     (+ (* b (- (* t i) (* z c))) (* y (- (* x z) (* i j))))
     (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5.6e+110) {
		tmp = a * ((c * j) - (x * t));
	} else if ((a <= 5.5e-204) || (!(a <= 4.2e-103) && (a <= 1.25e-26))) {
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-5.6d+110)) then
        tmp = a * ((c * j) - (x * t))
    else if ((a <= 5.5d-204) .or. (.not. (a <= 4.2d-103)) .and. (a <= 1.25d-26)) then
        tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -5.6e+110) {
		tmp = a * ((c * j) - (x * t));
	} else if ((a <= 5.5e-204) || (!(a <= 4.2e-103) && (a <= 1.25e-26))) {
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -5.6e+110:
		tmp = a * ((c * j) - (x * t))
	elif (a <= 5.5e-204) or (not (a <= 4.2e-103) and (a <= 1.25e-26)):
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -5.6e+110)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif ((a <= 5.5e-204) || (!(a <= 4.2e-103) && (a <= 1.25e-26)))
		tmp = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(y * Float64(Float64(x * z) - Float64(i * j))));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -5.6e+110)
		tmp = a * ((c * j) - (x * t));
	elseif ((a <= 5.5e-204) || (~((a <= 4.2e-103)) && (a <= 1.25e-26)))
		tmp = (b * ((t * i) - (z * c))) + (y * ((x * z) - (i * j)));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -5.6e+110], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 5.5e-204], And[N[Not[LessEqual[a, 4.2e-103]], $MachinePrecision], LessEqual[a, 1.25e-26]]], N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.59999999999999973e110

   1. Initial program 60.2%

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

   3. Taylor expanded in a around inf 73.9%

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

      1. +-commutative 73.9%

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

      2. mul-1-neg 73.9%

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

      3. unsub-neg 73.9%

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

      4. *-commutative 73.9%

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

   5. Simplified 73.9%

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

   if -5.59999999999999973e110 < a < 5.4999999999999999e-204 or 4.20000000000000009e-103 < a < 1.25000000000000005e-26

   1. Initial program 75.6%

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

   3. Taylor expanded in a around 0 73.8%

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

   5. Simplified 75.2%

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

   if 5.4999999999999999e-204 < a < 4.20000000000000009e-103 or 1.25000000000000005e-26 < a

   1. Initial program 70.3%

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

   3. Taylor expanded in b around 0 70.6%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.6 \cdot 10^{+110}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{-204} \lor \neg \left(a \leq 4.2 \cdot 10^{-103}\right) \land a \leq 1.25 \cdot 10^{-26}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ t_2 := y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{-8}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-154}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+17}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (+ (* b (- (* t i) (* z c))) (* x (* y z))))
        (t_2 (* y (- (* x z) (- (* i j) (/ (* j (* a c)) y))))))
   (if (<= b -2.5e-8)
     t_1
     (if (<= b -4.2e-154)
       t_2
       (if (<= b -8e-234)
         (* a (- (* c j) (* x t)))
         (if (<= b 1.22e+17) t_2 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((t * i) - (z * c))) + (x * (y * z));
	double t_2 = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	double tmp;
	if (b <= -2.5e-8) {
		tmp = t_1;
	} else if (b <= -4.2e-154) {
		tmp = t_2;
	} else if (b <= -8e-234) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1.22e+17) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * ((t * i) - (z * c))) + (x * (y * z))
    t_2 = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)))
    if (b <= (-2.5d-8)) then
        tmp = t_1
    else if (b <= (-4.2d-154)) then
        tmp = t_2
    else if (b <= (-8d-234)) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 1.22d+17) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((t * i) - (z * c))) + (x * (y * z));
	double t_2 = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	double tmp;
	if (b <= -2.5e-8) {
		tmp = t_1;
	} else if (b <= -4.2e-154) {
		tmp = t_2;
	} else if (b <= -8e-234) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 1.22e+17) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((t * i) - (z * c))) + (x * (y * z))
	t_2 = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)))
	tmp = 0
	if b <= -2.5e-8:
		tmp = t_1
	elif b <= -4.2e-154:
		tmp = t_2
	elif b <= -8e-234:
		tmp = a * ((c * j) - (x * t))
	elif b <= 1.22e+17:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) + Float64(x * Float64(y * z)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) - Float64(Float64(j * Float64(a * c)) / y))))
	tmp = 0.0
	if (b <= -2.5e-8)
		tmp = t_1;
	elseif (b <= -4.2e-154)
		tmp = t_2;
	elseif (b <= -8e-234)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 1.22e+17)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * ((t * i) - (z * c))) + (x * (y * z));
	t_2 = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	tmp = 0.0;
	if (b <= -2.5e-8)
		tmp = t_1;
	elseif (b <= -4.2e-154)
		tmp = t_2;
	elseif (b <= -8e-234)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 1.22e+17)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] - N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.5e-8], t$95$1, If[LessEqual[b, -4.2e-154], t$95$2, If[LessEqual[b, -8e-234], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.22e+17], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.4999999999999999e-8 or 1.22e17 < b

   1. Initial program 77.1%

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

   3. Taylor expanded in a around 0 73.8%

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

   5. Simplified 71.5%

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

   6. Taylor expanded in j around 0 68.2%

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

   if -2.4999999999999999e-8 < b < -4.19999999999999969e-154 or -7.9999999999999997e-234 < b < 1.22e17

   1. Initial program 66.5%

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

   3. Taylor expanded in y around -inf 69.8%

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

   5. Simplified 71.6%

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

   6. Taylor expanded in j around inf 60.6%

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

      1. associate-*r* 62.1%

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

      2. *-commutative 62.1%

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

   8. Simplified 62.1%

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

   if -4.19999999999999969e-154 < b < -7.9999999999999997e-234

   1. Initial program 71.1%

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

   3. Taylor expanded in a around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

      4. *-commutative 67.6%

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

   5. Simplified 67.6%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{-8}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-154}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-234}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+17}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+201}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-60}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-240}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* a (* t (- x)))))
   (if (<= t -2.5e+201)
     t_2
     (if (<= t -6.2e+106)
       t_1
       (if (<= t -4e-60)
         t_2
         (if (<= t -2.9e-136)
           (* y (* x z))
           (if (<= t -2.25e-240)
             (* i (* y (- j)))
             (if (<= t 3.1e-10) (* x (* y z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = a * (t * -x);
	double tmp;
	if (t <= -2.5e+201) {
		tmp = t_2;
	} else if (t <= -6.2e+106) {
		tmp = t_1;
	} else if (t <= -4e-60) {
		tmp = t_2;
	} else if (t <= -2.9e-136) {
		tmp = y * (x * z);
	} else if (t <= -2.25e-240) {
		tmp = i * (y * -j);
	} else if (t <= 3.1e-10) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = a * (t * -x)
    if (t <= (-2.5d+201)) then
        tmp = t_2
    else if (t <= (-6.2d+106)) then
        tmp = t_1
    else if (t <= (-4d-60)) then
        tmp = t_2
    else if (t <= (-2.9d-136)) then
        tmp = y * (x * z)
    else if (t <= (-2.25d-240)) then
        tmp = i * (y * -j)
    else if (t <= 3.1d-10) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = a * (t * -x);
	double tmp;
	if (t <= -2.5e+201) {
		tmp = t_2;
	} else if (t <= -6.2e+106) {
		tmp = t_1;
	} else if (t <= -4e-60) {
		tmp = t_2;
	} else if (t <= -2.9e-136) {
		tmp = y * (x * z);
	} else if (t <= -2.25e-240) {
		tmp = i * (y * -j);
	} else if (t <= 3.1e-10) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = a * (t * -x)
	tmp = 0
	if t <= -2.5e+201:
		tmp = t_2
	elif t <= -6.2e+106:
		tmp = t_1
	elif t <= -4e-60:
		tmp = t_2
	elif t <= -2.9e-136:
		tmp = y * (x * z)
	elif t <= -2.25e-240:
		tmp = i * (y * -j)
	elif t <= 3.1e-10:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (t <= -2.5e+201)
		tmp = t_2;
	elseif (t <= -6.2e+106)
		tmp = t_1;
	elseif (t <= -4e-60)
		tmp = t_2;
	elseif (t <= -2.9e-136)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= -2.25e-240)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (t <= 3.1e-10)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = a * (t * -x);
	tmp = 0.0;
	if (t <= -2.5e+201)
		tmp = t_2;
	elseif (t <= -6.2e+106)
		tmp = t_1;
	elseif (t <= -4e-60)
		tmp = t_2;
	elseif (t <= -2.9e-136)
		tmp = y * (x * z);
	elseif (t <= -2.25e-240)
		tmp = i * (y * -j);
	elseif (t <= 3.1e-10)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+201], t$95$2, If[LessEqual[t, -6.2e+106], t$95$1, If[LessEqual[t, -4e-60], t$95$2, If[LessEqual[t, -2.9e-136], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.25e-240], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-10], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.4999999999999998e201 or -6.1999999999999999e106 < t < -3.9999999999999999e-60

   1. Initial program 75.3%

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

   3. Taylor expanded in a around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in j around 0 48.8%

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

      1. associate-*r* 48.8%

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

      2. mul-1-neg 48.8%

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

   8. Simplified 48.8%

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

   if -2.4999999999999998e201 < t < -6.1999999999999999e106 or 3.10000000000000015e-10 < t

   1. Initial program 59.3%

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

   3. Taylor expanded in t around inf 60.7%

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

      1. distribute-lft-out-- 60.7%

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

      2. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in a around 0 44.0%

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

      1. *-commutative 44.0%

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

   8. Simplified 44.0%

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

   if -3.9999999999999999e-60 < t < -2.89999999999999995e-136

   1. Initial program 77.1%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

      5. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -2.89999999999999995e-136 < t < -2.2500000000000001e-240

   1. Initial program 86.5%

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

   3. Taylor expanded in y around inf 64.7%

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

      1. +-commutative 64.7%

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

      2. mul-1-neg 64.7%

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

      3. unsub-neg 64.7%

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

      4. *-commutative 64.7%

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

      5. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in z around 0 52.0%

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

      1. associate-*r* 52.0%

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

      2. mul-1-neg 52.0%

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

      3. *-commutative 52.0%

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

   8. Simplified 52.0%

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

   if -2.2500000000000001e-240 < t < 3.10000000000000015e-10

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in y around inf 36.6%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+201}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-60}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-136}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-240}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-10}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+201}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-244}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* a (* t (- x)))))
   (if (<= t -2.5e+201)
     t_2
     (if (<= t -8.5e+105)
       t_1
       (if (<= t -2e-59)
         t_2
         (if (<= t -2.65e-138)
           (* y (* x z))
           (if (<= t -2.95e-244)
             (* y (- (* i j)))
             (if (<= t 4e-11) (* x (* y z)) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = a * (t * -x);
	double tmp;
	if (t <= -2.5e+201) {
		tmp = t_2;
	} else if (t <= -8.5e+105) {
		tmp = t_1;
	} else if (t <= -2e-59) {
		tmp = t_2;
	} else if (t <= -2.65e-138) {
		tmp = y * (x * z);
	} else if (t <= -2.95e-244) {
		tmp = y * -(i * j);
	} else if (t <= 4e-11) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = a * (t * -x)
    if (t <= (-2.5d+201)) then
        tmp = t_2
    else if (t <= (-8.5d+105)) then
        tmp = t_1
    else if (t <= (-2d-59)) then
        tmp = t_2
    else if (t <= (-2.65d-138)) then
        tmp = y * (x * z)
    else if (t <= (-2.95d-244)) then
        tmp = y * -(i * j)
    else if (t <= 4d-11) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = a * (t * -x);
	double tmp;
	if (t <= -2.5e+201) {
		tmp = t_2;
	} else if (t <= -8.5e+105) {
		tmp = t_1;
	} else if (t <= -2e-59) {
		tmp = t_2;
	} else if (t <= -2.65e-138) {
		tmp = y * (x * z);
	} else if (t <= -2.95e-244) {
		tmp = y * -(i * j);
	} else if (t <= 4e-11) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = a * (t * -x)
	tmp = 0
	if t <= -2.5e+201:
		tmp = t_2
	elif t <= -8.5e+105:
		tmp = t_1
	elif t <= -2e-59:
		tmp = t_2
	elif t <= -2.65e-138:
		tmp = y * (x * z)
	elif t <= -2.95e-244:
		tmp = y * -(i * j)
	elif t <= 4e-11:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (t <= -2.5e+201)
		tmp = t_2;
	elseif (t <= -8.5e+105)
		tmp = t_1;
	elseif (t <= -2e-59)
		tmp = t_2;
	elseif (t <= -2.65e-138)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= -2.95e-244)
		tmp = Float64(y * Float64(-Float64(i * j)));
	elseif (t <= 4e-11)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = a * (t * -x);
	tmp = 0.0;
	if (t <= -2.5e+201)
		tmp = t_2;
	elseif (t <= -8.5e+105)
		tmp = t_1;
	elseif (t <= -2e-59)
		tmp = t_2;
	elseif (t <= -2.65e-138)
		tmp = y * (x * z);
	elseif (t <= -2.95e-244)
		tmp = y * -(i * j);
	elseif (t <= 4e-11)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.5e+201], t$95$2, If[LessEqual[t, -8.5e+105], t$95$1, If[LessEqual[t, -2e-59], t$95$2, If[LessEqual[t, -2.65e-138], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.95e-244], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, 4e-11], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.4999999999999998e201 or -8.49999999999999986e105 < t < -2.0000000000000001e-59

   1. Initial program 75.3%

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

   3. Taylor expanded in a around inf 55.9%

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

      1. +-commutative 55.9%

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

      2. mul-1-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. *-commutative 55.9%

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

   5. Simplified 55.9%

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

   6. Taylor expanded in j around 0 48.8%

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

      1. associate-*r* 48.8%

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

      2. mul-1-neg 48.8%

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

   8. Simplified 48.8%

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

   if -2.4999999999999998e201 < t < -8.49999999999999986e105 or 3.99999999999999976e-11 < t

   1. Initial program 59.3%

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

   3. Taylor expanded in t around inf 60.7%

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

      1. distribute-lft-out-- 60.7%

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

      2. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in a around 0 44.0%

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

      1. *-commutative 44.0%

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

   8. Simplified 44.0%

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

   if -2.0000000000000001e-59 < t < -2.65000000000000013e-138

   1. Initial program 77.1%

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

   3. Taylor expanded in y around inf 62.5%

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

      1. +-commutative 62.5%

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

      2. mul-1-neg 62.5%

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

      3. unsub-neg 62.5%

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

      4. *-commutative 62.5%

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

      5. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   6. Taylor expanded in z around inf 54.7%

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

      1. *-commutative 54.7%

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

   8. Simplified 54.7%

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

   if -2.65000000000000013e-138 < t < -2.9500000000000002e-244

   1. Initial program 86.5%

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

   3. Taylor expanded in y around inf 64.7%

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

      1. +-commutative 64.7%

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

      2. mul-1-neg 64.7%

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

      3. unsub-neg 64.7%

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

      4. *-commutative 64.7%

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

      5. *-commutative 64.7%

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

   5. Simplified 64.7%

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

   6. Taylor expanded in z around 0 47.4%

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

      1. mul-1-neg 47.4%

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

      2. distribute-rgt-neg-in 47.4%

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

   8. Simplified 47.4%

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

   if -2.9500000000000002e-244 < t < 3.99999999999999976e-11

   1. Initial program 76.9%

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

   3. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

      2. *-commutative 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in y around inf 36.6%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+201}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+105}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-59}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;t \leq -2.65 \cdot 10^{-138}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -2.95 \cdot 10^{-244}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -6.8 \cdot 10^{-22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-151}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3.9 \cdot 10^{-293}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 4.15 \cdot 10^{-63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (- (* x y) (* b c))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -6.8e-22)
     t_3
     (if (<= i -7.5e-151)
       t_2
       (if (<= i -5e-193)
         t_1
         (if (<= i -3.9e-293) t_2 (if (<= i 4.15e-63) 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 = z * ((x * y) - (b * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -6.8e-22) {
		tmp = t_3;
	} else if (i <= -7.5e-151) {
		tmp = t_2;
	} else if (i <= -5e-193) {
		tmp = t_1;
	} else if (i <= -3.9e-293) {
		tmp = t_2;
	} else if (i <= 4.15e-63) {
		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 = z * ((x * y) - (b * c))
    t_2 = a * ((c * j) - (x * t))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-6.8d-22)) then
        tmp = t_3
    else if (i <= (-7.5d-151)) then
        tmp = t_2
    else if (i <= (-5d-193)) then
        tmp = t_1
    else if (i <= (-3.9d-293)) then
        tmp = t_2
    else if (i <= 4.15d-63) 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 = z * ((x * y) - (b * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -6.8e-22) {
		tmp = t_3;
	} else if (i <= -7.5e-151) {
		tmp = t_2;
	} else if (i <= -5e-193) {
		tmp = t_1;
	} else if (i <= -3.9e-293) {
		tmp = t_2;
	} else if (i <= 4.15e-63) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * ((x * y) - (b * c))
	t_2 = a * ((c * j) - (x * t))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -6.8e-22:
		tmp = t_3
	elif i <= -7.5e-151:
		tmp = t_2
	elif i <= -5e-193:
		tmp = t_1
	elif i <= -3.9e-293:
		tmp = t_2
	elif i <= 4.15e-63:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -6.8e-22)
		tmp = t_3;
	elseif (i <= -7.5e-151)
		tmp = t_2;
	elseif (i <= -5e-193)
		tmp = t_1;
	elseif (i <= -3.9e-293)
		tmp = t_2;
	elseif (i <= 4.15e-63)
		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 = z * ((x * y) - (b * c));
	t_2 = a * ((c * j) - (x * t));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -6.8e-22)
		tmp = t_3;
	elseif (i <= -7.5e-151)
		tmp = t_2;
	elseif (i <= -5e-193)
		tmp = t_1;
	elseif (i <= -3.9e-293)
		tmp = t_2;
	elseif (i <= 4.15e-63)
		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[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.8e-22], t$95$3, If[LessEqual[i, -7.5e-151], t$95$2, If[LessEqual[i, -5e-193], t$95$1, If[LessEqual[i, -3.9e-293], t$95$2, If[LessEqual[i, 4.15e-63], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -6.7999999999999997e-22 or 4.1499999999999998e-63 < i

   1. Initial program 65.4%

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

   3. Taylor expanded in a around 0 67.5%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in i around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. unsub-neg 63.5%

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

      4. *-commutative 63.5%

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

   8. Simplified 63.5%

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

   if -6.7999999999999997e-22 < i < -7.5000000000000004e-151 or -5.0000000000000005e-193 < i < -3.9e-293

   1. Initial program 86.2%

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

   3. Taylor expanded in a around inf 67.3%

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

      1. +-commutative 67.3%

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

      2. mul-1-neg 67.3%

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

      3. unsub-neg 67.3%

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

      4. *-commutative 67.3%

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

   5. Simplified 67.3%

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

   if -7.5000000000000004e-151 < i < -5.0000000000000005e-193 or -3.9e-293 < i < 4.1499999999999998e-63

   1. Initial program 72.6%

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

   3. Taylor expanded in z around inf 55.6%

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

      1. *-commutative 55.6%

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

      2. *-commutative 55.6%

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

   5. Simplified 55.6%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.8 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-151}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -5 \cdot 10^{-193}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;i \leq -3.9 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 4.15 \cdot 10^{-63}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 50.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.65 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-297}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-189}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 7.4 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -3.65e-22)
     t_1
     (if (<= i 2.8e-297)
       (* a (- (* c j) (* x t)))
       (if (<= i 5.5e-189)
         (* b (- (* t i) (* z c)))
         (if (<= i 1.6e-77)
           (* y (- (* x z) (* i j)))
           (if (<= i 7.4e-51) (* c (- (* a j) (* z b))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.65e-22) {
		tmp = t_1;
	} else if (i <= 2.8e-297) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 5.5e-189) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 1.6e-77) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 7.4e-51) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-3.65d-22)) then
        tmp = t_1
    else if (i <= 2.8d-297) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 5.5d-189) then
        tmp = b * ((t * i) - (z * c))
    else if (i <= 1.6d-77) then
        tmp = y * ((x * z) - (i * j))
    else if (i <= 7.4d-51) then
        tmp = c * ((a * j) - (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.65e-22) {
		tmp = t_1;
	} else if (i <= 2.8e-297) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 5.5e-189) {
		tmp = b * ((t * i) - (z * c));
	} else if (i <= 1.6e-77) {
		tmp = y * ((x * z) - (i * j));
	} else if (i <= 7.4e-51) {
		tmp = c * ((a * j) - (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.65e-22:
		tmp = t_1
	elif i <= 2.8e-297:
		tmp = a * ((c * j) - (x * t))
	elif i <= 5.5e-189:
		tmp = b * ((t * i) - (z * c))
	elif i <= 1.6e-77:
		tmp = y * ((x * z) - (i * j))
	elif i <= 7.4e-51:
		tmp = c * ((a * j) - (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.65e-22)
		tmp = t_1;
	elseif (i <= 2.8e-297)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 5.5e-189)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (i <= 1.6e-77)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (i <= 7.4e-51)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.65e-22)
		tmp = t_1;
	elseif (i <= 2.8e-297)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 5.5e-189)
		tmp = b * ((t * i) - (z * c));
	elseif (i <= 1.6e-77)
		tmp = y * ((x * z) - (i * j));
	elseif (i <= 7.4e-51)
		tmp = c * ((a * j) - (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.65e-22], t$95$1, If[LessEqual[i, 2.8e-297], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.5e-189], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.6e-77], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.4e-51], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -3.65000000000000014e-22 or 7.39999999999999946e-51 < i

   1. Initial program 65.4%

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

   3. Taylor expanded in a around 0 67.5%

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

   5. Simplified 65.5%

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

   6. Taylor expanded in i around inf 64.1%

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

      1. +-commutative 64.1%

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

      2. mul-1-neg 64.1%

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

      3. unsub-neg 64.1%

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

      4. *-commutative 64.1%

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

   8. Simplified 64.1%

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

   if -3.65000000000000014e-22 < i < 2.79999999999999984e-297

   1. Initial program 82.9%

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

   3. Taylor expanded in a around inf 58.8%

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

      1. +-commutative 58.8%

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

      2. mul-1-neg 58.8%

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

      3. unsub-neg 58.8%

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

      4. *-commutative 58.8%

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

   5. Simplified 58.8%

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

   if 2.79999999999999984e-297 < i < 5.4999999999999999e-189

   1. Initial program 83.7%

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

   3. Taylor expanded in b around inf 59.3%

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

   if 5.4999999999999999e-189 < i < 1.6e-77

   1. Initial program 65.4%

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

   3. Taylor expanded in y around inf 44.1%

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

      1. +-commutative 44.1%

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

      2. mul-1-neg 44.1%

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

      3. unsub-neg 44.1%

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

      4. *-commutative 44.1%

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

      5. *-commutative 44.1%

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

   5. Simplified 44.1%

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

   if 1.6e-77 < i < 7.39999999999999946e-51

   1. Initial program 67.4%

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

   3. Taylor expanded in c around inf 83.5%

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

      1. *-commutative 83.5%

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

   5. Simplified 83.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.65 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 2.8 \cdot 10^{-297}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.5 \cdot 10^{-189}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;i \leq 7.4 \cdot 10^{-51}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 51.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -3.65 \cdot 10^{-22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-304}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-194}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-44}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -3.65e-22)
     t_3
     (if (<= i 8.5e-304)
       t_2
       (if (<= i 2e-194)
         t_1
         (if (<= i 2.5e-51) t_2 (if (<= i 4e-44) t_1 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.65e-22) {
		tmp = t_3;
	} else if (i <= 8.5e-304) {
		tmp = t_2;
	} else if (i <= 2e-194) {
		tmp = t_1;
	} else if (i <= 2.5e-51) {
		tmp = t_2;
	} else if (i <= 4e-44) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-3.65d-22)) then
        tmp = t_3
    else if (i <= 8.5d-304) then
        tmp = t_2
    else if (i <= 2d-194) then
        tmp = t_1
    else if (i <= 2.5d-51) then
        tmp = t_2
    else if (i <= 4d-44) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -3.65e-22) {
		tmp = t_3;
	} else if (i <= 8.5e-304) {
		tmp = t_2;
	} else if (i <= 2e-194) {
		tmp = t_1;
	} else if (i <= 2.5e-51) {
		tmp = t_2;
	} else if (i <= 4e-44) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -3.65e-22:
		tmp = t_3
	elif i <= 8.5e-304:
		tmp = t_2
	elif i <= 2e-194:
		tmp = t_1
	elif i <= 2.5e-51:
		tmp = t_2
	elif i <= 4e-44:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -3.65e-22)
		tmp = t_3;
	elseif (i <= 8.5e-304)
		tmp = t_2;
	elseif (i <= 2e-194)
		tmp = t_1;
	elseif (i <= 2.5e-51)
		tmp = t_2;
	elseif (i <= 4e-44)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -3.65e-22)
		tmp = t_3;
	elseif (i <= 8.5e-304)
		tmp = t_2;
	elseif (i <= 2e-194)
		tmp = t_1;
	elseif (i <= 2.5e-51)
		tmp = t_2;
	elseif (i <= 4e-44)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -3.65e-22], t$95$3, If[LessEqual[i, 8.5e-304], t$95$2, If[LessEqual[i, 2e-194], t$95$1, If[LessEqual[i, 2.5e-51], t$95$2, If[LessEqual[i, 4e-44], t$95$1, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.65000000000000014e-22 or 3.99999999999999981e-44 < i

   1. Initial program 64.8%

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

   3. Taylor expanded in a around 0 67.0%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in i around inf 64.2%

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

      1. +-commutative 64.2%

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

      2. mul-1-neg 64.2%

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

      3. unsub-neg 64.2%

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

      4. *-commutative 64.2%

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

   8. Simplified 64.2%

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

   if -3.65000000000000014e-22 < i < 8.5e-304 or 2.00000000000000004e-194 < i < 2.50000000000000002e-51

   1. Initial program 77.3%

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

   3. Taylor expanded in a around inf 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

      4. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   if 8.5e-304 < i < 2.00000000000000004e-194 or 2.50000000000000002e-51 < i < 3.99999999999999981e-44

   1. Initial program 85.4%

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

   3. Taylor expanded in b around inf 63.7%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.65 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 8.5 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-51}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 4 \cdot 10^{-44}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 41.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+98}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+92}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))) (t_2 (* x (* y z))))
   (if (<= z -4.6e+98)
     t_2
     (if (<= z -2.95e-304)
       t_1
       (if (<= z 1.4e-275) (* y (- (* i j))) (if (<= z 3.2e+92) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -4.6e+98) {
		tmp = t_2;
	} else if (z <= -2.95e-304) {
		tmp = t_1;
	} else if (z <= 1.4e-275) {
		tmp = y * -(i * j);
	} else if (z <= 3.2e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    t_2 = x * (y * z)
    if (z <= (-4.6d+98)) then
        tmp = t_2
    else if (z <= (-2.95d-304)) then
        tmp = t_1
    else if (z <= 1.4d-275) then
        tmp = y * -(i * j)
    else if (z <= 3.2d+92) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -4.6e+98) {
		tmp = t_2;
	} else if (z <= -2.95e-304) {
		tmp = t_1;
	} else if (z <= 1.4e-275) {
		tmp = y * -(i * j);
	} else if (z <= 3.2e+92) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	t_2 = x * (y * z)
	tmp = 0
	if z <= -4.6e+98:
		tmp = t_2
	elif z <= -2.95e-304:
		tmp = t_1
	elif z <= 1.4e-275:
		tmp = y * -(i * j)
	elif z <= 3.2e+92:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -4.6e+98)
		tmp = t_2;
	elseif (z <= -2.95e-304)
		tmp = t_1;
	elseif (z <= 1.4e-275)
		tmp = Float64(y * Float64(-Float64(i * j)));
	elseif (z <= 3.2e+92)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -4.6e+98)
		tmp = t_2;
	elseif (z <= -2.95e-304)
		tmp = t_1;
	elseif (z <= 1.4e-275)
		tmp = y * -(i * j);
	elseif (z <= 3.2e+92)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+98], t$95$2, If[LessEqual[z, -2.95e-304], t$95$1, If[LessEqual[z, 1.4e-275], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[z, 3.2e+92], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.60000000000000026e98 or 3.20000000000000025e92 < z

   1. Initial program 59.8%

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

   3. Taylor expanded in z around inf 67.8%

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

      1. *-commutative 67.8%

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

      2. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in y around inf 46.6%

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

   if -4.60000000000000026e98 < z < -2.95e-304 or 1.39999999999999997e-275 < z < 3.20000000000000025e92

   1. Initial program 77.6%

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

   3. Taylor expanded in a around inf 46.6%

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

      1. +-commutative 46.6%

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

      2. mul-1-neg 46.6%

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

      3. unsub-neg 46.6%

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

      4. *-commutative 46.6%

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

   5. Simplified 46.6%

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

   if -2.95e-304 < z < 1.39999999999999997e-275

   1. Initial program 79.7%

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

   3. Taylor expanded in y around inf 71.7%

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

      1. +-commutative 71.7%

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

      2. mul-1-neg 71.7%

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

      3. unsub-neg 71.7%

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

      4. *-commutative 71.7%

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

      5. *-commutative 71.7%

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

   5. Simplified 71.7%

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

   6. Taylor expanded in z around 0 71.7%

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

      1. mul-1-neg 71.7%

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

      2. distribute-rgt-neg-in 71.7%

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

   8. Simplified 71.7%

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

4. Final simplification 47.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+98}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-304}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-275}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+92}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 64.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -2.4e-16)
   (* y (- (* x z) (+ (* i j) (/ (* a (* x t)) y))))
   (if (<= y 4.8e+69)
     (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
     (* y (- (* x z) (- (* i j) (/ (* j (* a c)) y)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.4e-16) {
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	} else if (y <= 4.8e+69) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-2.4d-16)) then
        tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
    else if (y <= 4.8d+69) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else
        tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.4e-16) {
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	} else if (y <= 4.8e+69) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -2.4e-16:
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)))
	elif y <= 4.8e+69:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	else:
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -2.4e-16)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) + Float64(Float64(a * Float64(x * t)) / y))));
	elseif (y <= 4.8e+69)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(y * Float64(Float64(x * z) - Float64(Float64(i * j) - Float64(Float64(j * Float64(a * c)) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -2.4e-16)
		tmp = y * ((x * z) - ((i * j) + ((a * (x * t)) / y)));
	elseif (y <= 4.8e+69)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	else
		tmp = y * ((x * z) - ((i * j) - ((j * (a * c)) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -2.4e-16], N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] + N[(N[(a * N[(x * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e+69], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * z), $MachinePrecision] - N[(N[(i * j), $MachinePrecision] - N[(N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000005e-16

   1. Initial program 60.8%

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

   3. Taylor expanded in y around -inf 84.2%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in x around inf 73.9%

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

      1. associate-*r/ 73.9%

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

      2. associate-*r* 73.9%

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

      3. mul-1-neg 73.9%

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

   8. Simplified 73.9%

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

   if -2.40000000000000005e-16 < y < 4.8000000000000003e69

   1. Initial program 80.9%

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

   3. Taylor expanded in j around 0 69.2%

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

   if 4.8000000000000003e69 < y

   1. Initial program 63.9%

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

   3. Taylor expanded in y around -inf 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in j around inf 73.3%

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

      1. associate-*r* 79.6%

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

      2. *-commutative 79.6%

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

   8. Simplified 79.6%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j + \frac{a \cdot \left(x \cdot t\right)}{y}\right)\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+69}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - \left(i \cdot j - \frac{j \cdot \left(a \cdot c\right)}{y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 53.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq -8.6 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 7.9 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -2.9e-22)
   (* i (* y (- (* b (/ t y)) j)))
   (if (<= i -8.6e-293)
     (* a (- (* c j) (* x t)))
     (if (<= i 7.9e-53)
       (* z (* x (- y (* b (/ c x)))))
       (* i (- (* t b) (* y 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 <= -2.9e-22) {
		tmp = i * (y * ((b * (t / y)) - j));
	} else if (i <= -8.6e-293) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 7.9e-53) {
		tmp = z * (x * (y - (b * (c / x))));
	} else {
		tmp = i * ((t * b) - (y * 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 <= (-2.9d-22)) then
        tmp = i * (y * ((b * (t / y)) - j))
    else if (i <= (-8.6d-293)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 7.9d-53) then
        tmp = z * (x * (y - (b * (c / x))))
    else
        tmp = i * ((t * b) - (y * 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 <= -2.9e-22) {
		tmp = i * (y * ((b * (t / y)) - j));
	} else if (i <= -8.6e-293) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 7.9e-53) {
		tmp = z * (x * (y - (b * (c / x))));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -2.9e-22:
		tmp = i * (y * ((b * (t / y)) - j))
	elif i <= -8.6e-293:
		tmp = a * ((c * j) - (x * t))
	elif i <= 7.9e-53:
		tmp = z * (x * (y - (b * (c / x))))
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -2.9e-22)
		tmp = Float64(i * Float64(y * Float64(Float64(b * Float64(t / y)) - j)));
	elseif (i <= -8.6e-293)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 7.9e-53)
		tmp = Float64(z * Float64(x * Float64(y - Float64(b * Float64(c / x)))));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -2.9e-22)
		tmp = i * (y * ((b * (t / y)) - j));
	elseif (i <= -8.6e-293)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 7.9e-53)
		tmp = z * (x * (y - (b * (c / x))));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -2.9e-22], N[(i * N[(y * N[(N[(b * N[(t / y), $MachinePrecision]), $MachinePrecision] - j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8.6e-293], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.9e-53], N[(z * N[(x * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.9000000000000002e-22

   1. Initial program 60.7%

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

   3. Taylor expanded in y around -inf 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in i around inf 69.0%

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

      1. associate-*r* 69.0%

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

      2. mul-1-neg 69.0%

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

      3. associate-/l* 69.1%

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

   8. Simplified 69.1%

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

   if -2.9000000000000002e-22 < i < -8.5999999999999996e-293

   1. Initial program 84.4%

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

   3. Taylor expanded in a around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if -8.5999999999999996e-293 < i < 7.8999999999999998e-53

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. *-commutative 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in x around inf 52.4%

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

      1. mul-1-neg 52.4%

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

      2. unsub-neg 52.4%

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

      3. associate-/l* 55.8%

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

   8. Simplified 55.8%

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

   if 7.8999999999999998e-53 < i

   1. Initial program 69.7%

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

   3. Taylor expanded in a around 0 68.0%

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

   5. Simplified 64.2%

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

   6. Taylor expanded in i around inf 59.7%

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

      1. +-commutative 59.7%

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

      2. mul-1-neg 59.7%

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

      3. unsub-neg 59.7%

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

      4. *-commutative 59.7%

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

   8. Simplified 59.7%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.9 \cdot 10^{-22}:\\ \;\;\;\;i \cdot \left(y \cdot \left(b \cdot \frac{t}{y} - j\right)\right)\\ \mathbf{elif}\;i \leq -8.6 \cdot 10^{-293}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 7.9 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 53.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 6.7 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -6.8e-23)
     t_1
     (if (<= i -7.2e-294)
       (* a (- (* c j) (* x t)))
       (if (<= i 6.7e-53) (* z (* x (- y (* b (/ c x))))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -6.8e-23) {
		tmp = t_1;
	} else if (i <= -7.2e-294) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 6.7e-53) {
		tmp = z * (x * (y - (b * (c / x))));
	} 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 = i * ((t * b) - (y * j))
    if (i <= (-6.8d-23)) then
        tmp = t_1
    else if (i <= (-7.2d-294)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 6.7d-53) then
        tmp = z * (x * (y - (b * (c / x))))
    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 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -6.8e-23) {
		tmp = t_1;
	} else if (i <= -7.2e-294) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 6.7e-53) {
		tmp = z * (x * (y - (b * (c / x))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -6.8e-23:
		tmp = t_1
	elif i <= -7.2e-294:
		tmp = a * ((c * j) - (x * t))
	elif i <= 6.7e-53:
		tmp = z * (x * (y - (b * (c / x))))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -6.8e-23)
		tmp = t_1;
	elseif (i <= -7.2e-294)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 6.7e-53)
		tmp = Float64(z * Float64(x * Float64(y - Float64(b * Float64(c / x)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -6.8e-23)
		tmp = t_1;
	elseif (i <= -7.2e-294)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 6.7e-53)
		tmp = z * (x * (y - (b * (c / x))));
	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[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -6.8e-23], t$95$1, If[LessEqual[i, -7.2e-294], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.7e-53], N[(z * N[(x * N[(y - N[(b * N[(c / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if i < -6.8000000000000001e-23 or 6.69999999999999957e-53 < i

   1. Initial program 65.4%

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

   3. Taylor expanded in a around 0 67.5%

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

   5. Simplified 64.8%

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

   6. Taylor expanded in i around inf 63.5%

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

      1. +-commutative 63.5%

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

      2. mul-1-neg 63.5%

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

      3. unsub-neg 63.5%

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

      4. *-commutative 63.5%

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

   8. Simplified 63.5%

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

   if -6.8000000000000001e-23 < i < -7.2000000000000003e-294

   1. Initial program 84.4%

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

   3. Taylor expanded in a around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if -7.2000000000000003e-294 < i < 6.69999999999999957e-53

   1. Initial program 73.2%

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

   3. Taylor expanded in z around inf 54.0%

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

      1. *-commutative 54.0%

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

      2. *-commutative 54.0%

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

   5. Simplified 54.0%

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

   6. Taylor expanded in x around inf 52.4%

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

      1. mul-1-neg 52.4%

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

      2. unsub-neg 52.4%

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

      3. associate-/l* 55.8%

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

   8. Simplified 55.8%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6.8 \cdot 10^{-23}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -7.2 \cdot 10^{-294}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 6.7 \cdot 10^{-53}:\\ \;\;\;\;z \cdot \left(x \cdot \left(y - b \cdot \frac{c}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -4.5 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -4.5e+108)
     t_1
     (if (<= t -4.2e-135)
       (* y (* x z))
       (if (<= t -1.26e-247)
         (* y (- (* i j)))
         (if (<= t 2.7e-12) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (t <= -4.5e+108) {
		tmp = t_1;
	} else if (t <= -4.2e-135) {
		tmp = y * (x * z);
	} else if (t <= -1.26e-247) {
		tmp = y * -(i * j);
	} else if (t <= 2.7e-12) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (t <= (-4.5d+108)) then
        tmp = t_1
    else if (t <= (-4.2d-135)) then
        tmp = y * (x * z)
    else if (t <= (-1.26d-247)) then
        tmp = y * -(i * j)
    else if (t <= 2.7d-12) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (t <= -4.5e+108) {
		tmp = t_1;
	} else if (t <= -4.2e-135) {
		tmp = y * (x * z);
	} else if (t <= -1.26e-247) {
		tmp = y * -(i * j);
	} else if (t <= 2.7e-12) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if t <= -4.5e+108:
		tmp = t_1
	elif t <= -4.2e-135:
		tmp = y * (x * z)
	elif t <= -1.26e-247:
		tmp = y * -(i * j)
	elif t <= 2.7e-12:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -4.5e+108)
		tmp = t_1;
	elseif (t <= -4.2e-135)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= -1.26e-247)
		tmp = Float64(y * Float64(-Float64(i * j)));
	elseif (t <= 2.7e-12)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (t <= -4.5e+108)
		tmp = t_1;
	elseif (t <= -4.2e-135)
		tmp = y * (x * z);
	elseif (t <= -1.26e-247)
		tmp = y * -(i * j);
	elseif (t <= 2.7e-12)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.5e+108], t$95$1, If[LessEqual[t, -4.2e-135], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.26e-247], N[(y * (-N[(i * j), $MachinePrecision])), $MachinePrecision], If[LessEqual[t, 2.7e-12], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.5e108 or 2.6999999999999998e-12 < t

   1. Initial program 61.9%

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

   3. Taylor expanded in t around inf 68.4%

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

      1. distribute-lft-out-- 68.4%

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

      2. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   6. Taylor expanded in a around 0 41.9%

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

      1. *-commutative 41.9%

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

   8. Simplified 41.9%

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

   if -4.5e108 < t < -4.2e-135

   1. Initial program 79.9%

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

   3. Taylor expanded in y around inf 47.7%

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

      1. +-commutative 47.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 47.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 47.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 47.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

      5. *-commutative 47.7%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   5. Simplified 47.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   6. Taylor expanded in z around inf 34.2%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 34.2%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   8. Simplified 34.2%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -4.2e-135 < t < -1.25999999999999999e-247

   1. Initial program 86.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 64.7%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 64.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 64.7%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 64.7%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 64.7%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

      5. *-commutative 64.7%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   5. Simplified 64.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   6. Taylor expanded in z around 0 47.4%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 47.4%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-rgt-neg-in 47.4%

         \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   8. Simplified 47.4%

      \[\leadsto y \cdot \color{blue}{\left(i \cdot \left(-j\right)\right)} \]

   if -1.25999999999999999e-247 < t < 2.6999999999999998e-12

   1. Initial program 76.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 50.4%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.4%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 50.4%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 50.4%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 36.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-135}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq -1.26 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \left(-i \cdot j\right)\\ \mathbf{elif}\;t \leq 2.7 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;t \leq -6.2 \cdot 10^{+108}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-292}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-295}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= t -6.2e+108)
     t_1
     (if (<= t -4.4e-292)
       (* y (* x z))
       (if (<= t 3.5e-295)
         (* j (* a c))
         (if (<= t 1.75e-12) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (t <= -6.2e+108) {
		tmp = t_1;
	} else if (t <= -4.4e-292) {
		tmp = y * (x * z);
	} else if (t <= 3.5e-295) {
		tmp = j * (a * c);
	} else if (t <= 1.75e-12) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (t <= (-6.2d+108)) then
        tmp = t_1
    else if (t <= (-4.4d-292)) then
        tmp = y * (x * z)
    else if (t <= 3.5d-295) then
        tmp = j * (a * c)
    else if (t <= 1.75d-12) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (t <= -6.2e+108) {
		tmp = t_1;
	} else if (t <= -4.4e-292) {
		tmp = y * (x * z);
	} else if (t <= 3.5e-295) {
		tmp = j * (a * c);
	} else if (t <= 1.75e-12) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if t <= -6.2e+108:
		tmp = t_1
	elif t <= -4.4e-292:
		tmp = y * (x * z)
	elif t <= 3.5e-295:
		tmp = j * (a * c)
	elif t <= 1.75e-12:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (t <= -6.2e+108)
		tmp = t_1;
	elseif (t <= -4.4e-292)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 3.5e-295)
		tmp = Float64(j * Float64(a * c));
	elseif (t <= 1.75e-12)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (t <= -6.2e+108)
		tmp = t_1;
	elseif (t <= -4.4e-292)
		tmp = y * (x * z);
	elseif (t <= 3.5e-295)
		tmp = j * (a * c);
	elseif (t <= 1.75e-12)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.2e+108], t$95$1, If[LessEqual[t, -4.4e-292], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.5e-295], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.75e-12], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.2000000000000003e108 or 1.75e-12 < t

   1. Initial program 61.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 68.4%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 68.4%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 68.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0 41.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 41.9%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 41.9%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -6.2000000000000003e108 < t < -4.40000000000000023e-292

   1. Initial program 81.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 51.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 51.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 51.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 51.1%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

      5. *-commutative 51.1%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   5. Simplified 51.1%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   6. Taylor expanded in z around inf 30.3%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 30.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   8. Simplified 30.3%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if -4.40000000000000023e-292 < t < 3.49999999999999988e-295

   1. Initial program 72.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 47.9%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.9%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.9%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 47.9%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 47.9%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 47.9%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 59.9%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

      2. *-commutative 59.9%

         \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   8. Simplified 59.9%

      \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

   if 3.49999999999999988e-295 < t < 1.75e-12

   1. Initial program 77.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 49.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 49.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 49.7%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 49.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 38.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{+108}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-292}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-295}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+108} \lor \neg \left(t \leq 3.7 \cdot 10^{-10}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= t -7e+108) (not (<= t 3.7e-10))) (* b (* t i)) (* x (* y z))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((t <= -7e+108) || !(t <= 3.7e-10)) {
		tmp = b * (t * i);
	} else {
		tmp = x * (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) :: tmp
    if ((t <= (-7d+108)) .or. (.not. (t <= 3.7d-10))) then
        tmp = b * (t * i)
    else
        tmp = x * (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 tmp;
	if ((t <= -7e+108) || !(t <= 3.7e-10)) {
		tmp = b * (t * i);
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (t <= -7e+108) or not (t <= 3.7e-10):
		tmp = b * (t * i)
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((t <= -7e+108) || !(t <= 3.7e-10))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((t <= -7e+108) || ~((t <= 3.7e-10)))
		tmp = b * (t * i);
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[t, -7e+108], N[Not[LessEqual[t, 3.7e-10]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.0000000000000005e108 or 3.70000000000000015e-10 < t

   1. Initial program 61.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 68.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 68.4%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 68.4%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 68.4%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0 41.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 41.9%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 41.9%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -7.0000000000000005e108 < t < 3.70000000000000015e-10

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 43.7%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 43.7%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 43.7%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 43.7%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 31.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7 \cdot 10^{+108} \lor \neg \left(t \leq 3.7 \cdot 10^{-10}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 30.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.65 \cdot 10^{-6} \lor \neg \left(i \leq 9.6 \cdot 10^{-12}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.65e-6) (not (<= i 9.6e-12))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.65e-6) || !(i <= 9.6e-12)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.65d-6)) .or. (.not. (i <= 9.6d-12))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.65e-6) || !(i <= 9.6e-12)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.65e-6) or not (i <= 9.6e-12):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.65e-6) || !(i <= 9.6e-12))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.65e-6) || ~((i <= 9.6e-12)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.65e-6], N[Not[LessEqual[i, 9.6e-12]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.65000000000000008e-6 or 9.59999999999999948e-12 < i

   1. Initial program 62.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 51.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x\right) - -1 \cdot \left(b \cdot i\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 51.7%

         \[\leadsto t \cdot \color{blue}{\left(-1 \cdot \left(a \cdot x - b \cdot i\right)\right)} \]

      2. *-commutative 51.7%

         \[\leadsto t \cdot \left(-1 \cdot \left(a \cdot x - \color{blue}{i \cdot b}\right)\right) \]

   5. Simplified 51.7%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]

   6. Taylor expanded in a around 0 40.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -1.65000000000000008e-6 < i < 9.59999999999999948e-12

   1. Initial program 80.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 47.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 47.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 47.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 47.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 47.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 47.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 27.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.65 \cdot 10^{-6} \lor \neg \left(i \leq 9.6 \cdot 10^{-12}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 20.9% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.3e+161) (* b (* z c)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.3e+161) {
		tmp = b * (z * c);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-3.3d+161)) then
        tmp = b * (z * c)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.3e+161) {
		tmp = b * (z * c);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.3e+161:
		tmp = b * (z * c)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.3e+161)
		tmp = Float64(b * Float64(z * c));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.3e+161)
		tmp = b * (z * c);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.3e+161], N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.29999999999999997e161

   1. Initial program 71.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 43.3%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 43.3%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 43.3%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 43.3%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around 0 22.5%

      \[\leadsto z \cdot \color{blue}{\left(-1 \cdot \left(b \cdot c\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 22.5%

         \[\leadsto z \cdot \color{blue}{\left(-b \cdot c\right)} \]

      2. distribute-rgt-neg-in 22.5%

         \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]

   8. Simplified 22.5%

      \[\leadsto z \cdot \color{blue}{\left(b \cdot \left(-c\right)\right)} \]
   9. Step-by-step derivation

      1. pow1 22.5%

         \[\leadsto \color{blue}{{\left(z \cdot \left(b \cdot \left(-c\right)\right)\right)}^{1}} \]

      2. *-commutative 22.5%

         \[\leadsto {\left(z \cdot \color{blue}{\left(\left(-c\right) \cdot b\right)}\right)}^{1} \]

      3. add-sqr-sqrt 13.4%

         \[\leadsto {\left(z \cdot \left(\color{blue}{\left(\sqrt{-c} \cdot \sqrt{-c}\right)} \cdot b\right)\right)}^{1} \]

      4. sqrt-unprod 22.5%

         \[\leadsto {\left(z \cdot \left(\color{blue}{\sqrt{\left(-c\right) \cdot \left(-c\right)}} \cdot b\right)\right)}^{1} \]

      5. sqr-neg 22.5%

         \[\leadsto {\left(z \cdot \left(\sqrt{\color{blue}{c \cdot c}} \cdot b\right)\right)}^{1} \]

      6. sqrt-unprod 17.9%

         \[\leadsto {\left(z \cdot \left(\color{blue}{\left(\sqrt{c} \cdot \sqrt{c}\right)} \cdot b\right)\right)}^{1} \]

      7. add-sqr-sqrt 22.7%

         \[\leadsto {\left(z \cdot \left(\color{blue}{c} \cdot b\right)\right)}^{1} \]

   10. Applied egg-rr 22.7%

       \[\leadsto \color{blue}{{\left(z \cdot \left(c \cdot b\right)\right)}^{1}} \]
   11. Step-by-step derivation

       1. unpow1 22.7%

          \[\leadsto \color{blue}{z \cdot \left(c \cdot b\right)} \]

       2. associate-*r* 22.7%

          \[\leadsto \color{blue}{\left(z \cdot c\right) \cdot b} \]

       3. *-commutative 22.7%

          \[\leadsto \color{blue}{\left(c \cdot z\right)} \cdot b \]

       4. *-commutative 22.7%

          \[\leadsto \color{blue}{b \cdot \left(c \cdot z\right)} \]

   12. Simplified 22.7%

       \[\leadsto \color{blue}{b \cdot \left(c \cdot z\right)} \]

   if -3.29999999999999997e161 < b

   1. Initial program 71.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 38.8%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 38.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 38.8%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 38.8%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 38.8%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 38.8%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 19.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 19.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.3 \cdot 10^{+161}:\\ \;\;\;\;b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 22.0% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.9%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 36.9%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 36.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.9%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.9%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 36.9%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

5. Simplified 36.9%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf 17.9%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Add Preprocessing

Developer target: 59.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024091 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))