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

Percentage Accurate: 72.9% → 81.4%

Time: 22.5s

Alternatives: 23

Speedup: 0.5×

• 58.5% 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: 72.9% 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: 81.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = ((x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = y * ((x * z) - (i * j))
	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 = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in y around inf 51.8%

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

      1. +-commutative 51.8%

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

      2. mul-1-neg 51.8%

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

      3. unsub-neg 51.8%

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

      4. *-commutative 51.8%

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

      5. *-commutative 51.8%

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

   5. Simplified 51.8%

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

4. Final simplification 83.9%

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

Alternative 2: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := c \cdot \left(a \cdot j - z \cdot b\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_4 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;i \leq -4.8 \cdot 10^{+195}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-18}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -7.7 \cdot 10^{-118}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-214}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-301}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-295}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* c (- (* a j) (* z b))))
        (t_2 (* a (- (* c j) (* x t))))
        (t_3 (* i (- (* t b) (* y j))))
        (t_4 (* x (- (* y z) (* t a)))))
   (if (<= i -4.8e+195)
     t_3
     (if (<= i -5.2e+160)
       t_2
       (if (<= i -4.6e-18)
         t_3
         (if (<= i -7.7e-118)
           t_1
           (if (<= i -5.2e-214)
             t_4
             (if (<= i -1.35e-301)
               t_1
               (if (<= i 3.5e-295)
                 t_4
                 (if (<= i 3.2e-122)
                   t_2
                   (if (<= i 2.6e+110) (* z (- (* x y) (* b c))) t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (i <= -4.8e+195) {
		tmp = t_3;
	} else if (i <= -5.2e+160) {
		tmp = t_2;
	} else if (i <= -4.6e-18) {
		tmp = t_3;
	} else if (i <= -7.7e-118) {
		tmp = t_1;
	} else if (i <= -5.2e-214) {
		tmp = t_4;
	} else if (i <= -1.35e-301) {
		tmp = t_1;
	} else if (i <= 3.5e-295) {
		tmp = t_4;
	} else if (i <= 3.2e-122) {
		tmp = t_2;
	} else if (i <= 2.6e+110) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = c * ((a * j) - (z * b))
    t_2 = a * ((c * j) - (x * t))
    t_3 = i * ((t * b) - (y * j))
    t_4 = x * ((y * z) - (t * a))
    if (i <= (-4.8d+195)) then
        tmp = t_3
    else if (i <= (-5.2d+160)) then
        tmp = t_2
    else if (i <= (-4.6d-18)) then
        tmp = t_3
    else if (i <= (-7.7d-118)) then
        tmp = t_1
    else if (i <= (-5.2d-214)) then
        tmp = t_4
    else if (i <= (-1.35d-301)) then
        tmp = t_1
    else if (i <= 3.5d-295) then
        tmp = t_4
    else if (i <= 3.2d-122) then
        tmp = t_2
    else if (i <= 2.6d+110) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = c * ((a * j) - (z * b));
	double t_2 = a * ((c * j) - (x * t));
	double t_3 = i * ((t * b) - (y * j));
	double t_4 = x * ((y * z) - (t * a));
	double tmp;
	if (i <= -4.8e+195) {
		tmp = t_3;
	} else if (i <= -5.2e+160) {
		tmp = t_2;
	} else if (i <= -4.6e-18) {
		tmp = t_3;
	} else if (i <= -7.7e-118) {
		tmp = t_1;
	} else if (i <= -5.2e-214) {
		tmp = t_4;
	} else if (i <= -1.35e-301) {
		tmp = t_1;
	} else if (i <= 3.5e-295) {
		tmp = t_4;
	} else if (i <= 3.2e-122) {
		tmp = t_2;
	} else if (i <= 2.6e+110) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = c * ((a * j) - (z * b))
	t_2 = a * ((c * j) - (x * t))
	t_3 = i * ((t * b) - (y * j))
	t_4 = x * ((y * z) - (t * a))
	tmp = 0
	if i <= -4.8e+195:
		tmp = t_3
	elif i <= -5.2e+160:
		tmp = t_2
	elif i <= -4.6e-18:
		tmp = t_3
	elif i <= -7.7e-118:
		tmp = t_1
	elif i <= -5.2e-214:
		tmp = t_4
	elif i <= -1.35e-301:
		tmp = t_1
	elif i <= 3.5e-295:
		tmp = t_4
	elif i <= 3.2e-122:
		tmp = t_2
	elif i <= 2.6e+110:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(c * Float64(Float64(a * j) - Float64(z * b)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_4 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	tmp = 0.0
	if (i <= -4.8e+195)
		tmp = t_3;
	elseif (i <= -5.2e+160)
		tmp = t_2;
	elseif (i <= -4.6e-18)
		tmp = t_3;
	elseif (i <= -7.7e-118)
		tmp = t_1;
	elseif (i <= -5.2e-214)
		tmp = t_4;
	elseif (i <= -1.35e-301)
		tmp = t_1;
	elseif (i <= 3.5e-295)
		tmp = t_4;
	elseif (i <= 3.2e-122)
		tmp = t_2;
	elseif (i <= 2.6e+110)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = c * ((a * j) - (z * b));
	t_2 = a * ((c * j) - (x * t));
	t_3 = i * ((t * b) - (y * j));
	t_4 = x * ((y * z) - (t * a));
	tmp = 0.0;
	if (i <= -4.8e+195)
		tmp = t_3;
	elseif (i <= -5.2e+160)
		tmp = t_2;
	elseif (i <= -4.6e-18)
		tmp = t_3;
	elseif (i <= -7.7e-118)
		tmp = t_1;
	elseif (i <= -5.2e-214)
		tmp = t_4;
	elseif (i <= -1.35e-301)
		tmp = t_1;
	elseif (i <= 3.5e-295)
		tmp = t_4;
	elseif (i <= 3.2e-122)
		tmp = t_2;
	elseif (i <= 2.6e+110)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.8e+195], t$95$3, If[LessEqual[i, -5.2e+160], t$95$2, If[LessEqual[i, -4.6e-18], t$95$3, If[LessEqual[i, -7.7e-118], t$95$1, If[LessEqual[i, -5.2e-214], t$95$4, If[LessEqual[i, -1.35e-301], t$95$1, If[LessEqual[i, 3.5e-295], t$95$4, If[LessEqual[i, 3.2e-122], t$95$2, If[LessEqual[i, 2.6e+110], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -4.8000000000000005e195 or -5.2000000000000001e160 < i < -4.6000000000000002e-18 or 2.6e110 < i

   1. Initial program 65.9%

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

   3. Taylor expanded in x around inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. associate-*r/ 64.3%

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

      3. *-commutative 64.3%

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

      4. *-commutative 64.3%

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

      5. *-commutative 64.3%

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

      6. associate-*r* 64.3%

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

      7. neg-mul-1 64.3%

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

      8. associate-/l* 64.3%

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

      9. neg-sub0 64.3%

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

      10. *-commutative 64.3%

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

      11. *-commutative 64.3%

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

      12. associate--r- 64.3%

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

      13. neg-sub0 64.3%

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

      14. +-commutative 64.3%

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

      15. sub-neg 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in i around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

   8. Simplified 70.4%

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

   if -4.8000000000000005e195 < i < -5.2000000000000001e160 or 3.49999999999999988e-295 < i < 3.2000000000000002e-122

   1. Initial program 65.6%

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

   3. Taylor expanded in a around inf 73.2%

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

      1. +-commutative 73.2%

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

      2. mul-1-neg 73.2%

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

      3. unsub-neg 73.2%

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

      4. *-commutative 73.2%

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

   5. Simplified 73.2%

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

   if -4.6000000000000002e-18 < i < -7.6999999999999996e-118 or -5.2e-214 < i < -1.35e-301

   1. Initial program 78.5%

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

   3. Taylor expanded in c around inf 60.7%

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

      1. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   if -7.6999999999999996e-118 < i < -5.2e-214 or -1.35e-301 < i < 3.49999999999999988e-295

   1. Initial program 83.4%

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

   3. Taylor expanded in x around inf 75.5%

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

   if 3.2000000000000002e-122 < i < 2.6e110

   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 z around inf 65.3%

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

      1. *-commutative 65.3%

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

      2. *-commutative 65.3%

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

   5. Simplified 65.3%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.8 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -4.6 \cdot 10^{-18}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -7.7 \cdot 10^{-118}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-214}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -1.35 \cdot 10^{-301}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 3.5 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 3.2 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -4.8 \cdot 10^{+195}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -3.9 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-18}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-118}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-269}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -4.8e+195)
     t_1
     (if (<= i -3.9e+160)
       (* a (- (* c j) (* x t)))
       (if (<= i -1.05e-18)
         t_1
         (if (<= i -2.4e-118)
           (* c (- (* a j) (* z b)))
           (if (<= i -5.5e-269)
             (* x (- (* y z) (* t a)))
             (if (<= i 3.1e-123)
               (* a (* j (- c (* t (/ x j)))))
               (if (<= i 2.6e+110) (* z (- (* x y) (* b c))) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.8e+195) {
		tmp = t_1;
	} else if (i <= -3.9e+160) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= -1.05e-18) {
		tmp = t_1;
	} else if (i <= -2.4e-118) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= -5.5e-269) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 3.1e-123) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (i <= 2.6e+110) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-4.8d+195)) then
        tmp = t_1
    else if (i <= (-3.9d+160)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= (-1.05d-18)) then
        tmp = t_1
    else if (i <= (-2.4d-118)) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= (-5.5d-269)) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= 3.1d-123) then
        tmp = a * (j * (c - (t * (x / j))))
    else if (i <= 2.6d+110) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -4.8e+195) {
		tmp = t_1;
	} else if (i <= -3.9e+160) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= -1.05e-18) {
		tmp = t_1;
	} else if (i <= -2.4e-118) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= -5.5e-269) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= 3.1e-123) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (i <= 2.6e+110) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -4.8e+195:
		tmp = t_1
	elif i <= -3.9e+160:
		tmp = a * ((c * j) - (x * t))
	elif i <= -1.05e-18:
		tmp = t_1
	elif i <= -2.4e-118:
		tmp = c * ((a * j) - (z * b))
	elif i <= -5.5e-269:
		tmp = x * ((y * z) - (t * a))
	elif i <= 3.1e-123:
		tmp = a * (j * (c - (t * (x / j))))
	elif i <= 2.6e+110:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -4.8e+195)
		tmp = t_1;
	elseif (i <= -3.9e+160)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= -1.05e-18)
		tmp = t_1;
	elseif (i <= -2.4e-118)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= -5.5e-269)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= 3.1e-123)
		tmp = Float64(a * Float64(j * Float64(c - Float64(t * Float64(x / j)))));
	elseif (i <= 2.6e+110)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -4.8e+195)
		tmp = t_1;
	elseif (i <= -3.9e+160)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= -1.05e-18)
		tmp = t_1;
	elseif (i <= -2.4e-118)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= -5.5e-269)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= 3.1e-123)
		tmp = a * (j * (c - (t * (x / j))));
	elseif (i <= 2.6e+110)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.8e+195], t$95$1, If[LessEqual[i, -3.9e+160], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.05e-18], t$95$1, If[LessEqual[i, -2.4e-118], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.5e-269], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.1e-123], N[(a * N[(j * N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e+110], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -4.8000000000000005e195 or -3.90000000000000007e160 < i < -1.05e-18 or 2.6e110 < i

   1. Initial program 65.9%

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

   3. Taylor expanded in x around inf 64.3%

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

      1. associate--l+ 64.3%

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

      2. associate-*r/ 64.3%

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

      3. *-commutative 64.3%

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

      4. *-commutative 64.3%

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

      5. *-commutative 64.3%

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

      6. associate-*r* 64.3%

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

      7. neg-mul-1 64.3%

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

      8. associate-/l* 64.3%

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

      9. neg-sub0 64.3%

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

      10. *-commutative 64.3%

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

      11. *-commutative 64.3%

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

      12. associate--r- 64.3%

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

      13. neg-sub0 64.3%

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

      14. +-commutative 64.3%

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

      15. sub-neg 64.3%

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

   5. Simplified 64.3%

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

   6. Taylor expanded in i around inf 70.4%

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

      1. +-commutative 70.4%

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

      2. mul-1-neg 70.4%

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

      3. unsub-neg 70.4%

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

   8. Simplified 70.4%

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

   if -4.8000000000000005e195 < i < -3.90000000000000007e160

   1. Initial program 50.0%

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

   3. Taylor expanded in a around inf 88.4%

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

      1. +-commutative 88.4%

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

      2. mul-1-neg 88.4%

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

      3. unsub-neg 88.4%

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

      4. *-commutative 88.4%

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

   5. Simplified 88.4%

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

   if -1.05e-18 < i < -2.4000000000000001e-118

   1. Initial program 64.9%

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

   3. Taylor expanded in c around inf 62.2%

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

      1. *-commutative 62.2%

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

   5. Simplified 62.2%

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

   if -2.4000000000000001e-118 < i < -5.5000000000000001e-269

   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 x around inf 55.2%

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

   if -5.5000000000000001e-269 < i < 3.09999999999999998e-123

   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 a around inf 64.4%

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

      1. +-commutative 64.4%

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

      2. mul-1-neg 64.4%

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

      3. unsub-neg 64.4%

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

      4. *-commutative 64.4%

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

   5. Simplified 64.4%

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

   6. Taylor expanded in j around inf 64.4%

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

      1. mul-1-neg 64.4%

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

      2. unsub-neg 64.4%

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

      3. associate-/l* 67.5%

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

   8. Simplified 67.5%

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

   if 3.09999999999999998e-123 < i < 2.6e110

   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 z around inf 65.3%

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

      1. *-commutative 65.3%

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

      2. *-commutative 65.3%

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

   5. Simplified 65.3%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.8 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -3.9 \cdot 10^{+160}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -1.05 \cdot 10^{-18}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.4 \cdot 10^{-118}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq -5.5 \cdot 10^{-269}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq 3.1 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 30.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ t_2 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;i \leq -7.6 \cdot 10^{+168}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{+121}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq -2 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-299}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 3.65 \cdot 10^{-118}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 150000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))) (t_2 (* y (* i (- j)))))
   (if (<= i -7.6e+168)
     (* i (* t b))
     (if (<= i -9e+121)
       t_2
       (if (<= i -2.8e-35)
         (* b (* t i))
         (if (<= i -2e-217)
           t_1
           (if (<= i -1.4e-299)
             (* j (* a c))
             (if (<= i 3.65e-118)
               (* a (* x (- t)))
               (if (<= i 150000000.0) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = y * (i * -j);
	double tmp;
	if (i <= -7.6e+168) {
		tmp = i * (t * b);
	} else if (i <= -9e+121) {
		tmp = t_2;
	} else if (i <= -2.8e-35) {
		tmp = b * (t * i);
	} else if (i <= -2e-217) {
		tmp = t_1;
	} else if (i <= -1.4e-299) {
		tmp = j * (a * c);
	} else if (i <= 3.65e-118) {
		tmp = a * (x * -t);
	} else if (i <= 150000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * (x * z)
    t_2 = y * (i * -j)
    if (i <= (-7.6d+168)) then
        tmp = i * (t * b)
    else if (i <= (-9d+121)) then
        tmp = t_2
    else if (i <= (-2.8d-35)) then
        tmp = b * (t * i)
    else if (i <= (-2d-217)) then
        tmp = t_1
    else if (i <= (-1.4d-299)) then
        tmp = j * (a * c)
    else if (i <= 3.65d-118) then
        tmp = a * (x * -t)
    else if (i <= 150000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double t_2 = y * (i * -j);
	double tmp;
	if (i <= -7.6e+168) {
		tmp = i * (t * b);
	} else if (i <= -9e+121) {
		tmp = t_2;
	} else if (i <= -2.8e-35) {
		tmp = b * (t * i);
	} else if (i <= -2e-217) {
		tmp = t_1;
	} else if (i <= -1.4e-299) {
		tmp = j * (a * c);
	} else if (i <= 3.65e-118) {
		tmp = a * (x * -t);
	} else if (i <= 150000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	t_2 = y * (i * -j)
	tmp = 0
	if i <= -7.6e+168:
		tmp = i * (t * b)
	elif i <= -9e+121:
		tmp = t_2
	elif i <= -2.8e-35:
		tmp = b * (t * i)
	elif i <= -2e-217:
		tmp = t_1
	elif i <= -1.4e-299:
		tmp = j * (a * c)
	elif i <= 3.65e-118:
		tmp = a * (x * -t)
	elif i <= 150000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	t_2 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (i <= -7.6e+168)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -9e+121)
		tmp = t_2;
	elseif (i <= -2.8e-35)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= -2e-217)
		tmp = t_1;
	elseif (i <= -1.4e-299)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 3.65e-118)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 150000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	t_2 = y * (i * -j);
	tmp = 0.0;
	if (i <= -7.6e+168)
		tmp = i * (t * b);
	elseif (i <= -9e+121)
		tmp = t_2;
	elseif (i <= -2.8e-35)
		tmp = b * (t * i);
	elseif (i <= -2e-217)
		tmp = t_1;
	elseif (i <= -1.4e-299)
		tmp = j * (a * c);
	elseif (i <= 3.65e-118)
		tmp = a * (x * -t);
	elseif (i <= 150000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -7.6e+168], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -9e+121], t$95$2, If[LessEqual[i, -2.8e-35], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2e-217], t$95$1, If[LessEqual[i, -1.4e-299], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.65e-118], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 150000000.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -7.6000000000000005e168

   1. Initial program 50.2%

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

   3. Taylor expanded in x around inf 57.9%

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

      1. associate--l+ 57.9%

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

      2. associate-*r/ 57.9%

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

      3. *-commutative 57.9%

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

      4. *-commutative 57.9%

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

      5. *-commutative 57.9%

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

      6. associate-*r* 57.9%

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

      7. neg-mul-1 57.9%

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

      8. associate-/l* 57.9%

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

      9. neg-sub0 57.9%

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

      10. *-commutative 57.9%

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

      11. *-commutative 57.9%

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

      12. associate--r- 57.9%

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

      13. neg-sub0 57.9%

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

      14. +-commutative 57.9%

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

      15. sub-neg 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in i around inf 73.4%

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

      1. +-commutative 73.4%

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

      2. mul-1-neg 73.4%

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

      3. unsub-neg 73.4%

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

   8. Simplified 73.4%

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

   9. Taylor expanded in b around inf 54.6%

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

   if -7.6000000000000005e168 < i < -9.0000000000000007e121 or 1.5e8 < i

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf 60.1%

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

      1. +-commutative 60.1%

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

      2. mul-1-neg 60.1%

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

      3. unsub-neg 60.1%

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

      4. *-commutative 60.1%

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

      5. *-commutative 60.1%

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

   5. Simplified 60.1%

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

   6. Taylor expanded in z around 0 50.5%

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

      1. mul-1-neg 50.5%

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

      2. *-commutative 50.5%

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

      3. *-commutative 50.5%

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

      4. associate-*l* 51.9%

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

      5. distribute-rgt-neg-out 51.9%

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

      6. distribute-rgt-neg-in 51.9%

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

   8. Simplified 51.9%

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

   if -9.0000000000000007e121 < i < -2.8e-35

   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 x around inf 70.6%

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

      1. associate--l+ 70.6%

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

      2. associate-*r/ 70.6%

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

      3. *-commutative 70.6%

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

      4. *-commutative 70.6%

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

      5. *-commutative 70.6%

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

      6. associate-*r* 70.6%

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

      7. neg-mul-1 70.6%

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

      8. associate-/l* 70.5%

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

      9. neg-sub0 70.5%

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

      10. *-commutative 70.5%

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

      11. *-commutative 70.5%

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

      12. associate--r- 70.5%

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

      13. neg-sub0 70.5%

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

      14. +-commutative 70.5%

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

      15. sub-neg 70.5%

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

   5. Simplified 70.5%

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

   6. Taylor expanded in i around inf 54.6%

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

      1. +-commutative 54.6%

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

      2. mul-1-neg 54.6%

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

      3. unsub-neg 54.6%

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

   8. Simplified 54.6%

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

   9. Taylor expanded in b around inf 42.2%

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

   if -2.8e-35 < i < -2.00000000000000016e-217 or 3.65e-118 < i < 1.5e8

   1. Initial program 77.1%

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

   3. Taylor expanded in y around inf 50.6%

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

      1. +-commutative 50.6%

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

      2. mul-1-neg 50.6%

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

      3. unsub-neg 50.6%

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

      4. *-commutative 50.6%

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

      5. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in z around inf 37.4%

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

      1. *-commutative 37.4%

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

      2. associate-*r* 42.7%

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

      3. *-commutative 42.7%

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

   8. Simplified 42.7%

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

   if -2.00000000000000016e-217 < i < -1.4000000000000001e-299

   1. Initial program 91.5%

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

   3. Taylor expanded in j around inf 41.8%

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

   4. Taylor expanded in a around inf 37.5%

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

      1. *-commutative 37.5%

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

   6. Simplified 37.5%

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

   if -1.4000000000000001e-299 < i < 3.65e-118

   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 a around inf 63.4%

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

      1. +-commutative 63.4%

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

      2. mul-1-neg 63.4%

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

      3. unsub-neg 63.4%

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

      4. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in j around 0 47.2%

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

      1. neg-mul-1 47.2%

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

      2. distribute-lft-neg-in 47.2%

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

      3. *-commutative 47.2%

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

   8. Simplified 47.2%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -7.6 \cdot 10^{+168}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{+121}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -2.8 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq -2 \cdot 10^{-217}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq -1.4 \cdot 10^{-299}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 3.65 \cdot 10^{-118}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 150000000:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot i - z \cdot c\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+21}:\\ \;\;\;\;b \cdot t\_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-170}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \frac{t\_1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* t i) (* z c))))
   (if (<= b -1.4e+21)
     (* b t_1)
     (if (<= b -3.5e-108)
       (* t (- (* b i) (* x a)))
       (if (<= b -1.15e-237)
         (* y (- (* x z) (* i j)))
         (if (<= b 3.7e-170)
           (* j (* y (- (/ (* a c) y) i)))
           (if (<= b 4e-28)
             (* x (- (* y z) (* t a)))
             (* (* x b) (/ t_1 x)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * i) - (z * c);
	double tmp;
	if (b <= -1.4e+21) {
		tmp = b * t_1;
	} else if (b <= -3.5e-108) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= -1.15e-237) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 3.7e-170) {
		tmp = j * (y * (((a * c) / y) - i));
	} else if (b <= 4e-28) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = (x * b) * (t_1 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t * i) - (z * c)
    if (b <= (-1.4d+21)) then
        tmp = b * t_1
    else if (b <= (-3.5d-108)) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= (-1.15d-237)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 3.7d-170) then
        tmp = j * (y * (((a * c) / y) - i))
    else if (b <= 4d-28) then
        tmp = x * ((y * z) - (t * a))
    else
        tmp = (x * b) * (t_1 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (t * i) - (z * c);
	double tmp;
	if (b <= -1.4e+21) {
		tmp = b * t_1;
	} else if (b <= -3.5e-108) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= -1.15e-237) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 3.7e-170) {
		tmp = j * (y * (((a * c) / y) - i));
	} else if (b <= 4e-28) {
		tmp = x * ((y * z) - (t * a));
	} else {
		tmp = (x * b) * (t_1 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (t * i) - (z * c)
	tmp = 0
	if b <= -1.4e+21:
		tmp = b * t_1
	elif b <= -3.5e-108:
		tmp = t * ((b * i) - (x * a))
	elif b <= -1.15e-237:
		tmp = y * ((x * z) - (i * j))
	elif b <= 3.7e-170:
		tmp = j * (y * (((a * c) / y) - i))
	elif b <= 4e-28:
		tmp = x * ((y * z) - (t * a))
	else:
		tmp = (x * b) * (t_1 / x)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(t * i) - Float64(z * c))
	tmp = 0.0
	if (b <= -1.4e+21)
		tmp = Float64(b * t_1);
	elseif (b <= -3.5e-108)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= -1.15e-237)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 3.7e-170)
		tmp = Float64(j * Float64(y * Float64(Float64(Float64(a * c) / y) - i)));
	elseif (b <= 4e-28)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	else
		tmp = Float64(Float64(x * b) * Float64(t_1 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (t * i) - (z * c);
	tmp = 0.0;
	if (b <= -1.4e+21)
		tmp = b * t_1;
	elseif (b <= -3.5e-108)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= -1.15e-237)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 3.7e-170)
		tmp = j * (y * (((a * c) / y) - i));
	elseif (b <= 4e-28)
		tmp = x * ((y * z) - (t * a));
	else
		tmp = (x * b) * (t_1 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+21], N[(b * t$95$1), $MachinePrecision], If[LessEqual[b, -3.5e-108], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.15e-237], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-170], N[(j * N[(y * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 4e-28], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * b), $MachinePrecision] * N[(t$95$1 / x), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.4e21

   1. Initial program 69.6%

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

   3. Taylor expanded in b around inf 63.7%

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

   if -1.4e21 < b < -3.4999999999999999e-108

   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 t around inf 61.2%

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

      1. distribute-lft-out-- 61.2%

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

      2. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if -3.4999999999999999e-108 < b < -1.15000000000000006e-237

   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. Taylor expanded in y around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

      5. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   if -1.15000000000000006e-237 < b < 3.7e-170

   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 j around inf 66.4%

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

   4. Taylor expanded in y around inf 69.4%

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

   if 3.7e-170 < b < 3.99999999999999988e-28

   1. Initial program 72.6%

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

   3. Taylor expanded in x around inf 73.4%

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

   if 3.99999999999999988e-28 < b

   1. Initial program 70.3%

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

   3. Taylor expanded in x around inf 66.9%

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

      1. associate--l+ 66.9%

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

      2. associate-*r/ 66.9%

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

      3. *-commutative 66.9%

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

      4. *-commutative 66.9%

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

      5. *-commutative 66.9%

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

      6. associate-*r* 66.9%

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

      7. neg-mul-1 66.9%

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

      8. associate-/l* 68.2%

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

      9. neg-sub0 68.2%

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

      10. *-commutative 68.2%

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

      11. *-commutative 68.2%

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

      12. associate--r- 68.2%

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

      13. neg-sub0 68.2%

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

      14. +-commutative 68.2%

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

      15. sub-neg 68.2%

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

   5. Simplified 68.2%

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

   6. Taylor expanded in b around inf 54.7%

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

      1. associate-*r* 57.0%

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

      2. div-sub 59.3%

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

   8. Simplified 59.3%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+21}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -1.15 \cdot 10^{-237}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-170}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot b\right) \cdot \frac{t \cdot i - z \cdot c}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 55.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t\_1 + b \cdot \left(t \cdot i\right)\\ t_3 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{-80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-183}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+200}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (+ t_1 (* b (* t i))))
        (t_3 (* z (- (* x y) (* b c)))))
   (if (<= z -1.8e-22)
     t_3
     (if (<= z -6.7e-80)
       t_2
       (if (<= z -3.7e-183)
         (- t_1 (* b (* z c)))
         (if (<= z 1.15e+200) 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 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (b * (t * i));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.8e-22) {
		tmp = t_3;
	} else if (z <= -6.7e-80) {
		tmp = t_2;
	} else if (z <= -3.7e-183) {
		tmp = t_1 - (b * (z * c));
	} else if (z <= 1.15e+200) {
		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 = j * ((a * c) - (y * i))
    t_2 = t_1 + (b * (t * i))
    t_3 = z * ((x * y) - (b * c))
    if (z <= (-1.8d-22)) then
        tmp = t_3
    else if (z <= (-6.7d-80)) then
        tmp = t_2
    else if (z <= (-3.7d-183)) then
        tmp = t_1 - (b * (z * c))
    else if (z <= 1.15d+200) 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 = j * ((a * c) - (y * i));
	double t_2 = t_1 + (b * (t * i));
	double t_3 = z * ((x * y) - (b * c));
	double tmp;
	if (z <= -1.8e-22) {
		tmp = t_3;
	} else if (z <= -6.7e-80) {
		tmp = t_2;
	} else if (z <= -3.7e-183) {
		tmp = t_1 - (b * (z * c));
	} else if (z <= 1.15e+200) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t_1 + (b * (t * i))
	t_3 = z * ((x * y) - (b * c))
	tmp = 0
	if z <= -1.8e-22:
		tmp = t_3
	elif z <= -6.7e-80:
		tmp = t_2
	elif z <= -3.7e-183:
		tmp = t_1 - (b * (z * c))
	elif z <= 1.15e+200:
		tmp = t_2
	else:
		tmp = t_3
	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)))
	t_2 = Float64(t_1 + Float64(b * Float64(t * i)))
	t_3 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (z <= -1.8e-22)
		tmp = t_3;
	elseif (z <= -6.7e-80)
		tmp = t_2;
	elseif (z <= -3.7e-183)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (z <= 1.15e+200)
		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 = j * ((a * c) - (y * i));
	t_2 = t_1 + (b * (t * i));
	t_3 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (z <= -1.8e-22)
		tmp = t_3;
	elseif (z <= -6.7e-80)
		tmp = t_2;
	elseif (z <= -3.7e-183)
		tmp = t_1 - (b * (z * c));
	elseif (z <= 1.15e+200)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e-22], t$95$3, If[LessEqual[z, -6.7e-80], t$95$2, If[LessEqual[z, -3.7e-183], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e+200], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e-22 or 1.15000000000000002e200 < z

   1. Initial program 62.9%

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

   3. Taylor expanded in z around inf 63.8%

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

      1. *-commutative 63.8%

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

      2. *-commutative 63.8%

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

   5. Simplified 63.8%

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

   if -1.7999999999999999e-22 < z < -6.70000000000000002e-80 or -3.6999999999999999e-183 < z < 1.15000000000000002e200

   1. Initial program 76.2%

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

   3. Taylor expanded in i around inf 67.7%

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

   if -6.70000000000000002e-80 < z < -3.6999999999999999e-183

   1. Initial program 81.5%

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

   3. Taylor expanded in c around inf 73.0%

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

      1. associate-*r* 73.0%

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

      2. neg-mul-1 73.0%

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

   5. Simplified 73.0%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-22}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;z \leq -6.7 \cdot 10^{-80}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-183}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{+200}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-273}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-117}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -6e-118)
   (+ (* j (- (* a c) (* y i))) (* b (* t i)))
   (if (<= i -3.5e-217)
     (* x (- (* y z) (* t a)))
     (if (<= i -1e-273)
       (* c (- (* a j) (* z b)))
       (if (<= i 5.2e-117)
         (* a (* j (- c (* t (/ x j)))))
         (if (<= i 2.6e+110)
           (* z (- (* x y) (* b c)))
           (* i (- (* t b) (* y j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -6e-118) {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	} else if (i <= -3.5e-217) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= -1e-273) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 5.2e-117) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (i <= 2.6e+110) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-6d-118)) then
        tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
    else if (i <= (-3.5d-217)) then
        tmp = x * ((y * z) - (t * a))
    else if (i <= (-1d-273)) then
        tmp = c * ((a * j) - (z * b))
    else if (i <= 5.2d-117) then
        tmp = a * (j * (c - (t * (x / j))))
    else if (i <= 2.6d+110) then
        tmp = z * ((x * y) - (b * c))
    else
        tmp = i * ((t * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -6e-118) {
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	} else if (i <= -3.5e-217) {
		tmp = x * ((y * z) - (t * a));
	} else if (i <= -1e-273) {
		tmp = c * ((a * j) - (z * b));
	} else if (i <= 5.2e-117) {
		tmp = a * (j * (c - (t * (x / j))));
	} else if (i <= 2.6e+110) {
		tmp = z * ((x * y) - (b * c));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -6e-118:
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i))
	elif i <= -3.5e-217:
		tmp = x * ((y * z) - (t * a))
	elif i <= -1e-273:
		tmp = c * ((a * j) - (z * b))
	elif i <= 5.2e-117:
		tmp = a * (j * (c - (t * (x / j))))
	elif i <= 2.6e+110:
		tmp = z * ((x * y) - (b * c))
	else:
		tmp = i * ((t * b) - (y * j))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -6e-118)
		tmp = Float64(Float64(j * Float64(Float64(a * c) - Float64(y * i))) + Float64(b * Float64(t * i)));
	elseif (i <= -3.5e-217)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (i <= -1e-273)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (i <= 5.2e-117)
		tmp = Float64(a * Float64(j * Float64(c - Float64(t * Float64(x / j)))));
	elseif (i <= 2.6e+110)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -6e-118)
		tmp = (j * ((a * c) - (y * i))) + (b * (t * i));
	elseif (i <= -3.5e-217)
		tmp = x * ((y * z) - (t * a));
	elseif (i <= -1e-273)
		tmp = c * ((a * j) - (z * b));
	elseif (i <= 5.2e-117)
		tmp = a * (j * (c - (t * (x / j))));
	elseif (i <= 2.6e+110)
		tmp = z * ((x * y) - (b * c));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -6e-118], N[(N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.5e-217], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1e-273], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 5.2e-117], N[(a * N[(j * N[(c - N[(t * N[(x / j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.6e+110], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -6.00000000000000035e-118

   1. Initial program 63.8%

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

   3. Taylor expanded in i around inf 64.7%

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

   if -6.00000000000000035e-118 < i < -3.5e-217

   1. Initial program 85.8%

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

   3. Taylor expanded in x around inf 72.0%

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

   if -3.5e-217 < i < -1e-273

   1. Initial program 94.7%

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

   3. Taylor expanded in c around inf 55.8%

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

      1. *-commutative 55.8%

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

   5. Simplified 55.8%

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

   if -1e-273 < i < 5.19999999999999966e-117

   1. Initial program 72.5%

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

   3. Taylor expanded in a around 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%

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

   5. Simplified 63.2%

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

   6. Taylor expanded in j around inf 63.2%

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

      1. mul-1-neg 63.2%

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

      2. unsub-neg 63.2%

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

      3. associate-/l* 66.4%

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

   8. Simplified 66.4%

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

   if 5.19999999999999966e-117 < i < 2.6e110

   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 z around inf 65.3%

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

      1. *-commutative 65.3%

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

      2. *-commutative 65.3%

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

   5. Simplified 65.3%

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

   if 2.6e110 < i

   1. Initial program 67.6%

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

   3. Taylor expanded in x around inf 62.8%

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

      1. associate--l+ 62.8%

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

      2. associate-*r/ 62.8%

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

      3. *-commutative 62.8%

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

      4. *-commutative 62.8%

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

      5. *-commutative 62.8%

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

      6. associate-*r* 62.8%

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

      7. neg-mul-1 62.8%

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

      8. associate-/l* 62.8%

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

      9. neg-sub0 62.8%

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

      10. *-commutative 62.8%

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

      11. *-commutative 62.8%

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

      12. associate--r- 62.8%

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

      13. neg-sub0 62.8%

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

      14. +-commutative 62.8%

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

      15. sub-neg 62.8%

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

   5. Simplified 62.8%

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

   6. Taylor expanded in i around inf 77.8%

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

      1. +-commutative 77.8%

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

      2. mul-1-neg 77.8%

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

      3. unsub-neg 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -6 \cdot 10^{-118}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;i \leq -1 \cdot 10^{-273}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;i \leq 5.2 \cdot 10^{-117}:\\ \;\;\;\;a \cdot \left(j \cdot \left(c - t \cdot \frac{x}{j}\right)\right)\\ \mathbf{elif}\;i \leq 2.6 \cdot 10^{+110}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.65 \cdot 10^{+20}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-168}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -2.65e+20)
     t_1
     (if (<= b -3.5e-108)
       (* t (- (* b i) (* x a)))
       (if (<= b -3.2e-236)
         (* y (- (* x z) (* i j)))
         (if (<= b 2.6e-168)
           (* j (* y (- (/ (* a c) y) i)))
           (if (<= b 5e-29) (* 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.65e+20) {
		tmp = t_1;
	} else if (b <= -3.5e-108) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= -3.2e-236) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.6e-168) {
		tmp = j * (y * (((a * c) / y) - i));
	} else if (b <= 5e-29) {
		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 = b * ((t * i) - (z * c))
    if (b <= (-2.65d+20)) then
        tmp = t_1
    else if (b <= (-3.5d-108)) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= (-3.2d-236)) then
        tmp = y * ((x * z) - (i * j))
    else if (b <= 2.6d-168) then
        tmp = j * (y * (((a * c) / y) - i))
    else if (b <= 5d-29) 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.65e+20) {
		tmp = t_1;
	} else if (b <= -3.5e-108) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= -3.2e-236) {
		tmp = y * ((x * z) - (i * j));
	} else if (b <= 2.6e-168) {
		tmp = j * (y * (((a * c) / y) - i));
	} else if (b <= 5e-29) {
		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 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -2.65e+20:
		tmp = t_1
	elif b <= -3.5e-108:
		tmp = t * ((b * i) - (x * a))
	elif b <= -3.2e-236:
		tmp = y * ((x * z) - (i * j))
	elif b <= 2.6e-168:
		tmp = j * (y * (((a * c) / y) - i))
	elif b <= 5e-29:
		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(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.65e+20)
		tmp = t_1;
	elseif (b <= -3.5e-108)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= -3.2e-236)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (b <= 2.6e-168)
		tmp = Float64(j * Float64(y * Float64(Float64(Float64(a * c) / y) - i)));
	elseif (b <= 5e-29)
		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 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.65e+20)
		tmp = t_1;
	elseif (b <= -3.5e-108)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= -3.2e-236)
		tmp = y * ((x * z) - (i * j));
	elseif (b <= 2.6e-168)
		tmp = j * (y * (((a * c) / y) - i));
	elseif (b <= 5e-29)
		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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.65e+20], t$95$1, If[LessEqual[b, -3.5e-108], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.2e-236], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.6e-168], N[(j * N[(y * N[(N[(N[(a * c), $MachinePrecision] / y), $MachinePrecision] - i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5e-29], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.65e20 or 4.99999999999999986e-29 < b

   1. Initial program 70.0%

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

   3. Taylor expanded in b around inf 60.6%

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

   if -2.65e20 < b < -3.4999999999999999e-108

   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 t around inf 61.2%

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

      1. distribute-lft-out-- 61.2%

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

      2. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if -3.4999999999999999e-108 < b < -3.2e-236

   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. Taylor expanded in y around inf 71.5%

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

      1. +-commutative 71.5%

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

      2. mul-1-neg 71.5%

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

      3. unsub-neg 71.5%

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

      4. *-commutative 71.5%

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

      5. *-commutative 71.5%

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

   5. Simplified 71.5%

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

   if -3.2e-236 < b < 2.6000000000000001e-168

   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 j around inf 66.4%

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

   4. Taylor expanded in y around inf 69.4%

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

   if 2.6000000000000001e-168 < b < 4.99999999999999986e-29

   1. Initial program 72.6%

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

   3. Taylor expanded in x around inf 73.4%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.65 \cdot 10^{+20}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-108}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -3.2 \cdot 10^{-236}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-168}:\\ \;\;\;\;j \cdot \left(y \cdot \left(\frac{a \cdot c}{y} - i\right)\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-29}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 46.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.9 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -7.7 \cdot 10^{+15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+194}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -4.9e+140)
     (* c (- (* a j) (* z b)))
     (if (<= a -7.5e+105)
       (* x (- (* y z) (* t a)))
       (if (<= a -7.7e+15)
         t_1
         (if (<= a 5e-269)
           (* b (- (* t i) (* z c)))
           (if (<= a 1.05e+194) (* i (- (* t b) (* y j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.9e+140) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -7.5e+105) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -7.7e+15) {
		tmp = t_1;
	} else if (a <= 5e-269) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.05e+194) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-4.9d+140)) then
        tmp = c * ((a * j) - (z * b))
    else if (a <= (-7.5d+105)) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= (-7.7d+15)) then
        tmp = t_1
    else if (a <= 5d-269) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 1.05d+194) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.9e+140) {
		tmp = c * ((a * j) - (z * b));
	} else if (a <= -7.5e+105) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -7.7e+15) {
		tmp = t_1;
	} else if (a <= 5e-269) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.05e+194) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.9e+140:
		tmp = c * ((a * j) - (z * b))
	elif a <= -7.5e+105:
		tmp = x * ((y * z) - (t * a))
	elif a <= -7.7e+15:
		tmp = t_1
	elif a <= 5e-269:
		tmp = b * ((t * i) - (z * c))
	elif a <= 1.05e+194:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.9e+140)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (a <= -7.5e+105)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= -7.7e+15)
		tmp = t_1;
	elseif (a <= 5e-269)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 1.05e+194)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.9e+140)
		tmp = c * ((a * j) - (z * b));
	elseif (a <= -7.5e+105)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= -7.7e+15)
		tmp = t_1;
	elseif (a <= 5e-269)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 1.05e+194)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.9e+140], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.5e+105], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -7.7e+15], t$95$1, If[LessEqual[a, 5e-269], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.05e+194], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -4.89999999999999959e140

   1. Initial program 47.8%

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

   3. Taylor expanded in c around inf 70.0%

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

      1. *-commutative 70.0%

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

   5. Simplified 70.0%

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

   if -4.89999999999999959e140 < a < -7.5000000000000002e105

   1. Initial program 77.6%

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

   3. Taylor expanded in x around inf 89.1%

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

   if -7.5000000000000002e105 < a < -7.7e15 or 1.05000000000000008e194 < a

   1. Initial program 55.6%

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

   3. Taylor expanded in a around inf 68.1%

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

      1. +-commutative 68.1%

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

      2. mul-1-neg 68.1%

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

      3. unsub-neg 68.1%

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

      4. *-commutative 68.1%

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

   5. Simplified 68.1%

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

   if -7.7e15 < a < 4.99999999999999979e-269

   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 b around inf 51.2%

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

   if 4.99999999999999979e-269 < a < 1.05000000000000008e194

   1. Initial program 76.6%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. associate--l+ 75.9%

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

      2. associate-*r/ 75.9%

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

      3. *-commutative 75.9%

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

      4. *-commutative 75.9%

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

      5. *-commutative 75.9%

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

      6. associate-*r* 75.9%

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

      7. neg-mul-1 75.9%

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

      8. associate-/l* 73.1%

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

      9. neg-sub0 73.1%

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

      10. *-commutative 73.1%

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

      11. *-commutative 73.1%

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

      12. associate--r- 73.1%

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

      13. neg-sub0 73.1%

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

      14. +-commutative 73.1%

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

      15. sub-neg 73.1%

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

   5. Simplified 73.1%

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

   6. Taylor expanded in i around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

   8. Simplified 60.6%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.9 \cdot 10^{+140}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{+105}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -7.7 \cdot 10^{+15}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 5 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.05 \cdot 10^{+194}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 30.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;i \leq -5.8 \cdot 10^{-36}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-216}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -7.8 \cdot 10^{-300}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-115}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= i -5.8e-36)
     (* i (* t b))
     (if (<= i -5.2e-216)
       t_1
       (if (<= i -7.8e-300)
         (* j (* a c))
         (if (<= i 9.2e-115)
           (* a (* x (- t)))
           (if (<= i 2.3e+51) t_1 (* 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 = y * (x * z);
	double tmp;
	if (i <= -5.8e-36) {
		tmp = i * (t * b);
	} else if (i <= -5.2e-216) {
		tmp = t_1;
	} else if (i <= -7.8e-300) {
		tmp = j * (a * c);
	} else if (i <= 9.2e-115) {
		tmp = a * (x * -t);
	} else if (i <= 2.3e+51) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (i <= (-5.8d-36)) then
        tmp = i * (t * b)
    else if (i <= (-5.2d-216)) then
        tmp = t_1
    else if (i <= (-7.8d-300)) then
        tmp = j * (a * c)
    else if (i <= 9.2d-115) then
        tmp = a * (x * -t)
    else if (i <= 2.3d+51) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (i <= -5.8e-36) {
		tmp = i * (t * b);
	} else if (i <= -5.2e-216) {
		tmp = t_1;
	} else if (i <= -7.8e-300) {
		tmp = j * (a * c);
	} else if (i <= 9.2e-115) {
		tmp = a * (x * -t);
	} else if (i <= 2.3e+51) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if i <= -5.8e-36:
		tmp = i * (t * b)
	elif i <= -5.2e-216:
		tmp = t_1
	elif i <= -7.8e-300:
		tmp = j * (a * c)
	elif i <= 9.2e-115:
		tmp = a * (x * -t)
	elif i <= 2.3e+51:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (i <= -5.8e-36)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -5.2e-216)
		tmp = t_1;
	elseif (i <= -7.8e-300)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 9.2e-115)
		tmp = Float64(a * Float64(x * Float64(-t)));
	elseif (i <= 2.3e+51)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (i <= -5.8e-36)
		tmp = i * (t * b);
	elseif (i <= -5.2e-216)
		tmp = t_1;
	elseif (i <= -7.8e-300)
		tmp = j * (a * c);
	elseif (i <= 9.2e-115)
		tmp = a * (x * -t);
	elseif (i <= 2.3e+51)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.8e-36], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.2e-216], t$95$1, If[LessEqual[i, -7.8e-300], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 9.2e-115], N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.3e+51], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -5.80000000000000026e-36

   1. Initial program 63.9%

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

   3. Taylor expanded in x around inf 64.1%

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

      1. associate--l+ 64.1%

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

      2. associate-*r/ 64.1%

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

      3. *-commutative 64.1%

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

      4. *-commutative 64.1%

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

      5. *-commutative 64.1%

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

      6. associate-*r* 64.1%

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

      7. neg-mul-1 64.1%

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

      8. associate-/l* 65.3%

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

      9. neg-sub0 65.3%

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

      10. *-commutative 65.3%

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

      11. *-commutative 65.3%

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

      12. associate--r- 65.3%

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

      13. neg-sub0 65.3%

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

      14. +-commutative 65.3%

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

      15. sub-neg 65.3%

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

   5. Simplified 65.3%

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

   6. Taylor expanded in i around inf 62.4%

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

      1. +-commutative 62.4%

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

      2. mul-1-neg 62.4%

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

      3. unsub-neg 62.4%

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

   8. Simplified 62.4%

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

   9. Taylor expanded in b around inf 42.7%

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

   if -5.80000000000000026e-36 < i < -5.1999999999999997e-216 or 9.19999999999999938e-115 < i < 2.30000000000000005e51

   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. Taylor expanded in y around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

      4. *-commutative 52.5%

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

      5. *-commutative 52.5%

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

   5. Simplified 52.5%

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

   6. Taylor expanded in z around inf 39.5%

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

      1. *-commutative 39.5%

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

      2. associate-*r* 43.1%

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

      3. *-commutative 43.1%

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

   8. Simplified 43.1%

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

   if -5.1999999999999997e-216 < i < -7.8000000000000002e-300

   1. Initial program 91.5%

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

   3. Taylor expanded in j around inf 41.8%

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

   4. Taylor expanded in a around inf 37.5%

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

      1. *-commutative 37.5%

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

   6. Simplified 37.5%

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

   if -7.8000000000000002e-300 < i < 9.19999999999999938e-115

   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 a around inf 63.4%

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

      1. +-commutative 63.4%

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

      2. mul-1-neg 63.4%

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

      3. unsub-neg 63.4%

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

      4. *-commutative 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in j around 0 47.2%

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

      1. neg-mul-1 47.2%

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

      2. distribute-lft-neg-in 47.2%

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

      3. *-commutative 47.2%

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

   8. Simplified 47.2%

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

   if 2.30000000000000005e51 < i

   1. Initial program 67.4%

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

   3. Taylor expanded in x around inf 63.5%

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

      1. associate--l+ 63.5%

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

      2. associate-*r/ 63.5%

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

      3. *-commutative 63.5%

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

      4. *-commutative 63.5%

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

      5. *-commutative 63.5%

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

      6. associate-*r* 63.5%

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

      7. neg-mul-1 63.5%

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

      8. associate-/l* 63.5%

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

      9. neg-sub0 63.5%

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

      10. *-commutative 63.5%

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

      11. *-commutative 63.5%

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

      12. associate--r- 63.5%

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

      13. neg-sub0 63.5%

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

      14. +-commutative 63.5%

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

      15. sub-neg 63.5%

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

   5. Simplified 63.5%

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

   6. Taylor expanded in i around inf 73.8%

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

      1. +-commutative 73.8%

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

      2. mul-1-neg 73.8%

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

      3. unsub-neg 73.8%

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

   8. Simplified 73.8%

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

   9. Taylor expanded in b around inf 43.8%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.8 \cdot 10^{-36}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -5.2 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq -7.8 \cdot 10^{-300}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 9.2 \cdot 10^{-115}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{+51}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.5 \cdot 10^{+14}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-269}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-156}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;a \leq 530000000000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -6.5e+14)
     t_2
     (if (<= a 8.6e-269)
       t_1
       (if (<= a 8e-156)
         (* (* y j) (- i))
         (if (<= a 530000000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.5e+14) {
		tmp = t_2;
	} else if (a <= 8.6e-269) {
		tmp = t_1;
	} else if (a <= 8e-156) {
		tmp = (y * j) * -i;
	} else if (a <= 530000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-6.5d+14)) then
        tmp = t_2
    else if (a <= 8.6d-269) then
        tmp = t_1
    else if (a <= 8d-156) then
        tmp = (y * j) * -i
    else if (a <= 530000000000.0d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.5e+14) {
		tmp = t_2;
	} else if (a <= 8.6e-269) {
		tmp = t_1;
	} else if (a <= 8e-156) {
		tmp = (y * j) * -i;
	} else if (a <= 530000000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -6.5e+14:
		tmp = t_2
	elif a <= 8.6e-269:
		tmp = t_1
	elif a <= 8e-156:
		tmp = (y * j) * -i
	elif a <= 530000000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6.5e+14)
		tmp = t_2;
	elseif (a <= 8.6e-269)
		tmp = t_1;
	elseif (a <= 8e-156)
		tmp = Float64(Float64(y * j) * Float64(-i));
	elseif (a <= 530000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -6.5e+14)
		tmp = t_2;
	elseif (a <= 8.6e-269)
		tmp = t_1;
	elseif (a <= 8e-156)
		tmp = (y * j) * -i;
	elseif (a <= 530000000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.5e+14], t$95$2, If[LessEqual[a, 8.6e-269], t$95$1, If[LessEqual[a, 8e-156], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision], If[LessEqual[a, 530000000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.5e14 or 5.3e11 < a

   1. Initial program 63.9%

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

   3. Taylor expanded in 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%

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

   5. Simplified 55.2%

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

   if -6.5e14 < a < 8.59999999999999977e-269 or 8.00000000000000032e-156 < a < 5.3e11

   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 b around inf 53.1%

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

   if 8.59999999999999977e-269 < a < 8.00000000000000032e-156

   1. Initial program 77.1%

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

   3. Taylor expanded in x around inf 77.1%

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

      1. associate--l+ 77.1%

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

      2. associate-*r/ 77.1%

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

      3. *-commutative 77.1%

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

      4. *-commutative 77.1%

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

      5. *-commutative 77.1%

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

      6. associate-*r* 77.1%

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

      7. neg-mul-1 77.1%

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

      8. associate-/l* 77.1%

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

      9. neg-sub0 77.1%

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

      10. *-commutative 77.1%

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

      11. *-commutative 77.1%

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

      12. associate--r- 77.1%

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

      13. neg-sub0 77.1%

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

      14. +-commutative 77.1%

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

      15. sub-neg 77.1%

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

   5. Simplified 77.1%

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

   6. Taylor expanded in i around inf 73.2%

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

      1. +-commutative 73.2%

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

      2. mul-1-neg 73.2%

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

      3. unsub-neg 73.2%

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

   8. Simplified 73.2%

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

   9. Taylor expanded in b around 0 60.2%

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

       1. mul-1-neg 60.2%

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

       2. distribute-rgt-neg-out 60.2%

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

   11. Simplified 60.2%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+14}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-156}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \mathbf{elif}\;a \leq 530000000000:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 40.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;i \leq -4.8 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{+143}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -4 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 2050000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= i -4.8e+195)
     (* i (* t b))
     (if (<= i -4.2e+143)
       t_1
       (if (<= i -4e-20)
         (* b (* t i))
         (if (<= i 2050000.0) t_1 (* y (* i (- j)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (i <= -4.8e+195) {
		tmp = i * (t * b);
	} else if (i <= -4.2e+143) {
		tmp = t_1;
	} else if (i <= -4e-20) {
		tmp = b * (t * i);
	} else if (i <= 2050000.0) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (i <= (-4.8d+195)) then
        tmp = i * (t * b)
    else if (i <= (-4.2d+143)) then
        tmp = t_1
    else if (i <= (-4d-20)) then
        tmp = b * (t * i)
    else if (i <= 2050000.0d0) then
        tmp = t_1
    else
        tmp = y * (i * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (i <= -4.8e+195) {
		tmp = i * (t * b);
	} else if (i <= -4.2e+143) {
		tmp = t_1;
	} else if (i <= -4e-20) {
		tmp = b * (t * i);
	} else if (i <= 2050000.0) {
		tmp = t_1;
	} else {
		tmp = y * (i * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if i <= -4.8e+195:
		tmp = i * (t * b)
	elif i <= -4.2e+143:
		tmp = t_1
	elif i <= -4e-20:
		tmp = b * (t * i)
	elif i <= 2050000.0:
		tmp = t_1
	else:
		tmp = y * (i * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (i <= -4.8e+195)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -4.2e+143)
		tmp = t_1;
	elseif (i <= -4e-20)
		tmp = Float64(b * Float64(t * i));
	elseif (i <= 2050000.0)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(i * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (i <= -4.8e+195)
		tmp = i * (t * b);
	elseif (i <= -4.2e+143)
		tmp = t_1;
	elseif (i <= -4e-20)
		tmp = b * (t * i);
	elseif (i <= 2050000.0)
		tmp = t_1;
	else
		tmp = y * (i * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -4.8e+195], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -4.2e+143], t$95$1, If[LessEqual[i, -4e-20], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2050000.0], t$95$1, N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -4.8000000000000005e195

   1. Initial program 50.2%

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

   3. Taylor expanded in x around inf 60.2%

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

      1. associate--l+ 60.2%

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

      2. associate-*r/ 60.2%

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

      3. *-commutative 60.2%

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

      4. *-commutative 60.2%

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

      5. *-commutative 60.2%

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

      6. associate-*r* 60.2%

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

      7. neg-mul-1 60.2%

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

      8. associate-/l* 60.2%

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

      9. neg-sub0 60.2%

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

      10. *-commutative 60.2%

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

      11. *-commutative 60.2%

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

      12. associate--r- 60.2%

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

      13. neg-sub0 60.2%

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

      14. +-commutative 60.2%

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

      15. sub-neg 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in i around inf 85.2%

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

      1. +-commutative 85.2%

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

      2. mul-1-neg 85.2%

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

      3. unsub-neg 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in b around inf 60.3%

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

   if -4.8000000000000005e195 < i < -4.19999999999999975e143 or -3.99999999999999978e-20 < i < 2.05e6

   1. Initial program 77.0%

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

   3. Taylor expanded in a around inf 50.9%

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

      1. +-commutative 50.9%

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

      2. mul-1-neg 50.9%

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

      3. unsub-neg 50.9%

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

      4. *-commutative 50.9%

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

   5. Simplified 50.9%

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

   if -4.19999999999999975e143 < i < -3.99999999999999978e-20

   1. Initial program 69.8%

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

   3. Taylor expanded in x around inf 65.8%

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

      1. associate--l+ 65.8%

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

      2. associate-*r/ 65.8%

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

      3. *-commutative 65.8%

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

      4. *-commutative 65.8%

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

      5. *-commutative 65.8%

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

      6. associate-*r* 65.8%

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

      7. neg-mul-1 65.8%

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

      8. associate-/l* 65.7%

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

      9. neg-sub0 65.7%

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

      10. *-commutative 65.7%

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

      11. *-commutative 65.7%

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

      12. associate--r- 65.7%

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

      13. neg-sub0 65.7%

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

      14. +-commutative 65.7%

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

      15. sub-neg 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in i around inf 58.3%

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

      1. +-commutative 58.3%

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

      2. mul-1-neg 58.3%

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

      3. unsub-neg 58.3%

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

   8. Simplified 58.3%

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

   9. Taylor expanded in b around inf 43.2%

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

   if 2.05e6 < i

   1. Initial program 67.8%

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

   3. Taylor expanded in y around inf 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%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   6. Taylor expanded in z around 0 49.4%

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

      1. mul-1-neg 49.4%

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

      2. *-commutative 49.4%

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

      3. *-commutative 49.4%

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

      4. associate-*l* 49.4%

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

      5. distribute-rgt-neg-out 49.4%

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

      6. distribute-rgt-neg-in 49.4%

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

   8. Simplified 49.4%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -4.8 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -4.2 \cdot 10^{+143}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -4 \cdot 10^{-20}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 2050000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 62.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;i \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;t\_1 + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))))
   (if (<= i -1.85e-22)
     (+ t_1 (* b (* t i)))
     (if (<= i 2.5e+22)
       (+ t_1 (* x (- (* y z) (* t a))))
       (* i (- (* t b) (* y j)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -1.85e-22) {
		tmp = t_1 + (b * (t * i));
	} else if (i <= 2.5e+22) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    if (i <= (-1.85d-22)) then
        tmp = t_1 + (b * (t * i))
    else if (i <= 2.5d+22) then
        tmp = t_1 + (x * ((y * z) - (t * a)))
    else
        tmp = i * ((t * b) - (y * j))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double tmp;
	if (i <= -1.85e-22) {
		tmp = t_1 + (b * (t * i));
	} else if (i <= 2.5e+22) {
		tmp = t_1 + (x * ((y * z) - (t * a)));
	} else {
		tmp = i * ((t * b) - (y * j));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	tmp = 0
	if i <= -1.85e-22:
		tmp = t_1 + (b * (t * i))
	elif i <= 2.5e+22:
		tmp = t_1 + (x * ((y * z) - (t * a)))
	else:
		tmp = i * ((t * b) - (y * j))
	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 (i <= -1.85e-22)
		tmp = Float64(t_1 + Float64(b * Float64(t * i)));
	elseif (i <= 2.5e+22)
		tmp = Float64(t_1 + Float64(x * Float64(Float64(y * z) - Float64(t * a))));
	else
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (i <= -1.85e-22)
		tmp = t_1 + (b * (t * i));
	elseif (i <= 2.5e+22)
		tmp = t_1 + (x * ((y * z) - (t * a)));
	else
		tmp = i * ((t * b) - (y * j));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.85e-22], N[(t$95$1 + N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e+22], N[(t$95$1 + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if i < -1.85e-22

   1. Initial program 62.6%

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

   3. Taylor expanded in i around inf 67.3%

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

   if -1.85e-22 < i < 2.4999999999999998e22

   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 b around 0 69.0%

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

   if 2.4999999999999998e22 < i

   1. Initial program 65.5%

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

   3. Taylor expanded in x around inf 62.0%

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

      1. associate--l+ 62.0%

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

      2. associate-*r/ 62.0%

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

      3. *-commutative 62.0%

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

      4. *-commutative 62.0%

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

      5. *-commutative 62.0%

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

      6. associate-*r* 62.0%

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

      7. neg-mul-1 62.0%

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

      8. associate-/l* 62.0%

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

      9. neg-sub0 62.0%

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

      10. *-commutative 62.0%

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

      11. *-commutative 62.0%

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

      12. associate--r- 62.0%

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

      13. neg-sub0 62.0%

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

      14. +-commutative 62.0%

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

      15. sub-neg 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in i around inf 73.1%

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

      1. +-commutative 73.1%

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

      2. mul-1-neg 73.1%

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

      3. unsub-neg 73.1%

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

   8. Simplified 73.1%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.85 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{+22}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 29.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+98}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-263}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 10^{+90}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.1e+98)
   (* z (* x y))
   (if (<= y -7.2e-194)
     (* b (* t i))
     (if (<= y -2.65e-263)
       (* z (* c (- b)))
       (if (<= y 1e+90) (* t (* b i)) (* (* y j) (- 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 (y <= -1.1e+98) {
		tmp = z * (x * y);
	} else if (y <= -7.2e-194) {
		tmp = b * (t * i);
	} else if (y <= -2.65e-263) {
		tmp = z * (c * -b);
	} else if (y <= 1e+90) {
		tmp = t * (b * i);
	} else {
		tmp = (y * j) * -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 (y <= (-1.1d+98)) then
        tmp = z * (x * y)
    else if (y <= (-7.2d-194)) then
        tmp = b * (t * i)
    else if (y <= (-2.65d-263)) then
        tmp = z * (c * -b)
    else if (y <= 1d+90) then
        tmp = t * (b * i)
    else
        tmp = (y * j) * -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 (y <= -1.1e+98) {
		tmp = z * (x * y);
	} else if (y <= -7.2e-194) {
		tmp = b * (t * i);
	} else if (y <= -2.65e-263) {
		tmp = z * (c * -b);
	} else if (y <= 1e+90) {
		tmp = t * (b * i);
	} else {
		tmp = (y * j) * -i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.1e+98:
		tmp = z * (x * y)
	elif y <= -7.2e-194:
		tmp = b * (t * i)
	elif y <= -2.65e-263:
		tmp = z * (c * -b)
	elif y <= 1e+90:
		tmp = t * (b * i)
	else:
		tmp = (y * j) * -i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.1e+98)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= -7.2e-194)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= -2.65e-263)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (y <= 1e+90)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(Float64(y * j) * Float64(-i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.1e+98)
		tmp = z * (x * y);
	elseif (y <= -7.2e-194)
		tmp = b * (t * i);
	elseif (y <= -2.65e-263)
		tmp = z * (c * -b);
	elseif (y <= 1e+90)
		tmp = t * (b * i);
	else
		tmp = (y * j) * -i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.1e+98], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e-194], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.65e-263], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+90], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.10000000000000004e98

   1. Initial program 63.0%

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

   3. Taylor expanded in z around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around inf 46.6%

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

   if -1.10000000000000004e98 < y < -7.2e-194

   1. Initial program 82.8%

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

   3. Taylor expanded in x around inf 78.4%

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

      1. associate--l+ 78.4%

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

      2. associate-*r/ 78.4%

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

      3. *-commutative 78.4%

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

      4. *-commutative 78.4%

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

      5. *-commutative 78.4%

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

      6. associate-*r* 78.4%

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

      7. neg-mul-1 78.4%

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

      8. associate-/l* 78.3%

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

      9. neg-sub0 78.3%

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

      10. *-commutative 78.3%

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

      11. *-commutative 78.3%

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

      12. associate--r- 78.3%

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

      13. neg-sub0 78.3%

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

      14. +-commutative 78.3%

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

      15. sub-neg 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in i around inf 41.3%

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

      1. +-commutative 41.3%

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

      2. mul-1-neg 41.3%

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

      3. unsub-neg 41.3%

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

   8. Simplified 41.3%

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

   9. Taylor expanded in b around inf 38.1%

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

   if -7.2e-194 < y < -2.6499999999999999e-263

   1. Initial program 92.3%

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

   3. Taylor expanded in z around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. *-commutative 70.3%

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

   5. Simplified 70.3%

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

   6. Taylor expanded in y around 0 62.7%

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

      1. mul-1-neg 62.7%

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

      2. distribute-rgt-neg-in 62.7%

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

   8. Simplified 62.7%

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

   if -2.6499999999999999e-263 < y < 9.99999999999999966e89

   1. Initial program 70.5%

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

   3. Taylor expanded in x around inf 73.3%

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

      1. associate--l+ 73.3%

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

      2. associate-*r/ 73.3%

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

      3. *-commutative 73.3%

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

      4. *-commutative 73.3%

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

      5. *-commutative 73.3%

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

      6. associate-*r* 73.3%

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

      7. neg-mul-1 73.3%

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

      8. associate-/l* 74.7%

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

      9. neg-sub0 74.7%

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

      10. *-commutative 74.7%

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

      11. *-commutative 74.7%

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

      12. associate--r- 74.7%

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

      13. neg-sub0 74.7%

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

      14. +-commutative 74.7%

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

      15. sub-neg 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in i around inf 41.5%

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

      1. +-commutative 41.5%

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

      2. mul-1-neg 41.5%

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

      3. unsub-neg 41.5%

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

   8. Simplified 41.5%

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

   9. Taylor expanded in b around inf 31.1%

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

       1. associate-*r* 31.1%

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

       2. *-commutative 31.1%

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

   11. Simplified 31.1%

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

   if 9.99999999999999966e89 < y

   1. Initial program 62.6%

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

   3. Taylor expanded in x around inf 58.4%

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

      1. associate--l+ 58.4%

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

      2. associate-*r/ 58.4%

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

      3. *-commutative 58.4%

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

      4. *-commutative 58.4%

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

      5. *-commutative 58.4%

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

      6. associate-*r* 58.4%

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

      7. neg-mul-1 58.4%

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

      8. associate-/l* 56.5%

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

      9. neg-sub0 56.5%

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

      10. *-commutative 56.5%

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

      11. *-commutative 56.5%

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

      12. associate--r- 56.5%

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

      13. neg-sub0 56.5%

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

      14. +-commutative 56.5%

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

      15. sub-neg 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in i around inf 53.2%

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

      1. +-commutative 53.2%

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

      2. mul-1-neg 53.2%

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

      3. unsub-neg 53.2%

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

   8. Simplified 53.2%

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

   9. Taylor expanded in b around 0 51.4%

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

       1. mul-1-neg 51.4%

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

       2. distribute-rgt-neg-out 51.4%

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

   11. Simplified 51.4%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{+98}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-194}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq -2.65 \cdot 10^{-263}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;y \leq 10^{+90}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 29.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+98}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -1.9e+98)
   (* z (* x y))
   (if (<= y 8.5e-213)
     (* b (* t i))
     (if (<= y 5e-123)
       (* a (* c j))
       (if (<= y 5.3e-37) (* x (* t (- a))) (* (* y j) (- 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 (y <= -1.9e+98) {
		tmp = z * (x * y);
	} else if (y <= 8.5e-213) {
		tmp = b * (t * i);
	} else if (y <= 5e-123) {
		tmp = a * (c * j);
	} else if (y <= 5.3e-37) {
		tmp = x * (t * -a);
	} else {
		tmp = (y * j) * -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 (y <= (-1.9d+98)) then
        tmp = z * (x * y)
    else if (y <= 8.5d-213) then
        tmp = b * (t * i)
    else if (y <= 5d-123) then
        tmp = a * (c * j)
    else if (y <= 5.3d-37) then
        tmp = x * (t * -a)
    else
        tmp = (y * j) * -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 (y <= -1.9e+98) {
		tmp = z * (x * y);
	} else if (y <= 8.5e-213) {
		tmp = b * (t * i);
	} else if (y <= 5e-123) {
		tmp = a * (c * j);
	} else if (y <= 5.3e-37) {
		tmp = x * (t * -a);
	} else {
		tmp = (y * j) * -i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -1.9e+98:
		tmp = z * (x * y)
	elif y <= 8.5e-213:
		tmp = b * (t * i)
	elif y <= 5e-123:
		tmp = a * (c * j)
	elif y <= 5.3e-37:
		tmp = x * (t * -a)
	else:
		tmp = (y * j) * -i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -1.9e+98)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 8.5e-213)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 5e-123)
		tmp = Float64(a * Float64(c * j));
	elseif (y <= 5.3e-37)
		tmp = Float64(x * Float64(t * Float64(-a)));
	else
		tmp = Float64(Float64(y * j) * Float64(-i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -1.9e+98)
		tmp = z * (x * y);
	elseif (y <= 8.5e-213)
		tmp = b * (t * i);
	elseif (y <= 5e-123)
		tmp = a * (c * j);
	elseif (y <= 5.3e-37)
		tmp = x * (t * -a);
	else
		tmp = (y * j) * -i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -1.9e+98], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e-213], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-123], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.3e-37], N[(x * N[(t * (-a)), $MachinePrecision]), $MachinePrecision], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.89999999999999995e98

   1. Initial program 63.0%

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

   3. Taylor expanded in z around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around inf 46.6%

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

   if -1.89999999999999995e98 < y < 8.49999999999999994e-213

   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 x around inf 78.0%

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

      1. associate--l+ 78.0%

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

      2. associate-*r/ 78.0%

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

      3. *-commutative 78.0%

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

      4. *-commutative 78.0%

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

      5. *-commutative 78.0%

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

      6. associate-*r* 78.0%

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

      7. neg-mul-1 78.0%

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

      8. associate-/l* 79.9%

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

      9. neg-sub0 79.9%

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

      10. *-commutative 79.9%

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

      11. *-commutative 79.9%

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

      12. associate--r- 79.9%

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

      13. neg-sub0 79.9%

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

      14. +-commutative 79.9%

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

      15. sub-neg 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in i around inf 40.1%

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

      1. +-commutative 40.1%

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

      2. mul-1-neg 40.1%

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

      3. unsub-neg 40.1%

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

   8. Simplified 40.1%

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

   9. Taylor expanded in b around inf 37.0%

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

   if 8.49999999999999994e-213 < y < 5.0000000000000003e-123

   1. Initial program 59.5%

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

   3. Taylor expanded in a around inf 54.5%

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

      1. +-commutative 54.5%

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

      2. mul-1-neg 54.5%

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

      3. unsub-neg 54.5%

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

      4. *-commutative 54.5%

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

   5. Simplified 54.5%

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

   6. Taylor expanded in j around inf 43.5%

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

   if 5.0000000000000003e-123 < y < 5.29999999999999995e-37

   1. Initial program 88.1%

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

   3. Taylor expanded in x around inf 88.1%

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

      1. associate--l+ 88.1%

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

      2. associate-*r/ 88.1%

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

      3. *-commutative 88.1%

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

      4. *-commutative 88.1%

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

      5. *-commutative 88.1%

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

      6. associate-*r* 88.1%

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

      7. neg-mul-1 88.1%

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

      8. associate-/l* 82.5%

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

      9. neg-sub0 82.5%

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

      10. *-commutative 82.5%

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

      11. *-commutative 82.5%

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

      12. associate--r- 82.5%

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

      13. neg-sub0 82.5%

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

      14. +-commutative 82.5%

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

      15. sub-neg 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around inf 48.8%

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

      1. *-commutative 48.8%

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

      2. *-commutative 48.8%

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

   8. Simplified 48.8%

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

   9. Taylor expanded in z around 0 37.4%

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

       1. associate-*r* 37.4%

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

       2. neg-mul-1 37.4%

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

       3. *-commutative 37.4%

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

   11. Simplified 37.4%

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

   if 5.29999999999999995e-37 < y

   1. Initial program 63.8%

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

   3. Taylor expanded in x around inf 62.3%

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

      1. associate--l+ 62.3%

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

      2. associate-*r/ 62.3%

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

      3. *-commutative 62.3%

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

      4. *-commutative 62.3%

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

      5. *-commutative 62.3%

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

      6. associate-*r* 62.3%

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

      7. neg-mul-1 62.3%

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

      8. associate-/l* 61.0%

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

      9. neg-sub0 61.0%

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

      10. *-commutative 61.0%

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

      11. *-commutative 61.0%

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

      12. associate--r- 61.0%

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

      13. neg-sub0 61.0%

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

      14. +-commutative 61.0%

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

      15. sub-neg 61.0%

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

   5. Simplified 61.0%

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

   6. Taylor expanded in i around inf 52.5%

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

      1. +-commutative 52.5%

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

      2. mul-1-neg 52.5%

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

      3. unsub-neg 52.5%

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

   8. Simplified 52.5%

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

   9. Taylor expanded in b around 0 43.9%

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

       1. mul-1-neg 43.9%

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

       2. distribute-rgt-neg-out 43.9%

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

   11. Simplified 43.9%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+98}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-213}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-123}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{-37}:\\ \;\;\;\;x \cdot \left(t \cdot \left(-a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-88}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -7.2e+101)
   (* z (* x y))
   (if (<= y 1.4e-212)
     (* b (* t i))
     (if (<= y 2.3e-88)
       (* c (* a j))
       (if (<= y 9.5e+84) (* t (* b i)) (* (* y j) (- 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 (y <= -7.2e+101) {
		tmp = z * (x * y);
	} else if (y <= 1.4e-212) {
		tmp = b * (t * i);
	} else if (y <= 2.3e-88) {
		tmp = c * (a * j);
	} else if (y <= 9.5e+84) {
		tmp = t * (b * i);
	} else {
		tmp = (y * j) * -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 (y <= (-7.2d+101)) then
        tmp = z * (x * y)
    else if (y <= 1.4d-212) then
        tmp = b * (t * i)
    else if (y <= 2.3d-88) then
        tmp = c * (a * j)
    else if (y <= 9.5d+84) then
        tmp = t * (b * i)
    else
        tmp = (y * j) * -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 (y <= -7.2e+101) {
		tmp = z * (x * y);
	} else if (y <= 1.4e-212) {
		tmp = b * (t * i);
	} else if (y <= 2.3e-88) {
		tmp = c * (a * j);
	} else if (y <= 9.5e+84) {
		tmp = t * (b * i);
	} else {
		tmp = (y * j) * -i;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -7.2e+101:
		tmp = z * (x * y)
	elif y <= 1.4e-212:
		tmp = b * (t * i)
	elif y <= 2.3e-88:
		tmp = c * (a * j)
	elif y <= 9.5e+84:
		tmp = t * (b * i)
	else:
		tmp = (y * j) * -i
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -7.2e+101)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 1.4e-212)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 2.3e-88)
		tmp = Float64(c * Float64(a * j));
	elseif (y <= 9.5e+84)
		tmp = Float64(t * Float64(b * i));
	else
		tmp = Float64(Float64(y * j) * Float64(-i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -7.2e+101)
		tmp = z * (x * y);
	elseif (y <= 1.4e-212)
		tmp = b * (t * i);
	elseif (y <= 2.3e-88)
		tmp = c * (a * j);
	elseif (y <= 9.5e+84)
		tmp = t * (b * i);
	else
		tmp = (y * j) * -i;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -7.2e+101], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-212], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e-88], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+84], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(N[(y * j), $MachinePrecision] * (-i)), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.20000000000000058e101

   1. Initial program 63.0%

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

   3. Taylor expanded in z around inf 50.0%

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

      1. *-commutative 50.0%

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

      2. *-commutative 50.0%

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

   5. Simplified 50.0%

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

   6. Taylor expanded in y around inf 46.6%

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

   if -7.20000000000000058e101 < y < 1.40000000000000007e-212

   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 x around inf 78.0%

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

      1. associate--l+ 78.0%

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

      2. associate-*r/ 78.0%

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

      3. *-commutative 78.0%

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

      4. *-commutative 78.0%

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

      5. *-commutative 78.0%

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

      6. associate-*r* 78.0%

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

      7. neg-mul-1 78.0%

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

      8. associate-/l* 79.9%

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

      9. neg-sub0 79.9%

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

      10. *-commutative 79.9%

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

      11. *-commutative 79.9%

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

      12. associate--r- 79.9%

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

      13. neg-sub0 79.9%

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

      14. +-commutative 79.9%

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

      15. sub-neg 79.9%

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

   5. Simplified 79.9%

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

   6. Taylor expanded in i around inf 40.1%

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

      1. +-commutative 40.1%

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

      2. mul-1-neg 40.1%

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

      3. unsub-neg 40.1%

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

   8. Simplified 40.1%

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

   9. Taylor expanded in b around inf 37.0%

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

   if 1.40000000000000007e-212 < y < 2.29999999999999986e-88

   1. Initial program 68.7%

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

   3. Taylor expanded in x around inf 73.2%

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

      1. associate--l+ 73.2%

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

      2. associate-*r/ 73.2%

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

      3. *-commutative 73.2%

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

      4. *-commutative 73.2%

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

      5. *-commutative 73.2%

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

      6. associate-*r* 73.2%

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

      7. neg-mul-1 73.2%

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

      8. associate-/l* 73.2%

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

      9. neg-sub0 73.2%

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

      10. *-commutative 73.2%

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

      11. *-commutative 73.2%

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

      12. associate--r- 73.2%

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

      13. neg-sub0 73.2%

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

      14. +-commutative 73.2%

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

      15. sub-neg 73.2%

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

   5. Simplified 73.2%

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

   6. Taylor expanded in c around inf 53.3%

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

      1. mul-1-neg 53.3%

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

      2. associate-*r* 53.4%

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

      3. *-commutative 53.4%

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

      4. distribute-rgt-neg-in 53.4%

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

      5. *-commutative 53.4%

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

   8. Simplified 53.4%

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

   9. Taylor expanded in a around inf 34.2%

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

       1. *-commutative 34.2%

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

       2. associate-*r* 34.2%

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

   11. Simplified 34.2%

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

   if 2.29999999999999986e-88 < y < 9.49999999999999979e84

   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 x around inf 76.9%

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

      1. associate--l+ 76.9%

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

      2. associate-*r/ 76.9%

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

      3. *-commutative 76.9%

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

      4. *-commutative 76.9%

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

      5. *-commutative 76.9%

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

      6. associate-*r* 76.9%

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

      7. neg-mul-1 76.9%

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

      8. associate-/l* 73.7%

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

      9. neg-sub0 73.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 73.7%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 73.7%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 73.7%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 73.7%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 73.7%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 73.7%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 73.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 47.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 47.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 47.3%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 47.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 47.3%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 31.7%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 34.9%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 34.9%

          \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   11. Simplified 34.9%

       \[\leadsto \color{blue}{t \cdot \left(b \cdot i\right)} \]

   if 9.49999999999999979e84 < y

   1. Initial program 62.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 58.4%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 58.4%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 58.4%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 58.4%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 58.4%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 58.4%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 58.4%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 58.4%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 56.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 56.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 56.5%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 56.5%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 56.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 56.5%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 56.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 56.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 56.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 53.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 53.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 53.2%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 53.2%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 53.2%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around 0 51.4%

      \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y\right)\right)} \]
   10. Step-by-step derivation

       1. mul-1-neg 51.4%

          \[\leadsto i \cdot \color{blue}{\left(-j \cdot y\right)} \]

       2. distribute-rgt-neg-out 51.4%

          \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-y\right)\right)} \]

   11. Simplified 51.4%

       \[\leadsto i \cdot \color{blue}{\left(j \cdot \left(-y\right)\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+101}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-212}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{-88}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+84}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y \cdot j\right) \cdot \left(-i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 30.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{-36}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -9.2 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-257}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+62}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -1.05e-36)
   (* i (* t b))
   (if (<= i -9.2e-216)
     (* y (* x z))
     (if (<= i 2.5e-257)
       (* j (* a c))
       (if (<= i 6.8e+62) (* z (* x y)) (* 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 tmp;
	if (i <= -1.05e-36) {
		tmp = i * (t * b);
	} else if (i <= -9.2e-216) {
		tmp = y * (x * z);
	} else if (i <= 2.5e-257) {
		tmp = j * (a * c);
	} else if (i <= 6.8e+62) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-1.05d-36)) then
        tmp = i * (t * b)
    else if (i <= (-9.2d-216)) then
        tmp = y * (x * z)
    else if (i <= 2.5d-257) then
        tmp = j * (a * c)
    else if (i <= 6.8d+62) then
        tmp = z * (x * y)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -1.05e-36) {
		tmp = i * (t * b);
	} else if (i <= -9.2e-216) {
		tmp = y * (x * z);
	} else if (i <= 2.5e-257) {
		tmp = j * (a * c);
	} else if (i <= 6.8e+62) {
		tmp = z * (x * y);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -1.05e-36:
		tmp = i * (t * b)
	elif i <= -9.2e-216:
		tmp = y * (x * z)
	elif i <= 2.5e-257:
		tmp = j * (a * c)
	elif i <= 6.8e+62:
		tmp = z * (x * y)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -1.05e-36)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -9.2e-216)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 2.5e-257)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 6.8e+62)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -1.05e-36)
		tmp = i * (t * b);
	elseif (i <= -9.2e-216)
		tmp = y * (x * z);
	elseif (i <= 2.5e-257)
		tmp = j * (a * c);
	elseif (i <= 6.8e+62)
		tmp = z * (x * y);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -1.05e-36], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -9.2e-216], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.5e-257], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 6.8e+62], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -1.04999999999999995e-36

   1. Initial program 63.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 64.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 64.1%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 64.1%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 64.1%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 64.1%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.1%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 64.1%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 64.1%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 65.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 65.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 65.3%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 65.3%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 65.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 65.3%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 65.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 65.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 65.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 62.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 62.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 62.4%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 62.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 62.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 42.7%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if -1.04999999999999995e-36 < i < -9.19999999999999987e-216

   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 y around inf 50.5%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 50.5%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 50.5%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 50.5%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

      5. *-commutative 50.5%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   5. Simplified 50.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   6. Taylor expanded in z around inf 39.4%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.4%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*r* 44.0%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

      3. *-commutative 44.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   8. Simplified 44.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if -9.19999999999999987e-216 < i < 2.49999999999999994e-257

   1. Initial program 83.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 42.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   4. Taylor expanded in a around inf 38.9%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]

   6. Simplified 38.9%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]

   if 2.49999999999999994e-257 < i < 6.80000000000000028e62

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 58.0%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 58.0%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 58.0%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 58.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 35.5%

      \[\leadsto z \cdot \color{blue}{\left(x \cdot y\right)} \]

   if 6.80000000000000028e62 < i

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 63.5%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 63.5%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 63.5%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 63.5%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.5%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 63.5%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 63.5%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 63.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 63.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 63.5%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 63.5%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 63.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 63.5%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 63.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 63.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 63.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 73.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 73.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 73.8%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 73.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 73.8%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 43.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{-36}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -9.2 \cdot 10^{-216}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 2.5 \cdot 10^{-257}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 6.8 \cdot 10^{+62}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;i \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -2.75 \cdot 10^{-213}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{-257}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* y (* x z))))
   (if (<= i -2.7e-36)
     (* i (* t b))
     (if (<= i -2.75e-213)
       t_1
       (if (<= i 7.6e-257)
         (* j (* a c))
         (if (<= i 2.1e+54) t_1 (* 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 = y * (x * z);
	double tmp;
	if (i <= -2.7e-36) {
		tmp = i * (t * b);
	} else if (i <= -2.75e-213) {
		tmp = t_1;
	} else if (i <= 7.6e-257) {
		tmp = j * (a * c);
	} else if (i <= 2.1e+54) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (x * z)
    if (i <= (-2.7d-36)) then
        tmp = i * (t * b)
    else if (i <= (-2.75d-213)) then
        tmp = t_1
    else if (i <= 7.6d-257) then
        tmp = j * (a * c)
    else if (i <= 2.1d+54) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = y * (x * z);
	double tmp;
	if (i <= -2.7e-36) {
		tmp = i * (t * b);
	} else if (i <= -2.75e-213) {
		tmp = t_1;
	} else if (i <= 7.6e-257) {
		tmp = j * (a * c);
	} else if (i <= 2.1e+54) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = y * (x * z)
	tmp = 0
	if i <= -2.7e-36:
		tmp = i * (t * b)
	elif i <= -2.75e-213:
		tmp = t_1
	elif i <= 7.6e-257:
		tmp = j * (a * c)
	elif i <= 2.1e+54:
		tmp = t_1
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (i <= -2.7e-36)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -2.75e-213)
		tmp = t_1;
	elseif (i <= 7.6e-257)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 2.1e+54)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = y * (x * z);
	tmp = 0.0;
	if (i <= -2.7e-36)
		tmp = i * (t * b);
	elseif (i <= -2.75e-213)
		tmp = t_1;
	elseif (i <= 7.6e-257)
		tmp = j * (a * c);
	elseif (i <= 2.1e+54)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.7e-36], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -2.75e-213], t$95$1, If[LessEqual[i, 7.6e-257], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.1e+54], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.70000000000000007e-36

   1. Initial program 63.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 64.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 64.1%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 64.1%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 64.1%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 64.1%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.1%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 64.1%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 64.1%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 65.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 65.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 65.3%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 65.3%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 65.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 65.3%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 65.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 65.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 65.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 62.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 62.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 62.4%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 62.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 62.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 42.7%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if -2.70000000000000007e-36 < i < -2.75000000000000004e-213 or 7.6000000000000007e-257 < i < 2.09999999999999986e54

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 48.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 48.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 48.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 48.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

      5. *-commutative 48.8%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   5. Simplified 48.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   6. Taylor expanded in z around inf 37.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 37.0%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*r* 39.0%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

      3. *-commutative 39.0%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z\right)} \]

   8. Simplified 39.0%

      \[\leadsto \color{blue}{y \cdot \left(x \cdot z\right)} \]

   if -2.75000000000000004e-213 < i < 7.6000000000000007e-257

   1. Initial program 83.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 42.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   4. Taylor expanded in a around inf 38.9%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]

   6. Simplified 38.9%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]

   if 2.09999999999999986e54 < i

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 63.5%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 63.5%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 63.5%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 63.5%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.5%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 63.5%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 63.5%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 63.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 63.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 63.5%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 63.5%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 63.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 63.5%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 63.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 63.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 63.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 73.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 73.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 73.8%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 73.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 73.8%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 43.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.7 \cdot 10^{-36}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -2.75 \cdot 10^{-213}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{-257}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 2.1 \cdot 10^{+54}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 30.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;i \leq -2.8 \cdot 10^{-35}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-217}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-258}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+53}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (* y z))))
   (if (<= i -2.8e-35)
     (* i (* t b))
     (if (<= i -9e-217)
       t_1
       (if (<= i 3.9e-258)
         (* j (* a c))
         (if (<= i 1.1e+53) t_1 (* 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 = x * (y * z);
	double tmp;
	if (i <= -2.8e-35) {
		tmp = i * (t * b);
	} else if (i <= -9e-217) {
		tmp = t_1;
	} else if (i <= 3.9e-258) {
		tmp = j * (a * c);
	} else if (i <= 1.1e+53) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x * (y * z)
    if (i <= (-2.8d-35)) then
        tmp = i * (t * b)
    else if (i <= (-9d-217)) then
        tmp = t_1
    else if (i <= 3.9d-258) then
        tmp = j * (a * c)
    else if (i <= 1.1d+53) then
        tmp = t_1
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * (y * z);
	double tmp;
	if (i <= -2.8e-35) {
		tmp = i * (t * b);
	} else if (i <= -9e-217) {
		tmp = t_1;
	} else if (i <= 3.9e-258) {
		tmp = j * (a * c);
	} else if (i <= 1.1e+53) {
		tmp = t_1;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * (y * z)
	tmp = 0
	if i <= -2.8e-35:
		tmp = i * (t * b)
	elif i <= -9e-217:
		tmp = t_1
	elif i <= 3.9e-258:
		tmp = j * (a * c)
	elif i <= 1.1e+53:
		tmp = t_1
	else:
		tmp = b * (t * i)
	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 (i <= -2.8e-35)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= -9e-217)
		tmp = t_1;
	elseif (i <= 3.9e-258)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 1.1e+53)
		tmp = t_1;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * (y * z);
	tmp = 0.0;
	if (i <= -2.8e-35)
		tmp = i * (t * b);
	elseif (i <= -9e-217)
		tmp = t_1;
	elseif (i <= 3.9e-258)
		tmp = j * (a * c);
	elseif (i <= 1.1e+53)
		tmp = t_1;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -2.8e-35], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -9e-217], t$95$1, If[LessEqual[i, 3.9e-258], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e+53], t$95$1, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -2.8e-35

   1. Initial program 63.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 64.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 64.1%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 64.1%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 64.1%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 64.1%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.1%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 64.1%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 64.1%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 65.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 65.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 65.3%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 65.3%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 65.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 65.3%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 65.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 65.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 65.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 62.4%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 62.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 62.4%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 62.4%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 62.4%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 42.7%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if -2.8e-35 < i < -8.9999999999999997e-217 or 3.90000000000000004e-258 < i < 1.09999999999999999e53

   1. Initial program 75.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 48.8%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot \left(i \cdot j\right) + x \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 48.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z + -1 \cdot \left(i \cdot j\right)\right)} \]

      2. mul-1-neg 48.8%

         \[\leadsto y \cdot \left(x \cdot z + \color{blue}{\left(-i \cdot j\right)}\right) \]

      3. unsub-neg 48.8%

         \[\leadsto y \cdot \color{blue}{\left(x \cdot z - i \cdot j\right)} \]

      4. *-commutative 48.8%

         \[\leadsto y \cdot \left(\color{blue}{z \cdot x} - i \cdot j\right) \]

      5. *-commutative 48.8%

         \[\leadsto y \cdot \left(z \cdot x - \color{blue}{j \cdot i}\right) \]

   5. Simplified 48.8%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x - j \cdot i\right)} \]

   6. Taylor expanded in z around inf 37.0%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]

   if -8.9999999999999997e-217 < i < 3.90000000000000004e-258

   1. Initial program 83.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around inf 42.3%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]

   4. Taylor expanded in a around inf 38.9%

      \[\leadsto j \cdot \color{blue}{\left(a \cdot c\right)} \]
   5. Step-by-step derivation

      1. *-commutative 38.9%

         \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]

   6. Simplified 38.9%

      \[\leadsto j \cdot \color{blue}{\left(c \cdot a\right)} \]

   if 1.09999999999999999e53 < i

   1. Initial program 67.4%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 63.5%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 63.5%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 63.5%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 63.5%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.5%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 63.5%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 63.5%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 63.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 63.5%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 63.5%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 63.5%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 63.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 63.5%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 63.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 63.5%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 63.5%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 73.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 73.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 73.8%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 73.8%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 73.8%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 43.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.8 \cdot 10^{-35}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq -9 \cdot 10^{-217}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-258}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{+53}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 49.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -5.1 \cdot 10^{+16}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+190}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -5.1e+16)
     t_1
     (if (<= a 7.6e-269)
       (* b (- (* t i) (* z c)))
       (if (<= a 7.5e+190) (* i (- (* t b) (* y j))) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.1e+16) {
		tmp = t_1;
	} else if (a <= 7.6e-269) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 7.5e+190) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-5.1d+16)) then
        tmp = t_1
    else if (a <= 7.6d-269) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 7.5d+190) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -5.1e+16) {
		tmp = t_1;
	} else if (a <= 7.6e-269) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 7.5e+190) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -5.1e+16:
		tmp = t_1
	elif a <= 7.6e-269:
		tmp = b * ((t * i) - (z * c))
	elif a <= 7.5e+190:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -5.1e+16)
		tmp = t_1;
	elseif (a <= 7.6e-269)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 7.5e+190)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -5.1e+16)
		tmp = t_1;
	elseif (a <= 7.6e-269)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 7.5e+190)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.1e+16], t$95$1, If[LessEqual[a, 7.6e-269], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 7.5e+190], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.1e16 or 7.4999999999999994e190 < a

   1. Initial program 55.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 65.1%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 65.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 65.1%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 65.1%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 65.1%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 65.1%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if -5.1e16 < a < 7.6000000000000005e-269

   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 b around inf 51.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t - c \cdot z\right)} \]

   if 7.6000000000000005e-269 < a < 7.4999999999999994e190

   1. Initial program 76.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.9%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 75.9%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 75.9%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 75.9%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 75.9%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 75.9%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 75.9%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 75.9%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 73.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 73.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 73.1%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 73.1%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 73.1%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 73.1%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 73.1%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 73.1%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 73.1%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 60.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 60.6%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 60.6%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 60.6%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 60.6%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 59.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.1 \cdot 10^{+16}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-269}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+190}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{-22} \lor \neg \left(i \leq 1.9 \cdot 10^{-21}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.55e-22) (not (<= i 1.9e-21))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.55e-22) || !(i <= 1.9e-21)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.55d-22)) .or. (.not. (i <= 1.9d-21))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.55e-22) || !(i <= 1.9e-21)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.55e-22) or not (i <= 1.9e-21):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.55e-22) || !(i <= 1.9e-21))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.55e-22) || ~((i <= 1.9e-21)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.55e-22], N[Not[LessEqual[i, 1.9e-21]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.55000000000000006e-22 or 1.8999999999999999e-21 < i

   1. Initial program 64.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 63.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 63.7%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 63.7%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 63.7%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 63.7%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 63.7%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 63.7%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 63.7%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 63.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 63.7%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 63.7%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 63.7%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 63.7%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 63.7%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 63.7%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 63.7%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 63.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 65.7%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 65.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 65.7%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 65.7%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 65.7%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 41.5%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]

   if -1.55000000000000006e-22 < i < 1.8999999999999999e-21

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 49.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 49.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 49.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 49.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 30.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{-22} \lor \neg \left(i \leq 1.9 \cdot 10^{-21}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.7 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.7e-20)
   (* i (* t b))
   (if (<= i 1.1e-21) (* a (* c j)) (* 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 tmp;
	if (i <= -3.7e-20) {
		tmp = i * (t * b);
	} else if (i <= 1.1e-21) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-3.7d-20)) then
        tmp = i * (t * b)
    else if (i <= 1.1d-21) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.7e-20) {
		tmp = i * (t * b);
	} else if (i <= 1.1e-21) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.7e-20:
		tmp = i * (t * b)
	elif i <= 1.1e-21:
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.7e-20)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= 1.1e-21)
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.7e-20)
		tmp = i * (t * b);
	elseif (i <= 1.1e-21)
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.7e-20], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.1e-21], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if i < -3.7000000000000001e-20

   1. Initial program 62.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 62.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 62.7%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 62.7%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 62.7%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 62.7%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 62.7%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 62.7%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 62.7%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 64.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 64.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 64.0%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 64.0%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 64.0%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 64.0%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 64.0%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 64.0%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 64.0%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 63.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 63.6%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 63.6%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 63.6%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 63.6%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 44.3%

      \[\leadsto i \cdot \color{blue}{\left(b \cdot t\right)} \]

   if -3.7000000000000001e-20 < i < 1.1e-21

   1. Initial program 80.6%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 49.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 49.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 49.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 49.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 49.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 49.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 30.2%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]

   if 1.1e-21 < i

   1. Initial program 66.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 64.7%

      \[\leadsto \color{blue}{x \cdot \left(\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + y \cdot z\right) - a \cdot t\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]
   4. Step-by-step derivation

      1. associate--l+ 64.7%

         \[\leadsto x \cdot \color{blue}{\left(-1 \cdot \frac{b \cdot \left(c \cdot z - i \cdot t\right)}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

      2. associate-*r/ 64.7%

         \[\leadsto x \cdot \left(\color{blue}{\frac{-1 \cdot \left(b \cdot \left(c \cdot z - i \cdot t\right)\right)}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      3. *-commutative 64.7%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \color{blue}{\left(\left(c \cdot z - i \cdot t\right) \cdot b\right)}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      4. *-commutative 64.7%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(\color{blue}{z \cdot c} - i \cdot t\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      5. *-commutative 64.7%

         \[\leadsto x \cdot \left(\frac{-1 \cdot \left(\left(z \cdot c - \color{blue}{t \cdot i}\right) \cdot b\right)}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      6. associate-*r* 64.7%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-1 \cdot \left(z \cdot c - t \cdot i\right)\right) \cdot b}}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      7. neg-mul-1 64.7%

         \[\leadsto x \cdot \left(\frac{\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right)} \cdot b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      8. associate-/l* 63.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(-\left(z \cdot c - t \cdot i\right)\right) \cdot \frac{b}{x}} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      9. neg-sub0 63.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(z \cdot c - t \cdot i\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      10. *-commutative 63.3%

          \[\leadsto x \cdot \left(\left(0 - \left(\color{blue}{c \cdot z} - t \cdot i\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      11. *-commutative 63.3%

          \[\leadsto x \cdot \left(\left(0 - \left(c \cdot z - \color{blue}{i \cdot t}\right)\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      12. associate--r- 63.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - c \cdot z\right) + i \cdot t\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      13. neg-sub0 63.3%

          \[\leadsto x \cdot \left(\left(\color{blue}{\left(-c \cdot z\right)} + i \cdot t\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      14. +-commutative 63.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t + \left(-c \cdot z\right)\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

      15. sub-neg 63.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(i \cdot t - c \cdot z\right)} \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]

   5. Simplified 63.3%

      \[\leadsto \color{blue}{x \cdot \left(\left(i \cdot t - c \cdot z\right) \cdot \frac{b}{x} + \left(y \cdot z - a \cdot t\right)\right)} + j \cdot \left(c \cdot a - y \cdot i\right) \]

   6. Taylor expanded in i around inf 68.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) + b \cdot t\right)} \]
   7. Step-by-step derivation

      1. +-commutative 68.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t + -1 \cdot \left(j \cdot y\right)\right)} \]

      2. mul-1-neg 68.3%

         \[\leadsto i \cdot \left(b \cdot t + \color{blue}{\left(-j \cdot y\right)}\right) \]

      3. unsub-neg 68.3%

         \[\leadsto i \cdot \color{blue}{\left(b \cdot t - j \cdot y\right)} \]

   8. Simplified 68.3%

      \[\leadsto \color{blue}{i \cdot \left(b \cdot t - j \cdot y\right)} \]

   9. Taylor expanded in b around inf 38.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.7 \cdot 10^{-20}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq 1.1 \cdot 10^{-21}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 22.4% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.5%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 37.8%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 37.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 37.8%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 37.8%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 37.8%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

5. Simplified 37.8%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf 22.3%

   \[\leadsto a \cdot \color{blue}{\left(c \cdot j\right)} \]
7. Add Preprocessing

Developer target: 59.7% 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 2024101 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))