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

Percentage Accurate: 74.0% → 83.3%

Time: 38.6s

Alternatives: 30

Speedup: 0.5×

• 57.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

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: 74.0% accurate, 1.0× speedup

Math

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

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: 83.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_1 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{{\left(a \cdot \left(c \cdot j - x \cdot t\right)\right)}^{3}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1
         (+
          (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
          (* j (- (* a c) (* y i))))))
   (if (<= t_1 INFINITY) t_1 (cbrt (pow (* a (- (* c j) (* x t))) 3.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = cbrt(pow((a * ((c * j) - (x * t))), 3.0));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = Math.cbrt(Math.pow((a * ((c * j) - (x * t))), 3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = cbrt((Float64(a * Float64(Float64(c * j) - Float64(x * t))) ^ 3.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[Power[N[Power[N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision], 1/3], $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 92.4%

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

   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 a around inf 51.2%

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

      1. +-commutative 51.2%

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

      2. mul-1-neg 51.2%

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

      3. unsub-neg 51.2%

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

      4. *-commutative 51.2%

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

   5. Simplified 51.2%

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

      1. add-cbrt-cube 57.4%

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

      2. pow3 57.4%

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

      3. *-commutative 57.4%

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

   7. Applied egg-rr 57.4%

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

4. Final simplification 86.7%

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

Alternative 2: 81.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := \left(t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;t\_2 \leq \infty:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ (+ t_1 (* b (- (* t i) (* z c)))) (* j (- (* a c) (* y i))))))
   (if (<= t_2 INFINITY) t_2 (+ (* a (* c j)) t_1))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_2 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (a * (c * j)) + t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (t_1 + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (a * (c * j)) + t_1;
	}
	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)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_2 <= math.inf:
		tmp = t_2
	else:
		tmp = (a * (c * j)) + t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c)))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * Float64(c * j)) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = (t_1 + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (t_2 <= Inf)
		tmp = t_2;
	else
		tmp = (a * (c * j)) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, Infinity], t$95$2, N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + t$95$1), $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 92.4%

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

   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 b around 0 50.1%

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

   4. Taylor expanded in i around 0 57.3%

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

4. Final simplification 86.7%

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

Alternative 3: 54.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;z \leq -1.6 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-287}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+101}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (+ (* a (- (* c j) (* x t))) (* t (* b i)))))
   (if (<= z -1.6e+55)
     (* z (- (* x y) (* b c)))
     (if (<= z -1.16e-77)
       t_2
       (if (<= z -3.8e-199)
         t_1
         (if (<= z -5.7e-260)
           (* t (- (* b i) (* x a)))
           (if (<= z -3.9e-287)
             t_1
             (if (<= z 4.5e-170)
               t_2
               (if (<= z 8.5e-125)
                 (* j (- (* a c) (* y i)))
                 (if (<= z 1.7e+101)
                   t_2
                   (+ (* a (* c j)) (* x (- (* y z) (* t a))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = (a * ((c * j) - (x * t))) + (t * (b * i));
	double tmp;
	if (z <= -1.6e+55) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -1.16e-77) {
		tmp = t_2;
	} else if (z <= -3.8e-199) {
		tmp = t_1;
	} else if (z <= -5.7e-260) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= -3.9e-287) {
		tmp = t_1;
	} else if (z <= 4.5e-170) {
		tmp = t_2;
	} else if (z <= 8.5e-125) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 1.7e+101) {
		tmp = t_2;
	} else {
		tmp = (a * (c * j)) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = (a * ((c * j) - (x * t))) + (t * (b * i))
    if (z <= (-1.6d+55)) then
        tmp = z * ((x * y) - (b * c))
    else if (z <= (-1.16d-77)) then
        tmp = t_2
    else if (z <= (-3.8d-199)) then
        tmp = t_1
    else if (z <= (-5.7d-260)) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= (-3.9d-287)) then
        tmp = t_1
    else if (z <= 4.5d-170) then
        tmp = t_2
    else if (z <= 8.5d-125) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 1.7d+101) then
        tmp = t_2
    else
        tmp = (a * (c * j)) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = (a * ((c * j) - (x * t))) + (t * (b * i));
	double tmp;
	if (z <= -1.6e+55) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -1.16e-77) {
		tmp = t_2;
	} else if (z <= -3.8e-199) {
		tmp = t_1;
	} else if (z <= -5.7e-260) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= -3.9e-287) {
		tmp = t_1;
	} else if (z <= 4.5e-170) {
		tmp = t_2;
	} else if (z <= 8.5e-125) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 1.7e+101) {
		tmp = t_2;
	} else {
		tmp = (a * (c * j)) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = (a * ((c * j) - (x * t))) + (t * (b * i))
	tmp = 0
	if z <= -1.6e+55:
		tmp = z * ((x * y) - (b * c))
	elif z <= -1.16e-77:
		tmp = t_2
	elif z <= -3.8e-199:
		tmp = t_1
	elif z <= -5.7e-260:
		tmp = t * ((b * i) - (x * a))
	elif z <= -3.9e-287:
		tmp = t_1
	elif z <= 4.5e-170:
		tmp = t_2
	elif z <= 8.5e-125:
		tmp = j * ((a * c) - (y * i))
	elif z <= 1.7e+101:
		tmp = t_2
	else:
		tmp = (a * (c * j)) + (x * ((y * z) - (t * a)))
	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)))
	t_2 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(t * Float64(b * i)))
	tmp = 0.0
	if (z <= -1.6e+55)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (z <= -1.16e-77)
		tmp = t_2;
	elseif (z <= -3.8e-199)
		tmp = t_1;
	elseif (z <= -5.7e-260)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= -3.9e-287)
		tmp = t_1;
	elseif (z <= 4.5e-170)
		tmp = t_2;
	elseif (z <= 8.5e-125)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 1.7e+101)
		tmp = t_2;
	else
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	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));
	t_2 = (a * ((c * j) - (x * t))) + (t * (b * i));
	tmp = 0.0;
	if (z <= -1.6e+55)
		tmp = z * ((x * y) - (b * c));
	elseif (z <= -1.16e-77)
		tmp = t_2;
	elseif (z <= -3.8e-199)
		tmp = t_1;
	elseif (z <= -5.7e-260)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= -3.9e-287)
		tmp = t_1;
	elseif (z <= 4.5e-170)
		tmp = t_2;
	elseif (z <= 8.5e-125)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 1.7e+101)
		tmp = t_2;
	else
		tmp = (a * (c * j)) + (x * ((y * z) - (t * a)));
	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]}, Block[{t$95$2 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.6e+55], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.16e-77], t$95$2, If[LessEqual[z, -3.8e-199], t$95$1, If[LessEqual[z, -5.7e-260], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-287], t$95$1, If[LessEqual[z, 4.5e-170], t$95$2, If[LessEqual[z, 8.5e-125], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.7e+101], t$95$2, N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.6000000000000001e55

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 83.5%

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

   if -1.6000000000000001e55 < z < -1.16e-77 or -3.9e-287 < z < 4.50000000000000002e-170 or 8.5000000000000002e-125 < z < 1.70000000000000009e101

   1. Initial program 81.9%

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

   3. Taylor expanded in c around 0 75.8%

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

      1. associate-*r* 74.9%

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

      2. associate-*r* 74.9%

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

      3. *-commutative 74.9%

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

      4. mul-1-neg 74.9%

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

      5. *-commutative 74.9%

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

      6. distribute-rgt-neg-in 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in y around 0 66.1%

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

      1. cancel-sign-sub-inv 66.1%

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

      2. mul-1-neg 66.1%

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

      3. distribute-rgt-neg-in 66.1%

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

      4. distribute-lft-in 66.9%

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

      5. +-commutative 66.9%

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

      6. sub-neg 66.9%

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

      7. metadata-eval 66.9%

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

      8. *-lft-identity 66.9%

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

      9. associate-*r* 66.9%

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

      10. remove-double-neg 66.9%

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

      11. mul-1-neg 66.9%

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

      12. associate-*r* 66.9%

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

      13. neg-mul-1 66.9%

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

      14. *-commutative 66.9%

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

      15. distribute-lft-neg-in 66.9%

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

      16. *-commutative 66.9%

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

      17. distribute-rgt-neg-in 66.9%

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

      18. *-commutative 66.9%

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

      19. neg-mul-1 66.9%

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

      20. associate-*r* 66.9%

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

      21. mul-1-neg 66.9%

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

      22. remove-double-neg 66.9%

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

   8. Simplified 66.9%

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

   if -1.16e-77 < z < -3.7999999999999998e-199 or -5.6999999999999998e-260 < z < -3.9e-287

   1. Initial program 81.2%

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

   3. Taylor expanded in c around 0 76.2%

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

      1. associate-*r* 73.8%

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

      2. associate-*r* 73.8%

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

      3. *-commutative 73.8%

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

      4. mul-1-neg 73.8%

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

      5. *-commutative 73.8%

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

      6. distribute-rgt-neg-in 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in t around -inf 74.1%

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

   7. Taylor expanded in i around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

   9. Simplified 70.8%

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

   if -3.7999999999999998e-199 < z < -5.6999999999999998e-260

   1. Initial program 75.0%

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

   3. Taylor expanded in c around 0 58.8%

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

      1. associate-*r* 67.2%

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

      2. associate-*r* 67.2%

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

      3. *-commutative 67.2%

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

      4. mul-1-neg 67.2%

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

      5. *-commutative 67.2%

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

      6. distribute-rgt-neg-in 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in t around -inf 67.2%

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

   7. Taylor expanded in t around inf 67.3%

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

      1. associate-*r* 67.3%

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

      2. *-commutative 67.3%

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

      3. *-commutative 67.3%

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

      4. associate-*r* 67.3%

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

      5. neg-mul-1 67.3%

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

      6. neg-sub0 67.3%

         \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a - b \cdot i\right)\right)} \]

      7. cancel-sign-sub-inv 67.3%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(x \cdot a + \left(-b\right) \cdot i\right)}\right) \]

      8. *-commutative 67.3%

         \[\leadsto t \cdot \left(0 - \left(x \cdot a + \color{blue}{i \cdot \left(-b\right)}\right)\right) \]

      9. +-commutative 67.3%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(i \cdot \left(-b\right) + x \cdot a\right)}\right) \]

      10. associate--r+ 67.3%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - i \cdot \left(-b\right)\right) - x \cdot a\right)} \]

      11. neg-sub0 67.3%

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

      12. distribute-rgt-neg-in 67.3%

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

      13. remove-double-neg 67.3%

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

      14. *-commutative 67.3%

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

      15. *-commutative 67.3%

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

   9. Simplified 67.3%

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

   if 4.50000000000000002e-170 < z < 8.5000000000000002e-125

   1. Initial program 83.3%

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

   3. Taylor expanded in j around inf 75.8%

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

      1. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   if 1.70000000000000009e101 < z

   1. Initial program 67.5%

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

   3. Taylor expanded in b around 0 69.8%

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

   4. Taylor expanded in i around 0 69.9%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-77}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq -5.7 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-287}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+101}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-71}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-199}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-293}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+157}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (+ (* a (- (* c j) (* x t))) (* t (* b i)))))
   (if (<= z -1.4e+55)
     (* z (- (* x y) (* b c)))
     (if (<= z -1.95e-71)
       t_2
       (if (<= z -1.1e-199)
         t_1
         (if (<= z -4.5e-260)
           (* t (- (* b i) (* x a)))
           (if (<= z -9e-293)
             t_1
             (if (<= z 5.8e-174)
               t_2
               (if (<= z 2.2e-126)
                 (* j (- (* a c) (* y i)))
                 (if (<= z 7.2e+157)
                   t_2
                   (+ (* x (- (* y z) (* t a))) (* 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 * ((t * b) - (y * j));
	double t_2 = (a * ((c * j) - (x * t))) + (t * (b * i));
	double tmp;
	if (z <= -1.4e+55) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -1.95e-71) {
		tmp = t_2;
	} else if (z <= -1.1e-199) {
		tmp = t_1;
	} else if (z <= -4.5e-260) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= -9e-293) {
		tmp = t_1;
	} else if (z <= 5.8e-174) {
		tmp = t_2;
	} else if (z <= 2.2e-126) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 7.2e+157) {
		tmp = t_2;
	} else {
		tmp = (x * ((y * z) - (t * a))) + (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) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = (a * ((c * j) - (x * t))) + (t * (b * i))
    if (z <= (-1.4d+55)) then
        tmp = z * ((x * y) - (b * c))
    else if (z <= (-1.95d-71)) then
        tmp = t_2
    else if (z <= (-1.1d-199)) then
        tmp = t_1
    else if (z <= (-4.5d-260)) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= (-9d-293)) then
        tmp = t_1
    else if (z <= 5.8d-174) then
        tmp = t_2
    else if (z <= 2.2d-126) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 7.2d+157) then
        tmp = t_2
    else
        tmp = (x * ((y * z) - (t * a))) + (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 * ((t * b) - (y * j));
	double t_2 = (a * ((c * j) - (x * t))) + (t * (b * i));
	double tmp;
	if (z <= -1.4e+55) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -1.95e-71) {
		tmp = t_2;
	} else if (z <= -1.1e-199) {
		tmp = t_1;
	} else if (z <= -4.5e-260) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= -9e-293) {
		tmp = t_1;
	} else if (z <= 5.8e-174) {
		tmp = t_2;
	} else if (z <= 2.2e-126) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 7.2e+157) {
		tmp = t_2;
	} else {
		tmp = (x * ((y * z) - (t * a))) + (b * (t * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = (a * ((c * j) - (x * t))) + (t * (b * i))
	tmp = 0
	if z <= -1.4e+55:
		tmp = z * ((x * y) - (b * c))
	elif z <= -1.95e-71:
		tmp = t_2
	elif z <= -1.1e-199:
		tmp = t_1
	elif z <= -4.5e-260:
		tmp = t * ((b * i) - (x * a))
	elif z <= -9e-293:
		tmp = t_1
	elif z <= 5.8e-174:
		tmp = t_2
	elif z <= 2.2e-126:
		tmp = j * ((a * c) - (y * i))
	elif z <= 7.2e+157:
		tmp = t_2
	else:
		tmp = (x * ((y * z) - (t * a))) + (b * (t * i))
	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)))
	t_2 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(t * Float64(b * i)))
	tmp = 0.0
	if (z <= -1.4e+55)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (z <= -1.95e-71)
		tmp = t_2;
	elseif (z <= -1.1e-199)
		tmp = t_1;
	elseif (z <= -4.5e-260)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= -9e-293)
		tmp = t_1;
	elseif (z <= 5.8e-174)
		tmp = t_2;
	elseif (z <= 2.2e-126)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 7.2e+157)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + 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 * ((t * b) - (y * j));
	t_2 = (a * ((c * j) - (x * t))) + (t * (b * i));
	tmp = 0.0;
	if (z <= -1.4e+55)
		tmp = z * ((x * y) - (b * c));
	elseif (z <= -1.95e-71)
		tmp = t_2;
	elseif (z <= -1.1e-199)
		tmp = t_1;
	elseif (z <= -4.5e-260)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= -9e-293)
		tmp = t_1;
	elseif (z <= 5.8e-174)
		tmp = t_2;
	elseif (z <= 2.2e-126)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 7.2e+157)
		tmp = t_2;
	else
		tmp = (x * ((y * z) - (t * a))) + (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[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+55], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.95e-71], t$95$2, If[LessEqual[z, -1.1e-199], t$95$1, If[LessEqual[z, -4.5e-260], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9e-293], t$95$1, If[LessEqual[z, 5.8e-174], t$95$2, If[LessEqual[z, 2.2e-126], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e+157], t$95$2, N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.4e55

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 83.5%

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

   if -1.4e55 < z < -1.9500000000000001e-71 or -9.0000000000000005e-293 < z < 5.8000000000000002e-174 or 2.20000000000000014e-126 < z < 7.20000000000000049e157

   1. Initial program 79.0%

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

   3. Taylor expanded in c around 0 76.0%

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

      1. associate-*r* 75.2%

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

      2. associate-*r* 75.2%

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

      3. *-commutative 75.2%

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

      4. mul-1-neg 75.2%

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

      5. *-commutative 75.2%

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

      6. distribute-rgt-neg-in 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in y around 0 65.7%

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

      1. cancel-sign-sub-inv 65.7%

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

      2. mul-1-neg 65.7%

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

      3. distribute-rgt-neg-in 65.7%

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

      4. distribute-lft-in 66.5%

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

      5. +-commutative 66.5%

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

      6. sub-neg 66.5%

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

      7. metadata-eval 66.5%

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

      8. *-lft-identity 66.5%

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

      9. associate-*r* 66.5%

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

      10. remove-double-neg 66.5%

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

      11. mul-1-neg 66.5%

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

      12. associate-*r* 66.5%

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

      13. neg-mul-1 66.5%

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

      14. *-commutative 66.5%

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

      15. distribute-lft-neg-in 66.5%

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

      16. *-commutative 66.5%

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

      17. distribute-rgt-neg-in 66.5%

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

      18. *-commutative 66.5%

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

      19. neg-mul-1 66.5%

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

      20. associate-*r* 66.5%

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

      21. mul-1-neg 66.5%

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

      22. remove-double-neg 66.5%

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

   8. Simplified 66.5%

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

   if -1.9500000000000001e-71 < z < -1.0999999999999999e-199 or -4.4999999999999997e-260 < z < -9.0000000000000005e-293

   1. Initial program 81.2%

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

   3. Taylor expanded in c around 0 76.2%

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

      1. associate-*r* 73.8%

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

      2. associate-*r* 73.8%

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

      3. *-commutative 73.8%

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

      4. mul-1-neg 73.8%

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

      5. *-commutative 73.8%

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

      6. distribute-rgt-neg-in 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in t around -inf 74.1%

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

   7. Taylor expanded in i around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

   9. Simplified 70.8%

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

   if -1.0999999999999999e-199 < z < -4.4999999999999997e-260

   1. Initial program 75.0%

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

   3. Taylor expanded in c around 0 58.8%

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

      1. associate-*r* 67.2%

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

      2. associate-*r* 67.2%

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

      3. *-commutative 67.2%

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

      4. mul-1-neg 67.2%

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

      5. *-commutative 67.2%

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

      6. distribute-rgt-neg-in 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in t around -inf 67.2%

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

   7. Taylor expanded in t around inf 67.3%

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

      1. associate-*r* 67.3%

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

      2. *-commutative 67.3%

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

      3. *-commutative 67.3%

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

      4. associate-*r* 67.3%

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

      5. neg-mul-1 67.3%

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

      6. neg-sub0 67.3%

         \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a - b \cdot i\right)\right)} \]

      7. cancel-sign-sub-inv 67.3%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(x \cdot a + \left(-b\right) \cdot i\right)}\right) \]

      8. *-commutative 67.3%

         \[\leadsto t \cdot \left(0 - \left(x \cdot a + \color{blue}{i \cdot \left(-b\right)}\right)\right) \]

      9. +-commutative 67.3%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(i \cdot \left(-b\right) + x \cdot a\right)}\right) \]

      10. associate--r+ 67.3%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - i \cdot \left(-b\right)\right) - x \cdot a\right)} \]

      11. neg-sub0 67.3%

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

      12. distribute-rgt-neg-in 67.3%

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

      13. remove-double-neg 67.3%

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

      14. *-commutative 67.3%

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

      15. *-commutative 67.3%

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

   9. Simplified 67.3%

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

   if 5.8000000000000002e-174 < z < 2.20000000000000014e-126

   1. Initial program 83.3%

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

   3. Taylor expanded in j around inf 75.8%

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

      1. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   if 7.20000000000000049e157 < z

   1. Initial program 74.1%

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

   3. Taylor expanded in c around 0 76.5%

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

      1. associate-*r* 76.5%

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

      2. associate-*r* 76.5%

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

      3. *-commutative 76.5%

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

      4. mul-1-neg 76.5%

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

      5. *-commutative 76.5%

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

      6. distribute-rgt-neg-in 76.5%

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

   5. Simplified 76.5%

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

   6. Taylor expanded in j around 0 76.7%

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

      1. fma-neg 76.7%

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

      2. *-commutative 76.7%

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

      3. *-commutative 76.7%

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

      4. fma-udef 76.7%

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

      5. mul-1-neg 76.7%

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

      6. remove-double-neg 76.7%

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

   8. Simplified 76.7%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+55}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-71}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-199}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -9 \cdot 10^{-293}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-174}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+157}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{if}\;z \leq -9.5 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-193}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-290}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-170}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+131}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j))))
        (t_2 (+ (* a (- (* c j) (* x t))) (* t (* b i)))))
   (if (<= z -9.5e+54)
     (* z (- (* x y) (* b c)))
     (if (<= z -1.6e-75)
       t_2
       (if (<= z -8e-193)
         t_1
         (if (<= z -5.6e-260)
           (* t (- (* b i) (* x a)))
           (if (<= z -3.5e-290)
             t_1
             (if (<= z 4e-170)
               t_2
               (if (<= z 1.85e-125)
                 (* j (- (* a c) (* y i)))
                 (if (<= z 4.8e+131)
                   t_2
                   (+ (* x (* y z)) (* b (- (* t i) (* z c))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = (a * ((c * j) - (x * t))) + (t * (b * i));
	double tmp;
	if (z <= -9.5e+54) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -1.6e-75) {
		tmp = t_2;
	} else if (z <= -8e-193) {
		tmp = t_1;
	} else if (z <= -5.6e-260) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= -3.5e-290) {
		tmp = t_1;
	} else if (z <= 4e-170) {
		tmp = t_2;
	} else if (z <= 1.85e-125) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 4.8e+131) {
		tmp = t_2;
	} else {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = (a * ((c * j) - (x * t))) + (t * (b * i))
    if (z <= (-9.5d+54)) then
        tmp = z * ((x * y) - (b * c))
    else if (z <= (-1.6d-75)) then
        tmp = t_2
    else if (z <= (-8d-193)) then
        tmp = t_1
    else if (z <= (-5.6d-260)) then
        tmp = t * ((b * i) - (x * a))
    else if (z <= (-3.5d-290)) then
        tmp = t_1
    else if (z <= 4d-170) then
        tmp = t_2
    else if (z <= 1.85d-125) then
        tmp = j * ((a * c) - (y * i))
    else if (z <= 4.8d+131) then
        tmp = t_2
    else
        tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = (a * ((c * j) - (x * t))) + (t * (b * i));
	double tmp;
	if (z <= -9.5e+54) {
		tmp = z * ((x * y) - (b * c));
	} else if (z <= -1.6e-75) {
		tmp = t_2;
	} else if (z <= -8e-193) {
		tmp = t_1;
	} else if (z <= -5.6e-260) {
		tmp = t * ((b * i) - (x * a));
	} else if (z <= -3.5e-290) {
		tmp = t_1;
	} else if (z <= 4e-170) {
		tmp = t_2;
	} else if (z <= 1.85e-125) {
		tmp = j * ((a * c) - (y * i));
	} else if (z <= 4.8e+131) {
		tmp = t_2;
	} else {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = (a * ((c * j) - (x * t))) + (t * (b * i))
	tmp = 0
	if z <= -9.5e+54:
		tmp = z * ((x * y) - (b * c))
	elif z <= -1.6e-75:
		tmp = t_2
	elif z <= -8e-193:
		tmp = t_1
	elif z <= -5.6e-260:
		tmp = t * ((b * i) - (x * a))
	elif z <= -3.5e-290:
		tmp = t_1
	elif z <= 4e-170:
		tmp = t_2
	elif z <= 1.85e-125:
		tmp = j * ((a * c) - (y * i))
	elif z <= 4.8e+131:
		tmp = t_2
	else:
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
	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)))
	t_2 = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(t * Float64(b * i)))
	tmp = 0.0
	if (z <= -9.5e+54)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (z <= -1.6e-75)
		tmp = t_2;
	elseif (z <= -8e-193)
		tmp = t_1;
	elseif (z <= -5.6e-260)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (z <= -3.5e-290)
		tmp = t_1;
	elseif (z <= 4e-170)
		tmp = t_2;
	elseif (z <= 1.85e-125)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (z <= 4.8e+131)
		tmp = t_2;
	else
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	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));
	t_2 = (a * ((c * j) - (x * t))) + (t * (b * i));
	tmp = 0.0;
	if (z <= -9.5e+54)
		tmp = z * ((x * y) - (b * c));
	elseif (z <= -1.6e-75)
		tmp = t_2;
	elseif (z <= -8e-193)
		tmp = t_1;
	elseif (z <= -5.6e-260)
		tmp = t * ((b * i) - (x * a));
	elseif (z <= -3.5e-290)
		tmp = t_1;
	elseif (z <= 4e-170)
		tmp = t_2;
	elseif (z <= 1.85e-125)
		tmp = j * ((a * c) - (y * i));
	elseif (z <= 4.8e+131)
		tmp = t_2;
	else
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	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]}, Block[{t$95$2 = N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.5e+54], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.6e-75], t$95$2, If[LessEqual[z, -8e-193], t$95$1, If[LessEqual[z, -5.6e-260], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.5e-290], t$95$1, If[LessEqual[z, 4e-170], t$95$2, If[LessEqual[z, 1.85e-125], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.8e+131], t$95$2, N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -9.4999999999999999e54

   1. Initial program 69.4%

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

   3. Taylor expanded in z around inf 83.5%

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

   if -9.4999999999999999e54 < z < -1.59999999999999988e-75 or -3.49999999999999981e-290 < z < 3.99999999999999993e-170 or 1.85e-125 < z < 4.7999999999999999e131

   1. Initial program 80.0%

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

   3. Taylor expanded in c around 0 76.8%

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

      1. associate-*r* 75.9%

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

      2. associate-*r* 75.9%

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

      3. *-commutative 75.9%

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

      4. mul-1-neg 75.9%

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

      5. *-commutative 75.9%

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

      6. distribute-rgt-neg-in 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in y around 0 66.2%

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

      1. cancel-sign-sub-inv 66.2%

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

      2. mul-1-neg 66.2%

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

      3. distribute-rgt-neg-in 66.2%

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

      4. distribute-lft-in 67.0%

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

      5. +-commutative 67.0%

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

      6. sub-neg 67.0%

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

      7. metadata-eval 67.0%

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

      8. *-lft-identity 67.0%

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

      9. associate-*r* 67.0%

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

      10. remove-double-neg 67.0%

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

      11. mul-1-neg 67.0%

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

      12. associate-*r* 67.0%

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

      13. neg-mul-1 67.0%

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

      14. *-commutative 67.0%

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

      15. distribute-lft-neg-in 67.0%

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

      16. *-commutative 67.0%

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

      17. distribute-rgt-neg-in 67.0%

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

      18. *-commutative 67.0%

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

      19. neg-mul-1 67.0%

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

      20. associate-*r* 67.0%

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

      21. mul-1-neg 67.0%

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

      22. remove-double-neg 67.0%

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

   8. Simplified 67.0%

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

   if -1.59999999999999988e-75 < z < -8.0000000000000004e-193 or -5.5999999999999996e-260 < z < -3.49999999999999981e-290

   1. Initial program 81.2%

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

   3. Taylor expanded in c around 0 76.2%

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

      1. associate-*r* 73.8%

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

      2. associate-*r* 73.8%

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

      3. *-commutative 73.8%

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

      4. mul-1-neg 73.8%

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

      5. *-commutative 73.8%

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

      6. distribute-rgt-neg-in 73.8%

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

   5. Simplified 73.8%

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

   6. Taylor expanded in t around -inf 74.1%

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

   7. Taylor expanded in i around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

   9. Simplified 70.8%

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

   if -8.0000000000000004e-193 < z < -5.5999999999999996e-260

   1. Initial program 75.0%

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

   3. Taylor expanded in c around 0 58.8%

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

      1. associate-*r* 67.2%

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

      2. associate-*r* 67.2%

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

      3. *-commutative 67.2%

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

      4. mul-1-neg 67.2%

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

      5. *-commutative 67.2%

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

      6. distribute-rgt-neg-in 67.2%

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

   5. Simplified 67.2%

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

   6. Taylor expanded in t around -inf 67.2%

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

   7. Taylor expanded in t around inf 67.3%

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

      1. associate-*r* 67.3%

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

      2. *-commutative 67.3%

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

      3. *-commutative 67.3%

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

      4. associate-*r* 67.3%

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

      5. neg-mul-1 67.3%

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

      6. neg-sub0 67.3%

         \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a - b \cdot i\right)\right)} \]

      7. cancel-sign-sub-inv 67.3%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(x \cdot a + \left(-b\right) \cdot i\right)}\right) \]

      8. *-commutative 67.3%

         \[\leadsto t \cdot \left(0 - \left(x \cdot a + \color{blue}{i \cdot \left(-b\right)}\right)\right) \]

      9. +-commutative 67.3%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(i \cdot \left(-b\right) + x \cdot a\right)}\right) \]

      10. associate--r+ 67.3%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - i \cdot \left(-b\right)\right) - x \cdot a\right)} \]

      11. neg-sub0 67.3%

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

      12. distribute-rgt-neg-in 67.3%

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

      13. remove-double-neg 67.3%

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

      14. *-commutative 67.3%

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

      15. *-commutative 67.3%

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

   9. Simplified 67.3%

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

   if 3.99999999999999993e-170 < z < 1.85e-125

   1. Initial program 83.3%

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

   3. Taylor expanded in j around inf 75.8%

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

      1. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   if 4.7999999999999999e131 < z

   1. Initial program 71.0%

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

   3. Taylor expanded in j around 0 74.4%

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

   4. Taylor expanded in a around 0 74.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.5 \cdot 10^{+54}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -1.6 \cdot 10^{-75}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-193}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-260}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-290}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-170}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-125}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+131}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ t_2 := t\_1 + t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7.2 \cdot 10^{+174}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -2.45 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-183}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z)))
        (t_2 (+ t_1 (* t (- (* b i) (* x a)))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -7.2e+174)
     t_3
     (if (<= j -2.45e-7)
       (- (* x (- (* y z) (* t a))) (* j (* y i)))
       (if (<= j -1.7e-17)
         (* a (- (* c j) (* x t)))
         (if (<= j -6.5e-183)
           (+ t_1 (* b (- (* t i) (* z c))))
           (if (<= j 3.2e-160)
             t_2
             (if (<= j 1.4e-71)
               (* z (- (* x y) (* b c)))
               (if (<= j 1.55e+122) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = t_1 + (t * ((b * i) - (x * a)));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -7.2e+174) {
		tmp = t_3;
	} else if (j <= -2.45e-7) {
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i));
	} else if (j <= -1.7e-17) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -6.5e-183) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (j <= 3.2e-160) {
		tmp = t_2;
	} else if (j <= 1.4e-71) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 1.55e+122) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * (y * z)
    t_2 = t_1 + (t * ((b * i) - (x * a)))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-7.2d+174)) then
        tmp = t_3
    else if (j <= (-2.45d-7)) then
        tmp = (x * ((y * z) - (t * a))) - (j * (y * i))
    else if (j <= (-1.7d-17)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= (-6.5d-183)) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    else if (j <= 3.2d-160) then
        tmp = t_2
    else if (j <= 1.4d-71) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 1.55d+122) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double t_2 = t_1 + (t * ((b * i) - (x * a)));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -7.2e+174) {
		tmp = t_3;
	} else if (j <= -2.45e-7) {
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i));
	} else if (j <= -1.7e-17) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -6.5e-183) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} else if (j <= 3.2e-160) {
		tmp = t_2;
	} else if (j <= 1.4e-71) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 1.55e+122) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	t_2 = t_1 + (t * ((b * i) - (x * a)))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -7.2e+174:
		tmp = t_3
	elif j <= -2.45e-7:
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i))
	elif j <= -1.7e-17:
		tmp = a * ((c * j) - (x * t))
	elif j <= -6.5e-183:
		tmp = t_1 + (b * ((t * i) - (z * c)))
	elif j <= 3.2e-160:
		tmp = t_2
	elif j <= 1.4e-71:
		tmp = z * ((x * y) - (b * c))
	elif j <= 1.55e+122:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	t_2 = Float64(t_1 + Float64(t * Float64(Float64(b * i) - Float64(x * a))))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -7.2e+174)
		tmp = t_3;
	elseif (j <= -2.45e-7)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(j * Float64(y * i)));
	elseif (j <= -1.7e-17)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= -6.5e-183)
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= 3.2e-160)
		tmp = t_2;
	elseif (j <= 1.4e-71)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 1.55e+122)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	t_2 = t_1 + (t * ((b * i) - (x * a)));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -7.2e+174)
		tmp = t_3;
	elseif (j <= -2.45e-7)
		tmp = (x * ((y * z) - (t * a))) - (j * (y * i));
	elseif (j <= -1.7e-17)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= -6.5e-183)
		tmp = t_1 + (b * ((t * i) - (z * c)));
	elseif (j <= 3.2e-160)
		tmp = t_2;
	elseif (j <= 1.4e-71)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 1.55e+122)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.2e+174], t$95$3, If[LessEqual[j, -2.45e-7], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.7e-17], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -6.5e-183], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 3.2e-160], t$95$2, If[LessEqual[j, 1.4e-71], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.55e+122], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -7.2000000000000003e174 or 1.54999999999999999e122 < j

   1. Initial program 79.0%

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

   3. Taylor expanded in j around inf 75.0%

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

      1. *-commutative 75.0%

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

   5. Simplified 75.0%

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

   if -7.2000000000000003e174 < j < -2.4499999999999998e-7

   1. Initial program 78.3%

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

   3. Taylor expanded in b around 0 66.1%

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

   4. Taylor expanded in a around 0 61.1%

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

      1. neg-mul-1 61.1%

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

      2. distribute-lft-neg-in 61.1%

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

      3. *-commutative 61.1%

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

   6. Simplified 61.1%

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

   if -2.4499999999999998e-7 < j < -1.6999999999999999e-17

   1. Initial program 25.0%

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

   3. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -1.6999999999999999e-17 < j < -6.50000000000000014e-183

   1. Initial program 87.0%

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

   3. Taylor expanded in j around 0 83.9%

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

   4. Taylor expanded in a around 0 80.8%

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

   if -6.50000000000000014e-183 < j < 3.20000000000000009e-160 or 1.4e-71 < j < 1.54999999999999999e122

   1. Initial program 74.3%

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

   3. Taylor expanded in c around 0 74.3%

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

      1. associate-*r* 75.2%

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

      2. associate-*r* 75.2%

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

      3. *-commutative 75.2%

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

      4. mul-1-neg 75.2%

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

      5. *-commutative 75.2%

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

      6. distribute-rgt-neg-in 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in t around -inf 77.0%

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

   7. Taylor expanded in j around 0 71.0%

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

   if 3.20000000000000009e-160 < j < 1.4e-71

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf 80.3%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.2 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -2.45 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -6.5 \cdot 10^{-183}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 3.2 \cdot 10^{-160}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 1.4 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.55 \cdot 10^{+122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 + b \cdot \left(t \cdot i\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{+120}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{+85}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-17}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-206}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+32}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (+ t_1 (* b (* t i))))
        (t_3 (* j (- (* a c) (* y i)))))
   (if (<= j -1.7e+120)
     t_3
     (if (<= j -7.5e+85)
       t_2
       (if (<= j -2e-17)
         t_3
         (if (<= j -1.75e-171)
           (+ (* x (* y z)) (* b (- (* t i) (* z c))))
           (if (<= j 1.5e-206)
             t_2
             (if (<= j 5.6e+32) (- t_1 (* b (* z c))) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * (t * i));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.7e+120) {
		tmp = t_3;
	} else if (j <= -7.5e+85) {
		tmp = t_2;
	} else if (j <= -2e-17) {
		tmp = t_3;
	} else if (j <= -1.75e-171) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else if (j <= 1.5e-206) {
		tmp = t_2;
	} else if (j <= 5.6e+32) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 + (b * (t * i))
    t_3 = j * ((a * c) - (y * i))
    if (j <= (-1.7d+120)) then
        tmp = t_3
    else if (j <= (-7.5d+85)) then
        tmp = t_2
    else if (j <= (-2d-17)) then
        tmp = t_3
    else if (j <= (-1.75d-171)) then
        tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
    else if (j <= 1.5d-206) then
        tmp = t_2
    else if (j <= 5.6d+32) then
        tmp = t_1 - (b * (z * c))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 + (b * (t * i));
	double t_3 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.7e+120) {
		tmp = t_3;
	} else if (j <= -7.5e+85) {
		tmp = t_2;
	} else if (j <= -2e-17) {
		tmp = t_3;
	} else if (j <= -1.75e-171) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else if (j <= 1.5e-206) {
		tmp = t_2;
	} else if (j <= 5.6e+32) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = t_3;
	}
	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))
	t_3 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.7e+120:
		tmp = t_3
	elif j <= -7.5e+85:
		tmp = t_2
	elif j <= -2e-17:
		tmp = t_3
	elif j <= -1.75e-171:
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
	elif j <= 1.5e-206:
		tmp = t_2
	elif j <= 5.6e+32:
		tmp = t_1 - (b * (z * c))
	else:
		tmp = t_3
	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(t * i)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.7e+120)
		tmp = t_3;
	elseif (j <= -7.5e+85)
		tmp = t_2;
	elseif (j <= -2e-17)
		tmp = t_3;
	elseif (j <= -1.75e-171)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= 1.5e-206)
		tmp = t_2;
	elseif (j <= 5.6e+32)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 + (b * (t * i));
	t_3 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.7e+120)
		tmp = t_3;
	elseif (j <= -7.5e+85)
		tmp = t_2;
	elseif (j <= -2e-17)
		tmp = t_3;
	elseif (j <= -1.75e-171)
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	elseif (j <= 1.5e-206)
		tmp = t_2;
	elseif (j <= 5.6e+32)
		tmp = t_1 - (b * (z * c));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e+120], t$95$3, If[LessEqual[j, -7.5e+85], t$95$2, If[LessEqual[j, -2e-17], t$95$3, If[LessEqual[j, -1.75e-171], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e-206], t$95$2, If[LessEqual[j, 5.6e+32], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.69999999999999999e120 or -7.49999999999999942e85 < j < -2.00000000000000014e-17 or 5.6e32 < j

   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 j around inf 65.4%

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

      1. *-commutative 65.4%

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

   5. Simplified 65.4%

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

   if -1.69999999999999999e120 < j < -7.49999999999999942e85 or -1.74999999999999997e-171 < j < 1.5000000000000001e-206

   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 c around 0 77.2%

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

      1. associate-*r* 77.2%

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

      2. associate-*r* 77.2%

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

      3. *-commutative 77.2%

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

      4. mul-1-neg 77.2%

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

      5. *-commutative 77.2%

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

      6. distribute-rgt-neg-in 77.2%

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

   5. Simplified 77.2%

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

   6. Taylor expanded in j around 0 77.3%

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

      1. fma-neg 77.3%

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

      2. *-commutative 77.3%

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

      3. *-commutative 77.3%

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

      4. fma-udef 77.3%

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

      5. mul-1-neg 77.3%

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

      6. remove-double-neg 77.3%

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

   8. Simplified 77.3%

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

   if -2.00000000000000014e-17 < j < -1.74999999999999997e-171

   1. Initial program 85.1%

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

   3. Taylor expanded in j around 0 81.5%

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

   4. Taylor expanded in a around 0 78.0%

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

   if 1.5000000000000001e-206 < j < 5.6e32

   1. Initial program 73.8%

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

   3. Taylor expanded in j around 0 62.4%

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

   4. Taylor expanded in i around 0 64.2%

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

      1. *-commutative 64.2%

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

   6. Simplified 64.2%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{+120}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7.5 \cdot 10^{+85}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq -2 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.75 \cdot 10^{-171}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -7.5 \cdot 10^{+174}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-8}:\\ \;\;\;\;t\_1 - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-206}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{+32}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -7.5e+174)
     t_2
     (if (<= j -1.05e-8)
       (- t_1 (* j (* y i)))
       (if (<= j -1.05e-17)
         (* a (- (* c j) (* x t)))
         (if (<= j -2.8e-170)
           (+ (* x (* y z)) (* b (- (* t i) (* z c))))
           (if (<= j 1.45e-206)
             (+ t_1 (* b (* t i)))
             (if (<= j 5.2e+32) (- t_1 (* b (* z c))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -7.5e+174) {
		tmp = t_2;
	} else if (j <= -1.05e-8) {
		tmp = t_1 - (j * (y * i));
	} else if (j <= -1.05e-17) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -2.8e-170) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else if (j <= 1.45e-206) {
		tmp = t_1 + (b * (t * i));
	} else if (j <= 5.2e+32) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = j * ((a * c) - (y * i))
    if (j <= (-7.5d+174)) then
        tmp = t_2
    else if (j <= (-1.05d-8)) then
        tmp = t_1 - (j * (y * i))
    else if (j <= (-1.05d-17)) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= (-2.8d-170)) then
        tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
    else if (j <= 1.45d-206) then
        tmp = t_1 + (b * (t * i))
    else if (j <= 5.2d+32) then
        tmp = t_1 - (b * (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -7.5e+174) {
		tmp = t_2;
	} else if (j <= -1.05e-8) {
		tmp = t_1 - (j * (y * i));
	} else if (j <= -1.05e-17) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= -2.8e-170) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else if (j <= 1.45e-206) {
		tmp = t_1 + (b * (t * i));
	} else if (j <= 5.2e+32) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -7.5e+174:
		tmp = t_2
	elif j <= -1.05e-8:
		tmp = t_1 - (j * (y * i))
	elif j <= -1.05e-17:
		tmp = a * ((c * j) - (x * t))
	elif j <= -2.8e-170:
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
	elif j <= 1.45e-206:
		tmp = t_1 + (b * (t * i))
	elif j <= 5.2e+32:
		tmp = t_1 - (b * (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -7.5e+174)
		tmp = t_2;
	elseif (j <= -1.05e-8)
		tmp = Float64(t_1 - Float64(j * Float64(y * i)));
	elseif (j <= -1.05e-17)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= -2.8e-170)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (j <= 1.45e-206)
		tmp = Float64(t_1 + Float64(b * Float64(t * i)));
	elseif (j <= 5.2e+32)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -7.5e+174)
		tmp = t_2;
	elseif (j <= -1.05e-8)
		tmp = t_1 - (j * (y * i));
	elseif (j <= -1.05e-17)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= -2.8e-170)
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	elseif (j <= 1.45e-206)
		tmp = t_1 + (b * (t * i));
	elseif (j <= 5.2e+32)
		tmp = t_1 - (b * (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -7.5e+174], t$95$2, If[LessEqual[j, -1.05e-8], N[(t$95$1 - N[(j * N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.05e-17], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -2.8e-170], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.45e-206], N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.2e+32], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -7.5000000000000004e174 or 5.2000000000000004e32 < j

   1. Initial program 80.0%

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

   3. Taylor expanded in j around inf 68.3%

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

      1. *-commutative 68.3%

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

   5. Simplified 68.3%

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

   if -7.5000000000000004e174 < j < -1.04999999999999997e-8

   1. Initial program 78.3%

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

   3. Taylor expanded in b around 0 66.1%

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

   4. Taylor expanded in a around 0 61.1%

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

      1. neg-mul-1 61.1%

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

      2. distribute-lft-neg-in 61.1%

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

      3. *-commutative 61.1%

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

   6. Simplified 61.1%

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

   if -1.04999999999999997e-8 < j < -1.04999999999999996e-17

   1. Initial program 25.0%

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

   3. Taylor expanded in a around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. mul-1-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   if -1.04999999999999996e-17 < j < -2.79999999999999995e-170

   1. Initial program 85.1%

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

   3. Taylor expanded in j around 0 81.5%

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

   4. Taylor expanded in a around 0 78.0%

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

   if -2.79999999999999995e-170 < j < 1.4500000000000001e-206

   1. Initial program 73.8%

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

   3. Taylor expanded in c around 0 78.1%

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

      1. associate-*r* 78.1%

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

      2. associate-*r* 78.1%

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

      3. *-commutative 78.1%

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

      4. mul-1-neg 78.1%

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

      5. *-commutative 78.1%

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

      6. distribute-rgt-neg-in 78.1%

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

   5. Simplified 78.1%

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

   6. Taylor expanded in j around 0 80.0%

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

      1. fma-neg 80.0%

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

      2. *-commutative 80.0%

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

      3. *-commutative 80.0%

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

      4. fma-udef 80.0%

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

      5. mul-1-neg 80.0%

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

      6. remove-double-neg 80.0%

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

   8. Simplified 80.0%

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

   if 1.4500000000000001e-206 < j < 5.2000000000000004e32

   1. Initial program 73.8%

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

   3. Taylor expanded in j around 0 62.4%

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

   4. Taylor expanded in i around 0 64.2%

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

      1. *-commutative 64.2%

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

   6. Simplified 64.2%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -7.5 \cdot 10^{+174}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - j \cdot \left(y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.05 \cdot 10^{-17}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq -2.8 \cdot 10^{-170}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 1.45 \cdot 10^{-206}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 5.2 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 47.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-138}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-148}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+80}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= b -3.4e+51)
     (* b (- (* t i) (* z c)))
     (if (<= b -1.6e-7)
       (* a (- (* c j) (* x t)))
       (if (<= b -4.3e-138)
         (* i (- (* t b) (* y j)))
         (if (<= b 4.4e-148)
           t_1
           (if (<= b 1.4e-122)
             (* x (* y z))
             (if (<= b 2e+80) t_1 (* t (- (* b i) (* x a)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -3.4e+51) {
		tmp = b * ((t * i) - (z * c));
	} else if (b <= -1.6e-7) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= -4.3e-138) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= 4.4e-148) {
		tmp = t_1;
	} else if (b <= 1.4e-122) {
		tmp = x * (y * z);
	} else if (b <= 2e+80) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (b <= (-3.4d+51)) then
        tmp = b * ((t * i) - (z * c))
    else if (b <= (-1.6d-7)) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= (-4.3d-138)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= 4.4d-148) then
        tmp = t_1
    else if (b <= 1.4d-122) then
        tmp = x * (y * z)
    else if (b <= 2d+80) then
        tmp = t_1
    else
        tmp = t * ((b * i) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (b <= -3.4e+51) {
		tmp = b * ((t * i) - (z * c));
	} else if (b <= -1.6e-7) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= -4.3e-138) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= 4.4e-148) {
		tmp = t_1;
	} else if (b <= 1.4e-122) {
		tmp = x * (y * z);
	} else if (b <= 2e+80) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if b <= -3.4e+51:
		tmp = b * ((t * i) - (z * c))
	elif b <= -1.6e-7:
		tmp = a * ((c * j) - (x * t))
	elif b <= -4.3e-138:
		tmp = i * ((t * b) - (y * j))
	elif b <= 4.4e-148:
		tmp = t_1
	elif b <= 1.4e-122:
		tmp = x * (y * z)
	elif b <= 2e+80:
		tmp = t_1
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (b <= -3.4e+51)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (b <= -1.6e-7)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= -4.3e-138)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= 4.4e-148)
		tmp = t_1;
	elseif (b <= 1.4e-122)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= 2e+80)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	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));
	tmp = 0.0;
	if (b <= -3.4e+51)
		tmp = b * ((t * i) - (z * c));
	elseif (b <= -1.6e-7)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= -4.3e-138)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= 4.4e-148)
		tmp = t_1;
	elseif (b <= 1.4e-122)
		tmp = x * (y * z);
	elseif (b <= 2e+80)
		tmp = t_1;
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+51], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.6e-7], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4.3e-138], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4.4e-148], t$95$1, If[LessEqual[b, 1.4e-122], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2e+80], t$95$1, N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.39999999999999984e51

   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 inf 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if -3.39999999999999984e51 < b < -1.6e-7

   1. Initial program 62.4%

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

   3. Taylor expanded in a around inf 63.2%

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

      1. +-commutative 63.2%

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

      2. mul-1-neg 63.2%

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

      3. unsub-neg 63.2%

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

      4. *-commutative 63.2%

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

   5. Simplified 63.2%

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

   if -1.6e-7 < b < -4.3e-138

   1. Initial program 82.2%

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

   3. Taylor expanded in c around 0 82.5%

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

      1. associate-*r* 85.0%

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

      2. associate-*r* 85.0%

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

      3. *-commutative 85.0%

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

      4. mul-1-neg 85.0%

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

      5. *-commutative 85.0%

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

      6. distribute-rgt-neg-in 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in t around -inf 88.1%

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

   7. Taylor expanded in i around inf 53.4%

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

      1. +-commutative 53.4%

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

      2. mul-1-neg 53.4%

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

      3. unsub-neg 53.4%

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

   9. Simplified 53.4%

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

   if -4.3e-138 < b < 4.40000000000000034e-148 or 1.3999999999999999e-122 < b < 2e80

   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 j around inf 56.6%

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

      1. *-commutative 56.6%

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

   5. Simplified 56.6%

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

   if 4.40000000000000034e-148 < b < 1.3999999999999999e-122

   1. Initial program 85.5%

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

      1. add-cube-cbrt 85.5%

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

      2. pow3 85.5%

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

      3. *-commutative 85.5%

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

   4. Applied egg-rr 85.5%

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

   5. Taylor expanded in z around inf 84.0%

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

      1. *-commutative 84.0%

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

   7. Simplified 84.0%

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

   if 2e80 < b

   1. Initial program 82.3%

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

   3. Taylor expanded in c around 0 73.8%

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

      1. associate-*r* 68.8%

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

      2. associate-*r* 68.8%

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

      3. *-commutative 68.8%

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

      4. mul-1-neg 68.8%

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

      5. *-commutative 68.8%

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

      6. distribute-rgt-neg-in 68.8%

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

   5. Simplified 68.8%

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

   6. Taylor expanded in t around -inf 73.5%

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

   7. Taylor expanded in t around inf 57.3%

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

      1. associate-*r* 57.3%

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

      2. *-commutative 57.3%

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

      3. *-commutative 57.3%

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

      4. associate-*r* 57.3%

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

      5. neg-mul-1 57.3%

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

      6. neg-sub0 57.3%

         \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a - b \cdot i\right)\right)} \]

      7. cancel-sign-sub-inv 57.3%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(x \cdot a + \left(-b\right) \cdot i\right)}\right) \]

      8. *-commutative 57.3%

         \[\leadsto t \cdot \left(0 - \left(x \cdot a + \color{blue}{i \cdot \left(-b\right)}\right)\right) \]

      9. +-commutative 57.3%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(i \cdot \left(-b\right) + x \cdot a\right)}\right) \]

      10. associate--r+ 57.3%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - i \cdot \left(-b\right)\right) - x \cdot a\right)} \]

      11. neg-sub0 57.3%

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

      12. distribute-rgt-neg-in 57.3%

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

      13. remove-double-neg 57.3%

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

      14. *-commutative 57.3%

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

      15. *-commutative 57.3%

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

   9. Simplified 57.3%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+51}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{-7}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-138}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{-148}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-122}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{+80}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-183}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.7e-17)
     t_1
     (if (<= j -7e-183)
       (* b (- (* t i) (* z c)))
       (if (<= j 5.6e-249)
         (* t (- (* b i) (* x a)))
         (if (<= j 7.5e-71)
           (* z (- (* x y) (* b c)))
           (if (<= j 1.8e-21)
             (* a (- (* c j) (* x t)))
             (if (<= j 6.5e+32) (* x (- (* y z) (* t a))) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.7e-17) {
		tmp = t_1;
	} else if (j <= -7e-183) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 5.6e-249) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 7.5e-71) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 1.8e-21) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= 6.5e+32) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-1.7d-17)) then
        tmp = t_1
    else if (j <= (-7d-183)) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 5.6d-249) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 7.5d-71) then
        tmp = z * ((x * y) - (b * c))
    else if (j <= 1.8d-21) then
        tmp = a * ((c * j) - (x * t))
    else if (j <= 6.5d+32) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.7e-17) {
		tmp = t_1;
	} else if (j <= -7e-183) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 5.6e-249) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 7.5e-71) {
		tmp = z * ((x * y) - (b * c));
	} else if (j <= 1.8e-21) {
		tmp = a * ((c * j) - (x * t));
	} else if (j <= 6.5e+32) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.7e-17:
		tmp = t_1
	elif j <= -7e-183:
		tmp = b * ((t * i) - (z * c))
	elif j <= 5.6e-249:
		tmp = t * ((b * i) - (x * a))
	elif j <= 7.5e-71:
		tmp = z * ((x * y) - (b * c))
	elif j <= 1.8e-21:
		tmp = a * ((c * j) - (x * t))
	elif j <= 6.5e+32:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.7e-17)
		tmp = t_1;
	elseif (j <= -7e-183)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 5.6e-249)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 7.5e-71)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (j <= 1.8e-21)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (j <= 6.5e+32)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.7e-17)
		tmp = t_1;
	elseif (j <= -7e-183)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 5.6e-249)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 7.5e-71)
		tmp = z * ((x * y) - (b * c));
	elseif (j <= 1.8e-21)
		tmp = a * ((c * j) - (x * t));
	elseif (j <= 6.5e+32)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e-17], t$95$1, If[LessEqual[j, -7e-183], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5.6e-249], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e-71], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.8e-21], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6.5e+32], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if j < -1.6999999999999999e-17 or 6.4999999999999994e32 < j

   1. Initial program 77.7%

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

   3. Taylor expanded in j around inf 62.3%

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

      1. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if -1.6999999999999999e-17 < j < -6.99999999999999983e-183

   1. Initial program 87.0%

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

   3. Taylor expanded in b around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if -6.99999999999999983e-183 < j < 5.5999999999999998e-249

   1. Initial program 71.8%

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

   3. Taylor expanded in c around 0 77.5%

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

      1. associate-*r* 80.1%

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

      2. associate-*r* 80.1%

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

      3. *-commutative 80.1%

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

      4. mul-1-neg 80.1%

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

      5. *-commutative 80.1%

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

      6. distribute-rgt-neg-in 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around -inf 80.2%

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

   7. Taylor expanded in t around inf 74.5%

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

      1. associate-*r* 74.5%

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

      2. *-commutative 74.5%

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

      3. *-commutative 74.5%

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

      4. associate-*r* 74.5%

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

      5. neg-mul-1 74.5%

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

      6. neg-sub0 74.5%

         \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a - b \cdot i\right)\right)} \]

      7. cancel-sign-sub-inv 74.5%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(x \cdot a + \left(-b\right) \cdot i\right)}\right) \]

      8. *-commutative 74.5%

         \[\leadsto t \cdot \left(0 - \left(x \cdot a + \color{blue}{i \cdot \left(-b\right)}\right)\right) \]

      9. +-commutative 74.5%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(i \cdot \left(-b\right) + x \cdot a\right)}\right) \]

      10. associate--r+ 74.5%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - i \cdot \left(-b\right)\right) - x \cdot a\right)} \]

      11. neg-sub0 74.5%

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

      12. distribute-rgt-neg-in 74.5%

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

      13. remove-double-neg 74.5%

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

      14. *-commutative 74.5%

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

      15. *-commutative 74.5%

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

   9. Simplified 74.5%

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

   if 5.5999999999999998e-249 < j < 7.5000000000000004e-71

   1. Initial program 71.5%

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

   3. Taylor expanded in z around inf 66.6%

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

   if 7.5000000000000004e-71 < j < 1.79999999999999995e-21

   1. Initial program 64.4%

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

   3. Taylor expanded in a around inf 61.4%

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

      1. +-commutative 61.4%

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

      2. mul-1-neg 61.4%

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

      3. unsub-neg 61.4%

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

      4. *-commutative 61.4%

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

   5. Simplified 61.4%

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

   if 1.79999999999999995e-21 < j < 6.4999999999999994e32

   1. Initial program 81.1%

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

      1. add-cube-cbrt 81.1%

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

      2. pow3 81.1%

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

      3. *-commutative 81.1%

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

   4. Applied egg-rr 81.1%

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

   5. Taylor expanded in x around inf 62.2%

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

      1. *-commutative 62.2%

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

      2. *-commutative 62.2%

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

   7. Simplified 62.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7 \cdot 10^{-183}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-71}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;j \leq 1.8 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 6.5 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 54.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.55 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -7.4 \cdot 10^{-183}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8.6 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.55e-17)
     t_1
     (if (<= j -7.4e-183)
       (* b (- (* t i) (* z c)))
       (if (<= j 8.6e-276)
         (* t (- (* b i) (* x a)))
         (if (<= j 7e+38) (+ (* a (* c j)) (* x (- (* y z) (* t a)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.55e-17) {
		tmp = t_1;
	} else if (j <= -7.4e-183) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 8.6e-276) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 7e+38) {
		tmp = (a * (c * j)) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-1.55d-17)) then
        tmp = t_1
    else if (j <= (-7.4d-183)) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 8.6d-276) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 7d+38) then
        tmp = (a * (c * j)) + (x * ((y * z) - (t * a)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.55e-17) {
		tmp = t_1;
	} else if (j <= -7.4e-183) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 8.6e-276) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 7e+38) {
		tmp = (a * (c * j)) + (x * ((y * z) - (t * a)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.55e-17:
		tmp = t_1
	elif j <= -7.4e-183:
		tmp = b * ((t * i) - (z * c))
	elif j <= 8.6e-276:
		tmp = t * ((b * i) - (x * a))
	elif j <= 7e+38:
		tmp = (a * (c * j)) + (x * ((y * z) - (t * a)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.55e-17)
		tmp = t_1;
	elseif (j <= -7.4e-183)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 8.6e-276)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 7e+38)
		tmp = Float64(Float64(a * Float64(c * j)) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.55e-17)
		tmp = t_1;
	elseif (j <= -7.4e-183)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 8.6e-276)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 7e+38)
		tmp = (a * (c * j)) + (x * ((y * z) - (t * a)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.55e-17], t$95$1, If[LessEqual[j, -7.4e-183], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 8.6e-276], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7e+38], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.5499999999999999e-17 or 7.00000000000000003e38 < j

   1. Initial program 78.1%

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

   3. Taylor expanded in j around inf 62.5%

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

      1. *-commutative 62.5%

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

   5. Simplified 62.5%

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

   if -1.5499999999999999e-17 < j < -7.3999999999999997e-183

   1. Initial program 87.0%

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

   3. Taylor expanded in b around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if -7.3999999999999997e-183 < j < 8.59999999999999921e-276

   1. Initial program 74.2%

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

   3. Taylor expanded in c around 0 81.6%

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

      1. associate-*r* 84.9%

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

      2. associate-*r* 84.9%

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

      3. *-commutative 84.9%

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

      4. mul-1-neg 84.9%

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

      5. *-commutative 84.9%

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

      6. distribute-rgt-neg-in 84.9%

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

   5. Simplified 84.9%

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

   6. Taylor expanded in t around -inf 85.0%

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

   7. Taylor expanded in t around inf 78.0%

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

      1. associate-*r* 78.0%

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

      2. *-commutative 78.0%

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

      3. *-commutative 78.0%

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

      4. associate-*r* 78.0%

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

      5. neg-mul-1 78.0%

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

      6. neg-sub0 78.0%

         \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a - b \cdot i\right)\right)} \]

      7. cancel-sign-sub-inv 78.0%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(x \cdot a + \left(-b\right) \cdot i\right)}\right) \]

      8. *-commutative 78.0%

         \[\leadsto t \cdot \left(0 - \left(x \cdot a + \color{blue}{i \cdot \left(-b\right)}\right)\right) \]

      9. +-commutative 78.0%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(i \cdot \left(-b\right) + x \cdot a\right)}\right) \]

      10. associate--r+ 78.0%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - i \cdot \left(-b\right)\right) - x \cdot a\right)} \]

      11. neg-sub0 78.0%

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

      12. distribute-rgt-neg-in 78.0%

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

      13. remove-double-neg 78.0%

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

      14. *-commutative 78.0%

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

      15. *-commutative 78.0%

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

   9. Simplified 78.0%

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

   if 8.59999999999999921e-276 < j < 7.00000000000000003e38

   1. Initial program 71.0%

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

   3. Taylor expanded in b around 0 57.6%

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

   4. Taylor expanded in i around 0 58.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.55 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -7.4 \cdot 10^{-183}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 8.6 \cdot 10^{-276}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 7 \cdot 10^{+38}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-103} \lor \neg \left(a \leq 7 \cdot 10^{-60}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -3.7e+208)
   (+ (* a (- (* c j) (* x t))) (* t (* b i)))
   (if (or (<= a -2e-103) (not (<= a 7e-60)))
     (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))
     (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -3.7e+208) {
		tmp = (a * ((c * j) - (x * t))) + (t * (b * i));
	} else if ((a <= -2e-103) || !(a <= 7e-60)) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-3.7d+208)) then
        tmp = (a * ((c * j) - (x * t))) + (t * (b * i))
    else if ((a <= (-2d-103)) .or. (.not. (a <= 7d-60))) then
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    else
        tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -3.7e+208) {
		tmp = (a * ((c * j) - (x * t))) + (t * (b * i));
	} else if ((a <= -2e-103) || !(a <= 7e-60)) {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	} else {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -3.7e+208:
		tmp = (a * ((c * j) - (x * t))) + (t * (b * i))
	elif (a <= -2e-103) or not (a <= 7e-60):
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	else:
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -3.7e+208)
		tmp = Float64(Float64(a * Float64(Float64(c * j) - Float64(x * t))) + Float64(t * Float64(b * i)));
	elseif ((a <= -2e-103) || !(a <= 7e-60))
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -3.7e+208)
		tmp = (a * ((c * j) - (x * t))) + (t * (b * i));
	elseif ((a <= -2e-103) || ~((a <= 7e-60)))
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	else
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -3.7e+208], N[(N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, -2e-103], N[Not[LessEqual[a, 7e-60]], $MachinePrecision]], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.69999999999999989e208

   1. Initial program 51.4%

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

   3. Taylor expanded in c around 0 51.4%

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

      1. associate-*r* 51.4%

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

      2. associate-*r* 51.4%

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

      3. *-commutative 51.4%

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

      4. mul-1-neg 51.4%

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

      5. *-commutative 51.4%

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

      6. distribute-rgt-neg-in 51.4%

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

   5. Simplified 51.4%

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

   6. Taylor expanded in y around 0 78.5%

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

      1. cancel-sign-sub-inv 78.5%

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

      2. mul-1-neg 78.5%

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

      3. distribute-rgt-neg-in 78.5%

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

      4. distribute-lft-in 85.6%

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

      5. +-commutative 85.6%

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

      6. sub-neg 85.6%

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

      7. metadata-eval 85.6%

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

      8. *-lft-identity 85.6%

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

      9. associate-*r* 85.6%

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

      10. remove-double-neg 85.6%

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

      11. mul-1-neg 85.6%

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

      12. associate-*r* 85.6%

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

      13. neg-mul-1 85.6%

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

      14. *-commutative 85.6%

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

      15. distribute-lft-neg-in 85.6%

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

      16. *-commutative 85.6%

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

      17. distribute-rgt-neg-in 85.6%

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

      18. *-commutative 85.6%

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

      19. neg-mul-1 85.6%

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

      20. associate-*r* 85.6%

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

      21. mul-1-neg 85.6%

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

      22. remove-double-neg 85.6%

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

   8. Simplified 85.6%

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

   if -3.69999999999999989e208 < a < -1.99999999999999992e-103 or 6.99999999999999952e-60 < a

   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 b around 0 71.9%

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

   if -1.99999999999999992e-103 < a < 6.99999999999999952e-60

   1. Initial program 86.9%

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

   3. Taylor expanded in a around 0 80.7%

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

      1. cancel-sign-sub-inv 80.7%

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

      2. *-commutative 80.7%

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

      3. *-commutative 80.7%

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

      4. cancel-sign-sub-inv 80.7%

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

      5. sub-neg 80.7%

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

      6. distribute-rgt-neg-out 80.7%

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

   5. Simplified 83.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{+208}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-103} \lor \neg \left(a \leq 7 \cdot 10^{-60}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - \left(x \cdot \left(t \cdot a - y \cdot z\right) - t \cdot \left(b \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -3.6e+152)
   (* a (- (* c j) (* x t)))
   (if (<= a -4e-103)
     (- (* a (* c j)) (- (* x (- (* t a) (* y z))) (* t (* b i))))
     (if (<= a 1.4e-60)
       (+ (* y (- (* x z) (* i j))) (* b (- (* t i) (* z c))))
       (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -3.6e+152) {
		tmp = a * ((c * j) - (x * t));
	} else if (a <= -4e-103) {
		tmp = (a * (c * j)) - ((x * ((t * a) - (y * z))) - (t * (b * i)));
	} else if (a <= 1.4e-60) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-3.6d+152)) then
        tmp = a * ((c * j) - (x * t))
    else if (a <= (-4d-103)) then
        tmp = (a * (c * j)) - ((x * ((t * a) - (y * z))) - (t * (b * i)))
    else if (a <= 1.4d-60) then
        tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
    else
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -3.6e+152) {
		tmp = a * ((c * j) - (x * t));
	} else if (a <= -4e-103) {
		tmp = (a * (c * j)) - ((x * ((t * a) - (y * z))) - (t * (b * i)));
	} else if (a <= 1.4e-60) {
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -3.6e+152:
		tmp = a * ((c * j) - (x * t))
	elif a <= -4e-103:
		tmp = (a * (c * j)) - ((x * ((t * a) - (y * z))) - (t * (b * i)))
	elif a <= 1.4e-60:
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -3.6e+152)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (a <= -4e-103)
		tmp = Float64(Float64(a * Float64(c * j)) - Float64(Float64(x * Float64(Float64(t * a) - Float64(y * z))) - Float64(t * Float64(b * i))));
	elseif (a <= 1.4e-60)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -3.6e+152)
		tmp = a * ((c * j) - (x * t));
	elseif (a <= -4e-103)
		tmp = (a * (c * j)) - ((x * ((t * a) - (y * z))) - (t * (b * i)));
	elseif (a <= 1.4e-60)
		tmp = (y * ((x * z) - (i * j))) + (b * ((t * i) - (z * c)));
	else
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -3.6e+152], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4e-103], N[(N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.4e-60], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.5999999999999999e152

   1. Initial program 51.1%

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

   3. Taylor expanded in a around inf 83.0%

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

      1. +-commutative 83.0%

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

      2. mul-1-neg 83.0%

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

      3. unsub-neg 83.0%

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

      4. *-commutative 83.0%

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

   5. Simplified 83.0%

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

   if -3.5999999999999999e152 < a < -3.99999999999999983e-103

   1. Initial program 79.8%

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

   3. Taylor expanded in c around 0 82.7%

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

      1. associate-*r* 80.9%

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

      2. associate-*r* 80.9%

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

      3. *-commutative 80.9%

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

      4. mul-1-neg 80.9%

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

      5. *-commutative 80.9%

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

      6. distribute-rgt-neg-in 80.9%

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

   5. Simplified 80.9%

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

   6. Taylor expanded in c around inf 77.6%

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

   if -3.99999999999999983e-103 < a < 1.4000000000000001e-60

   1. Initial program 86.9%

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

   3. Taylor expanded in a around 0 80.7%

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

      1. cancel-sign-sub-inv 80.7%

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

      2. *-commutative 80.7%

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

      3. *-commutative 80.7%

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

      4. cancel-sign-sub-inv 80.7%

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

      5. sub-neg 80.7%

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

      6. distribute-rgt-neg-out 80.7%

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

   5. Simplified 83.4%

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

   if 1.4000000000000001e-60 < a

   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 b around 0 70.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+152}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-103}:\\ \;\;\;\;a \cdot \left(c \cdot j\right) - \left(x \cdot \left(t \cdot a - y \cdot z\right) - t \cdot \left(b \cdot i\right)\right)\\ \mathbf{elif}\;a \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 28.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -7.5 \cdot 10^{+59}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-227}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+153}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* c j))) (t_2 (* x (* y z))))
   (if (<= z -7.5e+59)
     t_2
     (if (<= z -4.1e-300)
       (* b (* t i))
       (if (<= z 5e-227)
         t_1
         (if (<= z 6.8e+52) (* t (* b i)) (if (<= z 1.75e+153) 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);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -7.5e+59) {
		tmp = t_2;
	} else if (z <= -4.1e-300) {
		tmp = b * (t * i);
	} else if (z <= 5e-227) {
		tmp = t_1;
	} else if (z <= 6.8e+52) {
		tmp = t * (b * i);
	} else if (z <= 1.75e+153) {
		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)
    t_2 = x * (y * z)
    if (z <= (-7.5d+59)) then
        tmp = t_2
    else if (z <= (-4.1d-300)) then
        tmp = b * (t * i)
    else if (z <= 5d-227) then
        tmp = t_1
    else if (z <= 6.8d+52) then
        tmp = t * (b * i)
    else if (z <= 1.75d+153) 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);
	double t_2 = x * (y * z);
	double tmp;
	if (z <= -7.5e+59) {
		tmp = t_2;
	} else if (z <= -4.1e-300) {
		tmp = b * (t * i);
	} else if (z <= 5e-227) {
		tmp = t_1;
	} else if (z <= 6.8e+52) {
		tmp = t * (b * i);
	} else if (z <= 1.75e+153) {
		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)
	t_2 = x * (y * z)
	tmp = 0
	if z <= -7.5e+59:
		tmp = t_2
	elif z <= -4.1e-300:
		tmp = b * (t * i)
	elif z <= 5e-227:
		tmp = t_1
	elif z <= 6.8e+52:
		tmp = t * (b * i)
	elif z <= 1.75e+153:
		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(c * j))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -7.5e+59)
		tmp = t_2;
	elseif (z <= -4.1e-300)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 5e-227)
		tmp = t_1;
	elseif (z <= 6.8e+52)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 1.75e+153)
		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);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (z <= -7.5e+59)
		tmp = t_2;
	elseif (z <= -4.1e-300)
		tmp = b * (t * i);
	elseif (z <= 5e-227)
		tmp = t_1;
	elseif (z <= 6.8e+52)
		tmp = t * (b * i);
	elseif (z <= 1.75e+153)
		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[(c * j), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -7.5e+59], t$95$2, If[LessEqual[z, -4.1e-300], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5e-227], t$95$1, If[LessEqual[z, 6.8e+52], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+153], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.4999999999999996e59 or 1.75e153 < z

   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. Step-by-step derivation

      1. add-cube-cbrt 72.2%

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

      2. pow3 72.2%

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

      3. *-commutative 72.2%

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

   4. Applied egg-rr 72.2%

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

   5. Taylor expanded in z around inf 57.6%

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

      1. *-commutative 57.6%

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

   7. Simplified 57.6%

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

   if -7.4999999999999996e59 < z < -4.1000000000000001e-300

   1. Initial program 75.7%

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

   3. Taylor expanded in c around 0 66.3%

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

      1. associate-*r* 66.4%

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

      2. associate-*r* 66.4%

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

      3. *-commutative 66.4%

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

      4. mul-1-neg 66.4%

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

      5. *-commutative 66.4%

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

      6. distribute-rgt-neg-in 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in b around inf 27.8%

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

   if -4.1000000000000001e-300 < z < 4.99999999999999961e-227 or 6.8e52 < z < 1.75e153

   1. Initial program 71.5%

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

      1. add-cube-cbrt 71.4%

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

      2. pow3 71.4%

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

      3. *-commutative 71.4%

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

   4. Applied egg-rr 71.4%

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

   5. Taylor expanded in c around inf 41.5%

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

   if 4.99999999999999961e-227 < z < 6.8e52

   1. Initial program 89.8%

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

   3. Taylor expanded in c around 0 81.7%

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

      1. associate-*r* 78.5%

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

      2. associate-*r* 78.5%

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

      3. *-commutative 78.5%

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

      4. mul-1-neg 78.5%

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

      5. *-commutative 78.5%

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

      6. distribute-rgt-neg-in 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in b around inf 33.9%

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

      1. associate-*r* 34.0%

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

      2. remove-double-neg 34.0%

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

      3. mul-1-neg 34.0%

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

      4. associate-*r* 34.0%

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

      5. neg-mul-1 34.0%

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

      6. *-commutative 34.0%

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

      7. distribute-lft-neg-in 34.0%

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

      8. *-commutative 34.0%

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

      9. distribute-rgt-neg-in 34.0%

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

      10. *-commutative 34.0%

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

      11. neg-mul-1 34.0%

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

      12. associate-*r* 34.0%

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

      13. mul-1-neg 34.0%

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

      14. remove-double-neg 34.0%

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

   8. Simplified 34.0%

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

4. Final simplification 39.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-227}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{+52}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+153}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 28.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-226}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+152}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= z -4.2e+55)
     t_1
     (if (<= z -1.35e-300)
       (* b (* t i))
       (if (<= z 2.2e-226)
         (* a (* c j))
         (if (<= z 3.7e+55)
           (* t (* b i))
           (if (<= z 1.35e+152) (* c (* a j)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -4.2e+55) {
		tmp = t_1;
	} else if (z <= -1.35e-300) {
		tmp = b * (t * i);
	} else if (z <= 2.2e-226) {
		tmp = a * (c * j);
	} else if (z <= 3.7e+55) {
		tmp = t * (b * i);
	} else if (z <= 1.35e+152) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (z <= (-4.2d+55)) then
        tmp = t_1
    else if (z <= (-1.35d-300)) then
        tmp = b * (t * i)
    else if (z <= 2.2d-226) then
        tmp = a * (c * j)
    else if (z <= 3.7d+55) then
        tmp = t * (b * i)
    else if (z <= 1.35d+152) then
        tmp = c * (a * j)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -4.2e+55) {
		tmp = t_1;
	} else if (z <= -1.35e-300) {
		tmp = b * (t * i);
	} else if (z <= 2.2e-226) {
		tmp = a * (c * j);
	} else if (z <= 3.7e+55) {
		tmp = t * (b * i);
	} else if (z <= 1.35e+152) {
		tmp = c * (a * j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if z <= -4.2e+55:
		tmp = t_1
	elif z <= -1.35e-300:
		tmp = b * (t * i)
	elif z <= 2.2e-226:
		tmp = a * (c * j)
	elif z <= 3.7e+55:
		tmp = t * (b * i)
	elif z <= 1.35e+152:
		tmp = c * (a * j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -4.2e+55)
		tmp = t_1;
	elseif (z <= -1.35e-300)
		tmp = Float64(b * Float64(t * i));
	elseif (z <= 2.2e-226)
		tmp = Float64(a * Float64(c * j));
	elseif (z <= 3.7e+55)
		tmp = Float64(t * Float64(b * i));
	elseif (z <= 1.35e+152)
		tmp = Float64(c * Float64(a * j));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -4.2e+55)
		tmp = t_1;
	elseif (z <= -1.35e-300)
		tmp = b * (t * i);
	elseif (z <= 2.2e-226)
		tmp = a * (c * j);
	elseif (z <= 3.7e+55)
		tmp = t * (b * i);
	elseif (z <= 1.35e+152)
		tmp = c * (a * j);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2e+55], t$95$1, If[LessEqual[z, -1.35e-300], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-226], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e+55], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.35e+152], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.2000000000000001e55 or 1.35000000000000007e152 < z

   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. Step-by-step derivation

      1. add-cube-cbrt 72.2%

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

      2. pow3 72.2%

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

      3. *-commutative 72.2%

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

   4. Applied egg-rr 72.2%

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

   5. Taylor expanded in z around inf 57.6%

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

      1. *-commutative 57.6%

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

   7. Simplified 57.6%

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

   if -4.2000000000000001e55 < z < -1.34999999999999998e-300

   1. Initial program 75.7%

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

   3. Taylor expanded in c around 0 66.3%

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

      1. associate-*r* 66.4%

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

      2. associate-*r* 66.4%

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

      3. *-commutative 66.4%

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

      4. mul-1-neg 66.4%

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

      5. *-commutative 66.4%

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

      6. distribute-rgt-neg-in 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in b around inf 27.8%

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

   if -1.34999999999999998e-300 < z < 2.2e-226

   1. Initial program 88.0%

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

      1. add-cube-cbrt 88.0%

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

      2. pow3 88.0%

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

      3. *-commutative 88.0%

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

   4. Applied egg-rr 88.0%

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

   5. Taylor expanded in c around inf 34.2%

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

   if 2.2e-226 < z < 3.7000000000000002e55

   1. Initial program 89.8%

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

   3. Taylor expanded in c around 0 81.7%

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

      1. associate-*r* 78.5%

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

      2. associate-*r* 78.5%

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

      3. *-commutative 78.5%

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

      4. mul-1-neg 78.5%

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

      5. *-commutative 78.5%

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

      6. distribute-rgt-neg-in 78.5%

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

   5. Simplified 78.5%

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

   6. Taylor expanded in b around inf 33.9%

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

      1. associate-*r* 34.0%

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

      2. remove-double-neg 34.0%

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

      3. mul-1-neg 34.0%

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

      4. associate-*r* 34.0%

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

      5. neg-mul-1 34.0%

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

      6. *-commutative 34.0%

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

      7. distribute-lft-neg-in 34.0%

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

      8. *-commutative 34.0%

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

      9. distribute-rgt-neg-in 34.0%

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

      10. *-commutative 34.0%

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

      11. neg-mul-1 34.0%

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

      12. associate-*r* 34.0%

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

      13. mul-1-neg 34.0%

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

      14. remove-double-neg 34.0%

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

   8. Simplified 34.0%

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

   if 3.7000000000000002e55 < z < 1.35000000000000007e152

   1. Initial program 53.5%

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

   3. Taylor expanded in c around 0 70.3%

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

      1. associate-*r* 73.9%

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

      2. associate-*r* 73.9%

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

      3. *-commutative 73.9%

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

      4. mul-1-neg 73.9%

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

      5. *-commutative 73.9%

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

      6. distribute-rgt-neg-in 73.9%

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

   5. Simplified 73.9%

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

   6. Taylor expanded in t around -inf 81.9%

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

   7. Taylor expanded in c around inf 49.5%

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

      1. *-commutative 49.5%

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

      2. associate-*r* 53.6%

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

   9. Simplified 53.6%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+55}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.35 \cdot 10^{-300}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-226}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+55}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+152}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - \left(x \cdot \left(t \cdot a - y \cdot z\right) - t \cdot \left(b \cdot i\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2.2e+51)
   (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
   (- (* j (- (* a c) (* y i))) (- (* x (- (* t a) (* y z))) (* t (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.2e+51) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) - ((x * ((t * a) - (y * z))) - (t * (b * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-2.2d+51)) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else
        tmp = (j * ((a * c) - (y * i))) - ((x * ((t * a) - (y * z))) - (t * (b * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.2e+51) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) - ((x * ((t * a) - (y * z))) - (t * (b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -2.2e+51:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	else:
		tmp = (j * ((a * c) - (y * i))) - ((x * ((t * a) - (y * z))) - (t * (b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -2.2e+51)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) - Float64(Float64(x * Float64(Float64(t * a) - Float64(y * z))) - Float64(t * Float64(b * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -2.2e+51)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	else
		tmp = (j * ((a * c) - (y * i))) - ((x * ((t * a) - (y * z))) - (t * (b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -2.2e+51], 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[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.19999999999999992e51

   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 j around 0 83.1%

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

   if -2.19999999999999992e51 < b

   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 c around 0 74.5%

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

      1. associate-*r* 75.4%

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

      2. associate-*r* 75.4%

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

      3. *-commutative 75.4%

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

      4. mul-1-neg 75.4%

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

      5. *-commutative 75.4%

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

      6. distribute-rgt-neg-in 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+51}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - \left(x \cdot \left(t \cdot a - y \cdot z\right) - t \cdot \left(b \cdot i\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 69.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right) - t \cdot \left(x \cdot a - b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.8e+59)
   (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
   (- (+ (* x (* y z)) (* j (- (* a c) (* y i)))) (* t (- (* x a) (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.8e+59) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = ((x * (y * z)) + (j * ((a * c) - (y * i)))) - (t * ((x * a) - (b * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-3.8d+59)) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else
        tmp = ((x * (y * z)) + (j * ((a * c) - (y * i)))) - (t * ((x * a) - (b * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.8e+59) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else {
		tmp = ((x * (y * z)) + (j * ((a * c) - (y * i)))) - (t * ((x * a) - (b * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.8e+59:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	else:
		tmp = ((x * (y * z)) + (j * ((a * c) - (y * i)))) - (t * ((x * a) - (b * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.8e+59)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(Float64(x * Float64(y * z)) + Float64(j * Float64(Float64(a * c) - Float64(y * i)))) - Float64(t * Float64(Float64(x * a) - Float64(b * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.8e+59)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	else
		tmp = ((x * (y * z)) + (j * ((a * c) - (y * i)))) - (t * ((x * a) - (b * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.8e+59], 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[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t * N[(N[(x * a), $MachinePrecision] - N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.8000000000000001e59

   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 j around 0 83.1%

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

   if -3.8000000000000001e59 < b

   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 c around 0 74.5%

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

      1. associate-*r* 75.4%

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

      2. associate-*r* 75.4%

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

      3. *-commutative 75.4%

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

      4. mul-1-neg 75.4%

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

      5. *-commutative 75.4%

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

      6. distribute-rgt-neg-in 75.4%

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

   5. Simplified 75.4%

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

   6. Taylor expanded in t around -inf 77.3%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+59}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) + j \cdot \left(a \cdot c - y \cdot i\right)\right) - t \cdot \left(x \cdot a - b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.15 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq -3.85 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{-252}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.15e-17)
     t_1
     (if (<= j -3.85e-184)
       (* b (- (* t i) (* z c)))
       (if (<= j 2.9e-252)
         (* t (- (* b i) (* x a)))
         (if (<= j 4.8e+32) (* x (- (* y z) (* t a))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.15e-17) {
		tmp = t_1;
	} else if (j <= -3.85e-184) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 2.9e-252) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 4.8e+32) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-1.15d-17)) then
        tmp = t_1
    else if (j <= (-3.85d-184)) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 2.9d-252) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= 4.8d+32) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.15e-17) {
		tmp = t_1;
	} else if (j <= -3.85e-184) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 2.9e-252) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= 4.8e+32) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.15e-17:
		tmp = t_1
	elif j <= -3.85e-184:
		tmp = b * ((t * i) - (z * c))
	elif j <= 2.9e-252:
		tmp = t * ((b * i) - (x * a))
	elif j <= 4.8e+32:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.15e-17)
		tmp = t_1;
	elseif (j <= -3.85e-184)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 2.9e-252)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= 4.8e+32)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.15e-17)
		tmp = t_1;
	elseif (j <= -3.85e-184)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 2.9e-252)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= 4.8e+32)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.15e-17], t$95$1, If[LessEqual[j, -3.85e-184], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.9e-252], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 4.8e+32], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.15000000000000004e-17 or 4.79999999999999983e32 < j

   1. Initial program 77.7%

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

   3. Taylor expanded in j around inf 62.3%

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

      1. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if -1.15000000000000004e-17 < j < -3.85000000000000005e-184

   1. Initial program 87.0%

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

   3. Taylor expanded in b around inf 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

   5. Simplified 67.5%

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

   if -3.85000000000000005e-184 < j < 2.9000000000000001e-252

   1. Initial program 71.8%

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

   3. Taylor expanded in c around 0 77.5%

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

      1. associate-*r* 80.1%

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

      2. associate-*r* 80.1%

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

      3. *-commutative 80.1%

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

      4. mul-1-neg 80.1%

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

      5. *-commutative 80.1%

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

      6. distribute-rgt-neg-in 80.1%

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

   5. Simplified 80.1%

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

   6. Taylor expanded in t around -inf 80.2%

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

   7. Taylor expanded in t around inf 74.5%

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

      1. associate-*r* 74.5%

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

      2. *-commutative 74.5%

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

      3. *-commutative 74.5%

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

      4. associate-*r* 74.5%

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

      5. neg-mul-1 74.5%

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

      6. neg-sub0 74.5%

         \[\leadsto t \cdot \color{blue}{\left(0 - \left(x \cdot a - b \cdot i\right)\right)} \]

      7. cancel-sign-sub-inv 74.5%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(x \cdot a + \left(-b\right) \cdot i\right)}\right) \]

      8. *-commutative 74.5%

         \[\leadsto t \cdot \left(0 - \left(x \cdot a + \color{blue}{i \cdot \left(-b\right)}\right)\right) \]

      9. +-commutative 74.5%

         \[\leadsto t \cdot \left(0 - \color{blue}{\left(i \cdot \left(-b\right) + x \cdot a\right)}\right) \]

      10. associate--r+ 74.5%

          \[\leadsto t \cdot \color{blue}{\left(\left(0 - i \cdot \left(-b\right)\right) - x \cdot a\right)} \]

      11. neg-sub0 74.5%

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

      12. distribute-rgt-neg-in 74.5%

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

      13. remove-double-neg 74.5%

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

      14. *-commutative 74.5%

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

      15. *-commutative 74.5%

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

   9. Simplified 74.5%

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

   if 2.9000000000000001e-252 < j < 4.79999999999999983e32

   1. Initial program 72.7%

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

      1. add-cube-cbrt 72.5%

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

      2. pow3 72.5%

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

      3. *-commutative 72.5%

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

   4. Applied egg-rr 72.5%

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

   5. Taylor expanded in x around inf 53.0%

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

      1. *-commutative 53.0%

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

      2. *-commutative 53.0%

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

   7. Simplified 53.0%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.15 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -3.85 \cdot 10^{-184}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 2.9 \cdot 10^{-252}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 68.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+54} \lor \neg \left(b \leq 8.8 \cdot 10^{+172}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.1e+54) (not (<= b 8.8e+172)))
   (+ (* x (* y z)) (* b (- (* t i) (* z c))))
   (+ (* j (- (* a c) (* y i))) (* x (- (* y z) (* t a))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.1e+54) || !(b <= 8.8e+172)) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-2.1d+54)) .or. (.not. (b <= 8.8d+172))) then
        tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
    else
        tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.1e+54) || !(b <= 8.8e+172)) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else {
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2.1e+54) or not (b <= 8.8e+172):
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
	else:
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2.1e+54) || !(b <= 8.8e+172))
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	else
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2.1e+54) || ~((b <= 8.8e+172)))
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	else
		tmp = (j * ((a * c) - (y * i))) + (x * ((y * z) - (t * a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2.1e+54], N[Not[LessEqual[b, 8.8e+172]], $MachinePrecision]], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.09999999999999986e54 or 8.8000000000000005e172 < b

   1. Initial program 83.5%

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

   3. Taylor expanded in j around 0 83.6%

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

   4. Taylor expanded in a around 0 79.7%

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

   if -2.09999999999999986e54 < b < 8.8000000000000005e172

   1. Initial program 74.8%

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

   3. Taylor expanded in b around 0 69.9%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.1 \cdot 10^{+54} \lor \neg \left(b \leq 8.8 \cdot 10^{+172}\right):\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{if}\;j \leq -1.26 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 1050000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+156}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* i (- y)))))
   (if (<= j -1.26e-17)
     t_1
     (if (<= j 3.8e-249)
       (* t (* b i))
       (if (<= j 1050000000.0)
         (* y (* x z))
         (if (<= j 1.5e+156) t_1 (* 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 t_1 = j * (i * -y);
	double tmp;
	if (j <= -1.26e-17) {
		tmp = t_1;
	} else if (j <= 3.8e-249) {
		tmp = t * (b * i);
	} else if (j <= 1050000000.0) {
		tmp = y * (x * z);
	} else if (j <= 1.5e+156) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = j * (i * -y)
    if (j <= (-1.26d-17)) then
        tmp = t_1
    else if (j <= 3.8d-249) then
        tmp = t * (b * i)
    else if (j <= 1050000000.0d0) then
        tmp = y * (x * z)
    else if (j <= 1.5d+156) then
        tmp = t_1
    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 t_1 = j * (i * -y);
	double tmp;
	if (j <= -1.26e-17) {
		tmp = t_1;
	} else if (j <= 3.8e-249) {
		tmp = t * (b * i);
	} else if (j <= 1050000000.0) {
		tmp = y * (x * z);
	} else if (j <= 1.5e+156) {
		tmp = t_1;
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (i * -y)
	tmp = 0
	if j <= -1.26e-17:
		tmp = t_1
	elif j <= 3.8e-249:
		tmp = t * (b * i)
	elif j <= 1050000000.0:
		tmp = y * (x * z)
	elif j <= 1.5e+156:
		tmp = t_1
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(i * Float64(-y)))
	tmp = 0.0
	if (j <= -1.26e-17)
		tmp = t_1;
	elseif (j <= 3.8e-249)
		tmp = Float64(t * Float64(b * i));
	elseif (j <= 1050000000.0)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.5e+156)
		tmp = t_1;
	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)
	t_1 = j * (i * -y);
	tmp = 0.0;
	if (j <= -1.26e-17)
		tmp = t_1;
	elseif (j <= 3.8e-249)
		tmp = t * (b * i);
	elseif (j <= 1050000000.0)
		tmp = y * (x * z);
	elseif (j <= 1.5e+156)
		tmp = t_1;
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.26e-17], t$95$1, If[LessEqual[j, 3.8e-249], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1050000000.0], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.5e+156], t$95$1, N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.2600000000000001e-17 or 1.05e9 < j < 1.5e156

   1. Initial program 77.9%

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

   3. Taylor expanded in y around inf 46.3%

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

      1. +-commutative 46.3%

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

      2. mul-1-neg 46.3%

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

      3. unsub-neg 46.3%

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

   5. Simplified 46.3%

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

   6. Taylor expanded in x around 0 37.8%

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

      1. neg-mul-1 37.8%

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

      2. distribute-lft-neg-in 37.8%

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

      3. *-commutative 37.8%

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

   8. Simplified 37.8%

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

   9. Taylor expanded in y around 0 38.6%

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

       1. associate-*r* 38.6%

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

       2. neg-mul-1 38.6%

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

       3. *-commutative 38.6%

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

       4. associate-*l* 36.1%

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

   11. Simplified 36.1%

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

   if -1.2600000000000001e-17 < j < 3.8000000000000001e-249

   1. Initial program 79.8%

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

   3. Taylor expanded in c around 0 73.6%

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

      1. associate-*r* 73.5%

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

      2. associate-*r* 73.5%

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

      3. *-commutative 73.5%

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

      4. mul-1-neg 73.5%

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

      5. *-commutative 73.5%

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

      6. distribute-rgt-neg-in 73.5%

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

   5. Simplified 73.5%

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

   6. Taylor expanded in b around inf 44.2%

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

      1. associate-*r* 45.4%

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

      2. remove-double-neg 45.4%

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

      3. mul-1-neg 45.4%

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

      4. associate-*r* 45.4%

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

      5. neg-mul-1 45.4%

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

      6. *-commutative 45.4%

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

      7. distribute-lft-neg-in 45.4%

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

      8. *-commutative 45.4%

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

      9. distribute-rgt-neg-in 45.4%

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

      10. *-commutative 45.4%

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

      11. neg-mul-1 45.4%

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

      12. associate-*r* 45.4%

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

      13. mul-1-neg 45.4%

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

      14. remove-double-neg 45.4%

          \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 45.4%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if 3.8000000000000001e-249 < j < 1.05e9

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 42.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 42.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 42.1%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   6. Taylor expanded in x around inf 39.3%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   8. Simplified 39.3%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if 1.5e156 < j

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 75.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in c around inf 53.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.26 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;j \leq 3.8 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 1050000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.5 \cdot 10^{+156}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;j \leq -1.25 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2500000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+155}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* i (- j)))))
   (if (<= j -1.25e-17)
     t_1
     (if (<= j 3.5e-245)
       (* t (* b i))
       (if (<= j 2500000000.0)
         (* y (* x z))
         (if (<= j 5e+155) t_1 (* 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 t_1 = y * (i * -j);
	double tmp;
	if (j <= -1.25e-17) {
		tmp = t_1;
	} else if (j <= 3.5e-245) {
		tmp = t * (b * i);
	} else if (j <= 2500000000.0) {
		tmp = y * (x * z);
	} else if (j <= 5e+155) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (i * -j)
    if (j <= (-1.25d-17)) then
        tmp = t_1
    else if (j <= 3.5d-245) then
        tmp = t * (b * i)
    else if (j <= 2500000000.0d0) then
        tmp = y * (x * z)
    else if (j <= 5d+155) then
        tmp = t_1
    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 t_1 = y * (i * -j);
	double tmp;
	if (j <= -1.25e-17) {
		tmp = t_1;
	} else if (j <= 3.5e-245) {
		tmp = t * (b * i);
	} else if (j <= 2500000000.0) {
		tmp = y * (x * z);
	} else if (j <= 5e+155) {
		tmp = t_1;
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (i * -j)
	tmp = 0
	if j <= -1.25e-17:
		tmp = t_1
	elif j <= 3.5e-245:
		tmp = t * (b * i)
	elif j <= 2500000000.0:
		tmp = y * (x * z)
	elif j <= 5e+155:
		tmp = t_1
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (j <= -1.25e-17)
		tmp = t_1;
	elseif (j <= 3.5e-245)
		tmp = Float64(t * Float64(b * i));
	elseif (j <= 2500000000.0)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 5e+155)
		tmp = t_1;
	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)
	t_1 = y * (i * -j);
	tmp = 0.0;
	if (j <= -1.25e-17)
		tmp = t_1;
	elseif (j <= 3.5e-245)
		tmp = t * (b * i);
	elseif (j <= 2500000000.0)
		tmp = y * (x * z);
	elseif (j <= 5e+155)
		tmp = t_1;
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.25e-17], t$95$1, If[LessEqual[j, 3.5e-245], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2500000000.0], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 5e+155], t$95$1, N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.25e-17 or 2.5e9 < j < 4.9999999999999999e155

   1. Initial program 77.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 46.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 46.3%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 46.3%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 46.3%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   6. Taylor expanded in x around 0 37.8%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 37.8%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-lft-neg-in 37.8%

         \[\leadsto y \cdot \color{blue}{\left(\left(-i\right) \cdot j\right)} \]

      3. *-commutative 37.8%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   8. Simplified 37.8%

      \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   if -1.25e-17 < j < 3.50000000000000016e-245

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 73.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - -1 \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot t\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right) \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(-1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. mul-1-neg 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(-b \cdot i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \left(-\color{blue}{i \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. distribute-rgt-neg-in 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 73.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in b around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 45.4%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. remove-double-neg 45.4%

         \[\leadsto \color{blue}{\left(-\left(-b \cdot i\right)\right)} \cdot t \]

      3. mul-1-neg 45.4%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot i\right)}\right) \cdot t \]

      4. associate-*r* 45.4%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \cdot t \]

      5. neg-mul-1 45.4%

         \[\leadsto \left(-\color{blue}{\left(-b\right)} \cdot i\right) \cdot t \]

      6. *-commutative 45.4%

         \[\leadsto \left(-\color{blue}{i \cdot \left(-b\right)}\right) \cdot t \]

      7. distribute-lft-neg-in 45.4%

         \[\leadsto \color{blue}{-\left(i \cdot \left(-b\right)\right) \cdot t} \]

      8. *-commutative 45.4%

         \[\leadsto -\color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)} \]

      9. distribute-rgt-neg-in 45.4%

         \[\leadsto \color{blue}{t \cdot \left(-i \cdot \left(-b\right)\right)} \]

      10. *-commutative 45.4%

          \[\leadsto t \cdot \left(-\color{blue}{\left(-b\right) \cdot i}\right) \]

      11. neg-mul-1 45.4%

          \[\leadsto t \cdot \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot i\right) \]

      12. associate-*r* 45.4%

          \[\leadsto t \cdot \left(-\color{blue}{-1 \cdot \left(b \cdot i\right)}\right) \]

      13. mul-1-neg 45.4%

          \[\leadsto t \cdot \left(-\color{blue}{\left(-b \cdot i\right)}\right) \]

      14. remove-double-neg 45.4%

          \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 45.4%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if 3.50000000000000016e-245 < j < 2.5e9

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 42.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 42.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 42.1%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   6. Taylor expanded in x around inf 39.3%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   8. Simplified 39.3%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if 4.9999999999999999e155 < j

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 75.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in c around inf 53.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.25 \cdot 10^{-17}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 3.5 \cdot 10^{-245}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2500000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 5 \cdot 10^{+155}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2300000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.62 \cdot 10^{+156}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -8.5e-18)
   (* y (* i (- j)))
   (if (<= j 6e-249)
     (* t (* b i))
     (if (<= j 2300000000.0)
       (* y (* x z))
       (if (<= j 1.62e+156) (* (- i) (* y j)) (* 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 (j <= -8.5e-18) {
		tmp = y * (i * -j);
	} else if (j <= 6e-249) {
		tmp = t * (b * i);
	} else if (j <= 2300000000.0) {
		tmp = y * (x * z);
	} else if (j <= 1.62e+156) {
		tmp = -i * (y * j);
	} 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 (j <= (-8.5d-18)) then
        tmp = y * (i * -j)
    else if (j <= 6d-249) then
        tmp = t * (b * i)
    else if (j <= 2300000000.0d0) then
        tmp = y * (x * z)
    else if (j <= 1.62d+156) then
        tmp = -i * (y * j)
    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 (j <= -8.5e-18) {
		tmp = y * (i * -j);
	} else if (j <= 6e-249) {
		tmp = t * (b * i);
	} else if (j <= 2300000000.0) {
		tmp = y * (x * z);
	} else if (j <= 1.62e+156) {
		tmp = -i * (y * j);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -8.5e-18:
		tmp = y * (i * -j)
	elif j <= 6e-249:
		tmp = t * (b * i)
	elif j <= 2300000000.0:
		tmp = y * (x * z)
	elif j <= 1.62e+156:
		tmp = -i * (y * j)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -8.5e-18)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (j <= 6e-249)
		tmp = Float64(t * Float64(b * i));
	elseif (j <= 2300000000.0)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 1.62e+156)
		tmp = Float64(Float64(-i) * Float64(y * j));
	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 (j <= -8.5e-18)
		tmp = y * (i * -j);
	elseif (j <= 6e-249)
		tmp = t * (b * i);
	elseif (j <= 2300000000.0)
		tmp = y * (x * z);
	elseif (j <= 1.62e+156)
		tmp = -i * (y * j);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -8.5e-18], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e-249], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2300000000.0], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.62e+156], N[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -8.4999999999999995e-18

   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 50.0%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 50.0%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 50.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 50.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   6. Taylor expanded in x around 0 38.3%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 38.3%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-lft-neg-in 38.3%

         \[\leadsto y \cdot \color{blue}{\left(\left(-i\right) \cdot j\right)} \]

      3. *-commutative 38.3%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   8. Simplified 38.3%

      \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   if -8.4999999999999995e-18 < j < 6.00000000000000008e-249

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 73.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - -1 \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot t\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right) \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(-1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. mul-1-neg 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(-b \cdot i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \left(-\color{blue}{i \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. distribute-rgt-neg-in 73.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 73.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in b around inf 44.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 45.4%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. remove-double-neg 45.4%

         \[\leadsto \color{blue}{\left(-\left(-b \cdot i\right)\right)} \cdot t \]

      3. mul-1-neg 45.4%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot i\right)}\right) \cdot t \]

      4. associate-*r* 45.4%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \cdot t \]

      5. neg-mul-1 45.4%

         \[\leadsto \left(-\color{blue}{\left(-b\right)} \cdot i\right) \cdot t \]

      6. *-commutative 45.4%

         \[\leadsto \left(-\color{blue}{i \cdot \left(-b\right)}\right) \cdot t \]

      7. distribute-lft-neg-in 45.4%

         \[\leadsto \color{blue}{-\left(i \cdot \left(-b\right)\right) \cdot t} \]

      8. *-commutative 45.4%

         \[\leadsto -\color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)} \]

      9. distribute-rgt-neg-in 45.4%

         \[\leadsto \color{blue}{t \cdot \left(-i \cdot \left(-b\right)\right)} \]

      10. *-commutative 45.4%

          \[\leadsto t \cdot \left(-\color{blue}{\left(-b\right) \cdot i}\right) \]

      11. neg-mul-1 45.4%

          \[\leadsto t \cdot \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot i\right) \]

      12. associate-*r* 45.4%

          \[\leadsto t \cdot \left(-\color{blue}{-1 \cdot \left(b \cdot i\right)}\right) \]

      13. mul-1-neg 45.4%

          \[\leadsto t \cdot \left(-\color{blue}{\left(-b \cdot i\right)}\right) \]

      14. remove-double-neg 45.4%

          \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 45.4%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if 6.00000000000000008e-249 < j < 2.3e9

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 42.1%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 42.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 42.1%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 42.1%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 42.1%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   6. Taylor expanded in x around inf 39.3%

      \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.3%

         \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   8. Simplified 39.3%

      \[\leadsto y \cdot \color{blue}{\left(z \cdot x\right)} \]

   if 2.3e9 < j < 1.62000000000000006e156

   1. Initial program 75.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.5%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 75.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 39.2%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 39.2%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 39.2%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. distribute-rgt-neg-in 39.2%

         \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

   7. Simplified 39.2%

      \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

   if 1.62000000000000006e156 < j

   1. Initial program 75.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.8%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 75.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in c around inf 53.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -8.5 \cdot 10^{-18}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{-249}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;j \leq 2300000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 1.62 \cdot 10^{+156}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 50.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= j -1.7e-17)
     t_1
     (if (<= j 6.2e-210)
       (* b (- (* t i) (* z c)))
       (if (<= j 7.5e+34) (* a (- (* c j) (* x t))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.7e-17) {
		tmp = t_1;
	} else if (j <= 6.2e-210) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 7.5e+34) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (j <= (-1.7d-17)) then
        tmp = t_1
    else if (j <= 6.2d-210) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 7.5d+34) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.7e-17) {
		tmp = t_1;
	} else if (j <= 6.2e-210) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 7.5e+34) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.7e-17:
		tmp = t_1
	elif j <= 6.2e-210:
		tmp = b * ((t * i) - (z * c))
	elif j <= 7.5e+34:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.7e-17)
		tmp = t_1;
	elseif (j <= 6.2e-210)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 7.5e+34)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.7e-17)
		tmp = t_1;
	elseif (j <= 6.2e-210)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 7.5e+34)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.7e-17], t$95$1, If[LessEqual[j, 6.2e-210], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e+34], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if j < -1.6999999999999999e-17 or 7.49999999999999976e34 < j

   1. Initial program 78.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 62.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   4. Step-by-step derivation

      1. *-commutative 62.5%

         \[\leadsto j \cdot \left(a \cdot c - \color{blue}{y \cdot i}\right) \]

   5. Simplified 62.5%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   if -1.6999999999999999e-17 < j < 6.19999999999999973e-210

   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 b around inf 60.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 60.4%

         \[\leadsto b \cdot \left(\color{blue}{t \cdot i} - c \cdot z\right) \]

      2. *-commutative 60.4%

         \[\leadsto b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 60.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]

   if 6.19999999999999973e-210 < j < 7.49999999999999976e34

   1. Initial program 72.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 43.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 43.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 43.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 43.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 43.6%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 43.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.7 \cdot 10^{-17}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 6.2 \cdot 10^{-210}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{+34}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 41.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+81}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+216}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.4e+105)
   (* j (* i (- y)))
   (if (<= i 5.2e+81)
     (* a (- (* c j) (* x t)))
     (if (<= i 5.2e+216) (* b (* t i)) (* (- i) (* 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 <= -1.4e+105) {
		tmp = j * (i * -y);
	} else if (i <= 5.2e+81) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 5.2e+216) {
		tmp = b * (t * i);
	} else {
		tmp = -i * (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 <= (-1.4d+105)) then
        tmp = j * (i * -y)
    else if (i <= 5.2d+81) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 5.2d+216) then
        tmp = b * (t * i)
    else
        tmp = -i * (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 <= -1.4e+105) {
		tmp = j * (i * -y);
	} else if (i <= 5.2e+81) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 5.2e+216) {
		tmp = b * (t * i);
	} else {
		tmp = -i * (y * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.4e+105:
		tmp = j * (i * -y)
	elif i <= 5.2e+81:
		tmp = a * ((c * j) - (x * t))
	elif i <= 5.2e+216:
		tmp = b * (t * i)
	else:
		tmp = -i * (y * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.4e+105)
		tmp = Float64(j * Float64(i * Float64(-y)));
	elseif (i <= 5.2e+81)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 5.2e+216)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(Float64(-i) * 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 <= -1.4e+105)
		tmp = j * (i * -y);
	elseif (i <= 5.2e+81)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 5.2e+216)
		tmp = b * (t * i);
	else
		tmp = -i * (y * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.4e+105], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e+81], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e+216], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[((-i) * N[(y * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.4000000000000001e105

   1. Initial program 68.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 61.2%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 61.2%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 61.2%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

   5. Simplified 61.2%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z - i \cdot j\right)} \]

   6. Taylor expanded in x around 0 50.7%

      \[\leadsto y \cdot \color{blue}{\left(-1 \cdot \left(i \cdot j\right)\right)} \]
   7. Step-by-step derivation

      1. neg-mul-1 50.7%

         \[\leadsto y \cdot \color{blue}{\left(-i \cdot j\right)} \]

      2. distribute-lft-neg-in 50.7%

         \[\leadsto y \cdot \color{blue}{\left(\left(-i\right) \cdot j\right)} \]

      3. *-commutative 50.7%

         \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   8. Simplified 50.7%

      \[\leadsto y \cdot \color{blue}{\left(j \cdot \left(-i\right)\right)} \]

   9. Taylor expanded in y around 0 46.6%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 46.6%

          \[\leadsto \color{blue}{\left(-1 \cdot i\right) \cdot \left(j \cdot y\right)} \]

       2. neg-mul-1 46.6%

          \[\leadsto \color{blue}{\left(-i\right)} \cdot \left(j \cdot y\right) \]

       3. *-commutative 46.6%

          \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

       4. associate-*l* 53.2%

          \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   11. Simplified 53.2%

       \[\leadsto \color{blue}{j \cdot \left(y \cdot \left(-i\right)\right)} \]

   if -1.4000000000000001e105 < i < 5.19999999999999984e81

   1. Initial program 80.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 46.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 46.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 46.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 46.1%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 46.1%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   if 5.19999999999999984e81 < i < 5.1999999999999997e216

   1. Initial program 79.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 84.8%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - -1 \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot t\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right) \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(-1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. mul-1-neg 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(-b \cdot i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \left(-\color{blue}{i \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. distribute-rgt-neg-in 80.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 80.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in b around inf 63.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if 5.1999999999999997e216 < 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. Step-by-step derivation

      1. add-cube-cbrt 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 64.2%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 64.2%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in i around inf 63.8%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 63.8%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. *-commutative 63.8%

         \[\leadsto -\color{blue}{\left(j \cdot y\right) \cdot i} \]

      3. distribute-rgt-neg-in 63.8%

         \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]

   7. Simplified 63.8%

      \[\leadsto \color{blue}{\left(j \cdot y\right) \cdot \left(-i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.4 \cdot 10^{+105}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+81}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{+216}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-i\right) \cdot \left(y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 28.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(x \cdot y\right)\\ \mathbf{if}\;x \leq -2.6 \cdot 10^{+151}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* z (* x y))))
   (if (<= x -2.6e+151)
     t_1
     (if (<= x -3.9e+33)
       (* a (* c j))
       (if (<= x 1.1e-106) (* b (* t i)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -2.6e+151) {
		tmp = t_1;
	} else if (x <= -3.9e+33) {
		tmp = a * (c * j);
	} else if (x <= 1.1e-106) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (x * y)
    if (x <= (-2.6d+151)) then
        tmp = t_1
    else if (x <= (-3.9d+33)) then
        tmp = a * (c * j)
    else if (x <= 1.1d-106) then
        tmp = b * (t * i)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = z * (x * y);
	double tmp;
	if (x <= -2.6e+151) {
		tmp = t_1;
	} else if (x <= -3.9e+33) {
		tmp = a * (c * j);
	} else if (x <= 1.1e-106) {
		tmp = b * (t * i);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = z * (x * y)
	tmp = 0
	if x <= -2.6e+151:
		tmp = t_1
	elif x <= -3.9e+33:
		tmp = a * (c * j)
	elif x <= 1.1e-106:
		tmp = b * (t * i)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(z * Float64(x * y))
	tmp = 0.0
	if (x <= -2.6e+151)
		tmp = t_1;
	elseif (x <= -3.9e+33)
		tmp = Float64(a * Float64(c * j));
	elseif (x <= 1.1e-106)
		tmp = Float64(b * Float64(t * i));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = z * (x * y);
	tmp = 0.0;
	if (x <= -2.6e+151)
		tmp = t_1;
	elseif (x <= -3.9e+33)
		tmp = a * (c * j);
	elseif (x <= 1.1e-106)
		tmp = b * (t * i);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.6e+151], t$95$1, If[LessEqual[x, -3.9e+33], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e-106], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.60000000000000013e151 or 1.09999999999999997e-106 < x

   1. Initial program 73.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 74.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - -1 \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot t\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right) \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(-1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. mul-1-neg 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(-b \cdot i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \left(-\color{blue}{i \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. distribute-rgt-neg-in 73.3%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 73.3%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in t around -inf 73.3%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right)} \]

   7. Taylor expanded in z around inf 36.6%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 40.5%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   9. Simplified 40.5%

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

   if -2.60000000000000013e151 < x < -3.9000000000000002e33

   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. Step-by-step derivation

      1. add-cube-cbrt 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 77.1%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 77.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in c around inf 34.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if -3.9000000000000002e33 < x < 1.09999999999999997e-106

   1. Initial program 81.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 72.7%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - -1 \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot t\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right) \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(-1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. mul-1-neg 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(-b \cdot i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \left(-\color{blue}{i \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. distribute-rgt-neg-in 70.0%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 70.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in b around inf 34.6%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+151}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+33}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 51.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-103} \lor \neg \left(a \leq 1.6 \cdot 10^{-36}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -5.2e-103) (not (<= a 1.6e-36)))
   (* a (- (* c j) (* x t)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -5.2e-103) || !(a <= 1.6e-36)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-5.2d-103)) .or. (.not. (a <= 1.6d-36))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -5.2e-103) || !(a <= 1.6e-36)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -5.2e-103) or not (a <= 1.6e-36):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -5.2e-103) || !(a <= 1.6e-36))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -5.2e-103) || ~((a <= 1.6e-36)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -5.2e-103], N[Not[LessEqual[a, 1.6e-36]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -5.19999999999999993e-103 or 1.60000000000000011e-36 < a

   1. Initial program 70.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 55.2%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 55.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 55.2%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 55.2%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 55.2%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 55.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   if -5.19999999999999993e-103 < a < 1.60000000000000011e-36

   1. Initial program 86.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in b around inf 50.3%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. *-commutative 50.3%

         \[\leadsto b \cdot \left(\color{blue}{t \cdot i} - c \cdot z\right) \]

      2. *-commutative 50.3%

         \[\leadsto b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 50.3%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{-103} \lor \neg \left(a \leq 1.6 \cdot 10^{-36}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 52.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+25} \lor \neg \left(a \leq 9.2 \cdot 10^{+70}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.6e+25) (not (<= a 9.2e+70)))
   (* a (- (* c j) (* x t)))
   (* 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 ((a <= -1.6e+25) || !(a <= 9.2e+70)) {
		tmp = a * ((c * j) - (x * t));
	} 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 ((a <= (-1.6d+25)) .or. (.not. (a <= 9.2d+70))) then
        tmp = a * ((c * j) - (x * t))
    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 ((a <= -1.6e+25) || !(a <= 9.2e+70)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.6e+25) or not (a <= 9.2e+70):
		tmp = a * ((c * j) - (x * t))
	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 ((a <= -1.6e+25) || !(a <= 9.2e+70))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	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 ((a <= -1.6e+25) || ~((a <= 9.2e+70)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.6e+25], N[Not[LessEqual[a, 9.2e+70]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.6e25 or 9.19999999999999975e70 < a

   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 a around inf 61.6%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 61.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 61.6%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 61.6%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 61.6%

         \[\leadsto a \cdot \left(c \cdot j - \color{blue}{x \cdot t}\right) \]

   5. Simplified 61.6%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j - x \cdot t\right)} \]

   if -1.6e25 < a < 9.19999999999999975e70

   1. Initial program 87.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 78.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - -1 \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot t\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right) \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(-1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. mul-1-neg 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(-b \cdot i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \left(-\color{blue}{i \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. distribute-rgt-neg-in 76.6%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 76.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in t around -inf 78.0%

      \[\leadsto \color{blue}{-1 \cdot \left(t \cdot \left(a \cdot x - b \cdot i\right)\right) + \left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right)} \]

   7. Taylor expanded in i around inf 51.1%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   8. Step-by-step derivation

      1. +-commutative 51.1%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 51.1%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 51.1%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   9. Simplified 51.1%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.6 \cdot 10^{+25} \lor \neg \left(a \leq 9.2 \cdot 10^{+70}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 28.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-142} \lor \neg \left(b \leq 5.4 \cdot 10^{+114}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.4e-142) (not (<= b 5.4e+114))) (* 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 ((b <= -2.4e-142) || !(b <= 5.4e+114)) {
		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 ((b <= (-2.4d-142)) .or. (.not. (b <= 5.4d+114))) 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 ((b <= -2.4e-142) || !(b <= 5.4e+114)) {
		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 (b <= -2.4e-142) or not (b <= 5.4e+114):
		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 ((b <= -2.4e-142) || !(b <= 5.4e+114))
		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 ((b <= -2.4e-142) || ~((b <= 5.4e+114)))
		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[b, -2.4e-142], N[Not[LessEqual[b, 5.4e+114]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.39999999999999988e-142 or 5.4000000000000001e114 < b

   1. Initial program 80.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 74.6%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 70.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - -1 \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot t\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 70.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right) \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 70.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(-1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. mul-1-neg 70.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(-b \cdot i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 70.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \left(-\color{blue}{i \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. distribute-rgt-neg-in 70.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 70.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in b around inf 36.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -2.39999999999999988e-142 < b < 5.4000000000000001e114

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 72.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 72.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 72.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 72.9%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in c around inf 29.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-142} \lor \neg \left(b \leq 5.4 \cdot 10^{+114}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 29: 29.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{-142}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -3.2e-142)
   (* b (* t i))
   (if (<= b 7e+114) (* a (* c j)) (* t (* b i)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.2e-142) {
		tmp = b * (t * i);
	} else if (b <= 7e+114) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-3.2d-142)) then
        tmp = b * (t * i)
    else if (b <= 7d+114) then
        tmp = a * (c * j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -3.2e-142) {
		tmp = b * (t * i);
	} else if (b <= 7e+114) {
		tmp = a * (c * j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -3.2e-142:
		tmp = b * (t * i)
	elif b <= 7e+114:
		tmp = a * (c * j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -3.2e-142)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= 7e+114)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -3.2e-142)
		tmp = b * (t * i);
	elseif (b <= 7e+114)
		tmp = a * (c * j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -3.2e-142], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7e+114], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1999999999999998e-142

   1. Initial program 79.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 74.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - -1 \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot t\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right) \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(-1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. mul-1-neg 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(-b \cdot i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \left(-\color{blue}{i \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. distribute-rgt-neg-in 70.7%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 70.7%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in b around inf 35.9%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -3.1999999999999998e-142 < b < 7.0000000000000001e114

   1. Initial program 73.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. add-cube-cbrt 72.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. pow3 72.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 72.9%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   4. Applied egg-rr 72.9%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Taylor expanded in c around inf 29.7%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

   if 7.0000000000000001e114 < b

   1. Initial program 84.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in c around 0 75.5%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{-1 \cdot \left(b \cdot \left(i \cdot t\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate-*r* 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - -1 \cdot \color{blue}{\left(\left(b \cdot i\right) \cdot t\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r* 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(-1 \cdot \left(b \cdot i\right)\right) \cdot t}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(-1 \cdot \left(b \cdot i\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. mul-1-neg 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(-b \cdot i\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \left(-\color{blue}{i \cdot b}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. distribute-rgt-neg-in 69.4%

         \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - t \cdot \color{blue}{\left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 69.4%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in b around inf 39.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 48.1%

         \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

      2. remove-double-neg 48.1%

         \[\leadsto \color{blue}{\left(-\left(-b \cdot i\right)\right)} \cdot t \]

      3. mul-1-neg 48.1%

         \[\leadsto \left(-\color{blue}{-1 \cdot \left(b \cdot i\right)}\right) \cdot t \]

      4. associate-*r* 48.1%

         \[\leadsto \left(-\color{blue}{\left(-1 \cdot b\right) \cdot i}\right) \cdot t \]

      5. neg-mul-1 48.1%

         \[\leadsto \left(-\color{blue}{\left(-b\right)} \cdot i\right) \cdot t \]

      6. *-commutative 48.1%

         \[\leadsto \left(-\color{blue}{i \cdot \left(-b\right)}\right) \cdot t \]

      7. distribute-lft-neg-in 48.1%

         \[\leadsto \color{blue}{-\left(i \cdot \left(-b\right)\right) \cdot t} \]

      8. *-commutative 48.1%

         \[\leadsto -\color{blue}{t \cdot \left(i \cdot \left(-b\right)\right)} \]

      9. distribute-rgt-neg-in 48.1%

         \[\leadsto \color{blue}{t \cdot \left(-i \cdot \left(-b\right)\right)} \]

      10. *-commutative 48.1%

          \[\leadsto t \cdot \left(-\color{blue}{\left(-b\right) \cdot i}\right) \]

      11. neg-mul-1 48.1%

          \[\leadsto t \cdot \left(-\color{blue}{\left(-1 \cdot b\right)} \cdot i\right) \]

      12. associate-*r* 48.1%

          \[\leadsto t \cdot \left(-\color{blue}{-1 \cdot \left(b \cdot i\right)}\right) \]

      13. mul-1-neg 48.1%

          \[\leadsto t \cdot \left(-\color{blue}{\left(-b \cdot i\right)}\right) \]

      14. remove-double-neg 48.1%

          \[\leadsto t \cdot \color{blue}{\left(b \cdot i\right)} \]

   8. Simplified 48.1%

      \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 34.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.2 \cdot 10^{-142}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{+114}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 30: 22.7% 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 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. Step-by-step derivation

   1. add-cube-cbrt 77.0%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   2. pow3 77.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(c \cdot z - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   3. *-commutative 77.1%

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - {\left(\sqrt[3]{b \cdot \left(\color{blue}{z \cdot c} - t \cdot i\right)}\right)}^{3}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

4. Applied egg-rr 77.1%

   \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{{\left(\sqrt[3]{b \cdot \left(z \cdot c - t \cdot i\right)}\right)}^{3}}\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

5. Taylor expanded in c around inf 20.4%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

6. Final simplification 20.4%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
7. Add Preprocessing

Developer target: 60.2% 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 2024031 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (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)))))