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

Percentage Accurate: 73.3% → 81.5%

Time: 38.1s

Alternatives: 25

Speedup: 0.5×

• 58.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 73.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 81.5% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(N[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $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[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $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 90.0%

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

   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 17.6%

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

   5. Simplified 21.6%

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

   6. Taylor expanded in a around 0 41.2%

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

   7. Taylor expanded in t around 0 47.7%

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

      1. distribute-lft-out 47.7%

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

      2. *-commutative 47.7%

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

   9. Simplified 47.7%

      \[\leadsto \color{blue}{-1 \cdot \left(b \cdot \left(z \cdot c\right) + y \cdot \left(i \cdot j - x \cdot z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.5%

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

Alternative 2: 54.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := t\_1 - i \cdot \left(y \cdot j\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+222}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-126}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-294}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+46}:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- (* y (- (* x z) (* i j))) (* b (* z c))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (- t_1 (* i (* y j)))))
   (if (<= b -2.8e+222)
     t_2
     (if (<= b -2.8e+195)
       (* i (- (* t b) (* y j)))
       (if (<= b -1.7e+65)
         t_2
         (if (<= b -4.2e-8)
           (* t (- (* b i) (* x a)))
           (if (<= b -1.3e-126)
             t_3
             (if (<= b 7e-294)
               (+ t_1 (* j (* a c)))
               (if (<= b 1.9e-46)
                 t_4
                 (if (<= b 5.1e-8)
                   t_3
                   (if (<= b 1.1e+46) t_4 (* b (- (* t i) (* z c))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (y * ((x * z) - (i * j))) - (b * (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = t_1 - (i * (y * j));
	double tmp;
	if (b <= -2.8e+222) {
		tmp = t_2;
	} else if (b <= -2.8e+195) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -1.7e+65) {
		tmp = t_2;
	} else if (b <= -4.2e-8) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= -1.3e-126) {
		tmp = t_3;
	} else if (b <= 7e-294) {
		tmp = t_1 + (j * (a * c));
	} else if (b <= 1.9e-46) {
		tmp = t_4;
	} else if (b <= 5.1e-8) {
		tmp = t_3;
	} else if (b <= 1.1e+46) {
		tmp = t_4;
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = (y * ((x * z) - (i * j))) - (b * (z * c))
    t_3 = j * ((a * c) - (y * i))
    t_4 = t_1 - (i * (y * j))
    if (b <= (-2.8d+222)) then
        tmp = t_2
    else if (b <= (-2.8d+195)) then
        tmp = i * ((t * b) - (y * j))
    else if (b <= (-1.7d+65)) then
        tmp = t_2
    else if (b <= (-4.2d-8)) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= (-1.3d-126)) then
        tmp = t_3
    else if (b <= 7d-294) then
        tmp = t_1 + (j * (a * c))
    else if (b <= 1.9d-46) then
        tmp = t_4
    else if (b <= 5.1d-8) then
        tmp = t_3
    else if (b <= 1.1d+46) then
        tmp = t_4
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = (y * ((x * z) - (i * j))) - (b * (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = t_1 - (i * (y * j));
	double tmp;
	if (b <= -2.8e+222) {
		tmp = t_2;
	} else if (b <= -2.8e+195) {
		tmp = i * ((t * b) - (y * j));
	} else if (b <= -1.7e+65) {
		tmp = t_2;
	} else if (b <= -4.2e-8) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= -1.3e-126) {
		tmp = t_3;
	} else if (b <= 7e-294) {
		tmp = t_1 + (j * (a * c));
	} else if (b <= 1.9e-46) {
		tmp = t_4;
	} else if (b <= 5.1e-8) {
		tmp = t_3;
	} else if (b <= 1.1e+46) {
		tmp = t_4;
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = (y * ((x * z) - (i * j))) - (b * (z * c))
	t_3 = j * ((a * c) - (y * i))
	t_4 = t_1 - (i * (y * j))
	tmp = 0
	if b <= -2.8e+222:
		tmp = t_2
	elif b <= -2.8e+195:
		tmp = i * ((t * b) - (y * j))
	elif b <= -1.7e+65:
		tmp = t_2
	elif b <= -4.2e-8:
		tmp = t * ((b * i) - (x * a))
	elif b <= -1.3e-126:
		tmp = t_3
	elif b <= 7e-294:
		tmp = t_1 + (j * (a * c))
	elif b <= 1.9e-46:
		tmp = t_4
	elif b <= 5.1e-8:
		tmp = t_3
	elif b <= 1.1e+46:
		tmp = t_4
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(t_1 - Float64(i * Float64(y * j)))
	tmp = 0.0
	if (b <= -2.8e+222)
		tmp = t_2;
	elseif (b <= -2.8e+195)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (b <= -1.7e+65)
		tmp = t_2;
	elseif (b <= -4.2e-8)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= -1.3e-126)
		tmp = t_3;
	elseif (b <= 7e-294)
		tmp = Float64(t_1 + Float64(j * Float64(a * c)));
	elseif (b <= 1.9e-46)
		tmp = t_4;
	elseif (b <= 5.1e-8)
		tmp = t_3;
	elseif (b <= 1.1e+46)
		tmp = t_4;
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = (y * ((x * z) - (i * j))) - (b * (z * c));
	t_3 = j * ((a * c) - (y * i));
	t_4 = t_1 - (i * (y * j));
	tmp = 0.0;
	if (b <= -2.8e+222)
		tmp = t_2;
	elseif (b <= -2.8e+195)
		tmp = i * ((t * b) - (y * j));
	elseif (b <= -1.7e+65)
		tmp = t_2;
	elseif (b <= -4.2e-8)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= -1.3e-126)
		tmp = t_3;
	elseif (b <= 7e-294)
		tmp = t_1 + (j * (a * c));
	elseif (b <= 1.9e-46)
		tmp = t_4;
	elseif (b <= 5.1e-8)
		tmp = t_3;
	elseif (b <= 1.1e+46)
		tmp = t_4;
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+222], t$95$2, If[LessEqual[b, -2.8e+195], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.7e+65], t$95$2, If[LessEqual[b, -4.2e-8], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.3e-126], t$95$3, If[LessEqual[b, 7e-294], N[(t$95$1 + N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.9e-46], t$95$4, If[LessEqual[b, 5.1e-8], t$95$3, If[LessEqual[b, 1.1e+46], t$95$4, N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if b < -2.8000000000000001e222 or -2.7999999999999998e195 < b < -1.7e65

   1. Initial program 62.2%

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

   3. Taylor expanded in y around -inf 62.2%

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

   5. Simplified 62.2%

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

   6. Taylor expanded in a around 0 67.3%

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

   7. Taylor expanded in t around 0 65.9%

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

      1. distribute-lft-out 65.9%

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

      2. *-commutative 65.9%

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

   9. Simplified 65.9%

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

   if -2.8000000000000001e222 < b < -2.7999999999999998e195

   1. Initial program 56.9%

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

   3. Taylor expanded in y around -inf 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in i around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. *-commutative 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. +-commutative 99.6%

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

      5. mul-1-neg 99.6%

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

      6. unsub-neg 99.6%

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

      7. *-commutative 99.6%

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

      8. *-commutative 99.6%

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

   8. Simplified 99.6%

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

   if -1.7e65 < b < -4.19999999999999989e-8

   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 y around -inf 74.7%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in t around -inf 83.3%

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

      1. mul-1-neg 83.3%

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

      2. distribute-rgt-neg-in 83.3%

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

      3. +-commutative 83.3%

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

      4. mul-1-neg 83.3%

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

      5. unsub-neg 83.3%

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

   8. Simplified 83.3%

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

   if -4.19999999999999989e-8 < b < -1.3e-126 or 1.8999999999999998e-46 < b < 5.10000000000000001e-8

   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 j around inf 66.4%

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

   if -1.3e-126 < b < 7.00000000000000064e-294

   1. Initial program 87.4%

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

   3. Taylor expanded in b around 0 87.4%

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

   4. Taylor expanded in a around inf 72.5%

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

   if 7.00000000000000064e-294 < b < 1.8999999999999998e-46 or 5.10000000000000001e-8 < b < 1.1e46

   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 b around 0 73.3%

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

   4. Taylor expanded in c around 0 71.5%

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

      1. +-commutative 71.5%

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

      2. *-commutative 71.5%

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

      3. mul-1-neg 71.5%

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

      4. unsub-neg 71.5%

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

      5. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   if 1.1e46 < b

   1. Initial program 80.3%

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

   3. Taylor expanded in b around inf 74.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+222}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{+195}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-126}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 7 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.9 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 5.1 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 29.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := j \cdot \left(a \cdot c\right)\\ t_3 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_4 := a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{if}\;b \leq -6 \cdot 10^{+221}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+206}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+79}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -0.95:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-113}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-211}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-242}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-46}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i)))
        (t_2 (* j (* a c)))
        (t_3 (* b (* z (- c))))
        (t_4 (* a (* t (- x)))))
   (if (<= b -6e+221)
     t_3
     (if (<= b -3.9e+206)
       t_1
       (if (<= b -2.55e+79)
         t_3
         (if (<= b -0.95)
           t_4
           (if (<= b -1.02e-113)
             t_2
             (if (<= b -4.5e-211)
               t_4
               (if (<= b 5.2e-242)
                 t_2
                 (if (<= b 2.8e-46)
                   t_4
                   (if (<= b 1.26e+39) (* j (* i (- y))) t_1)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = j * (a * c);
	double t_3 = b * (z * -c);
	double t_4 = a * (t * -x);
	double tmp;
	if (b <= -6e+221) {
		tmp = t_3;
	} else if (b <= -3.9e+206) {
		tmp = t_1;
	} else if (b <= -2.55e+79) {
		tmp = t_3;
	} else if (b <= -0.95) {
		tmp = t_4;
	} else if (b <= -1.02e-113) {
		tmp = t_2;
	} else if (b <= -4.5e-211) {
		tmp = t_4;
	} else if (b <= 5.2e-242) {
		tmp = t_2;
	} else if (b <= 2.8e-46) {
		tmp = t_4;
	} else if (b <= 1.26e+39) {
		tmp = j * (i * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = j * (a * c)
    t_3 = b * (z * -c)
    t_4 = a * (t * -x)
    if (b <= (-6d+221)) then
        tmp = t_3
    else if (b <= (-3.9d+206)) then
        tmp = t_1
    else if (b <= (-2.55d+79)) then
        tmp = t_3
    else if (b <= (-0.95d0)) then
        tmp = t_4
    else if (b <= (-1.02d-113)) then
        tmp = t_2
    else if (b <= (-4.5d-211)) then
        tmp = t_4
    else if (b <= 5.2d-242) then
        tmp = t_2
    else if (b <= 2.8d-46) then
        tmp = t_4
    else if (b <= 1.26d+39) then
        tmp = j * (i * -y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = j * (a * c);
	double t_3 = b * (z * -c);
	double t_4 = a * (t * -x);
	double tmp;
	if (b <= -6e+221) {
		tmp = t_3;
	} else if (b <= -3.9e+206) {
		tmp = t_1;
	} else if (b <= -2.55e+79) {
		tmp = t_3;
	} else if (b <= -0.95) {
		tmp = t_4;
	} else if (b <= -1.02e-113) {
		tmp = t_2;
	} else if (b <= -4.5e-211) {
		tmp = t_4;
	} else if (b <= 5.2e-242) {
		tmp = t_2;
	} else if (b <= 2.8e-46) {
		tmp = t_4;
	} else if (b <= 1.26e+39) {
		tmp = j * (i * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = j * (a * c)
	t_3 = b * (z * -c)
	t_4 = a * (t * -x)
	tmp = 0
	if b <= -6e+221:
		tmp = t_3
	elif b <= -3.9e+206:
		tmp = t_1
	elif b <= -2.55e+79:
		tmp = t_3
	elif b <= -0.95:
		tmp = t_4
	elif b <= -1.02e-113:
		tmp = t_2
	elif b <= -4.5e-211:
		tmp = t_4
	elif b <= 5.2e-242:
		tmp = t_2
	elif b <= 2.8e-46:
		tmp = t_4
	elif b <= 1.26e+39:
		tmp = j * (i * -y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(j * Float64(a * c))
	t_3 = Float64(b * Float64(z * Float64(-c)))
	t_4 = Float64(a * Float64(t * Float64(-x)))
	tmp = 0.0
	if (b <= -6e+221)
		tmp = t_3;
	elseif (b <= -3.9e+206)
		tmp = t_1;
	elseif (b <= -2.55e+79)
		tmp = t_3;
	elseif (b <= -0.95)
		tmp = t_4;
	elseif (b <= -1.02e-113)
		tmp = t_2;
	elseif (b <= -4.5e-211)
		tmp = t_4;
	elseif (b <= 5.2e-242)
		tmp = t_2;
	elseif (b <= 2.8e-46)
		tmp = t_4;
	elseif (b <= 1.26e+39)
		tmp = Float64(j * Float64(i * Float64(-y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = j * (a * c);
	t_3 = b * (z * -c);
	t_4 = a * (t * -x);
	tmp = 0.0;
	if (b <= -6e+221)
		tmp = t_3;
	elseif (b <= -3.9e+206)
		tmp = t_1;
	elseif (b <= -2.55e+79)
		tmp = t_3;
	elseif (b <= -0.95)
		tmp = t_4;
	elseif (b <= -1.02e-113)
		tmp = t_2;
	elseif (b <= -4.5e-211)
		tmp = t_4;
	elseif (b <= 5.2e-242)
		tmp = t_2;
	elseif (b <= 2.8e-46)
		tmp = t_4;
	elseif (b <= 1.26e+39)
		tmp = j * (i * -y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -6e+221], t$95$3, If[LessEqual[b, -3.9e+206], t$95$1, If[LessEqual[b, -2.55e+79], t$95$3, If[LessEqual[b, -0.95], t$95$4, If[LessEqual[b, -1.02e-113], t$95$2, If[LessEqual[b, -4.5e-211], t$95$4, If[LessEqual[b, 5.2e-242], t$95$2, If[LessEqual[b, 2.8e-46], t$95$4, If[LessEqual[b, 1.26e+39], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.0000000000000003e221 or -3.9e206 < b < -2.5500000000000001e79

   1. Initial program 60.2%

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

   3. Taylor expanded in y around -inf 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in a around 0 65.5%

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

   7. Taylor expanded in c around inf 49.0%

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

      1. mul-1-neg 49.0%

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

      2. *-commutative 49.0%

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

   9. Simplified 49.0%

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

   if -6.0000000000000003e221 < b < -3.9e206 or 1.26000000000000001e39 < b

   1. Initial program 79.2%

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

   3. Taylor expanded in y around -inf 82.5%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in a around 0 86.1%

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

   7. Taylor expanded in t around inf 54.3%

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

   if -2.5500000000000001e79 < b < -0.94999999999999996 or -1.02e-113 < b < -4.4999999999999999e-211 or 5.20000000000000034e-242 < b < 2.7999999999999998e-46

   1. Initial program 72.9%

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

   3. Taylor expanded in a around inf 53.3%

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

      1. +-commutative 53.3%

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

      2. mul-1-neg 53.3%

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

      3. unsub-neg 53.3%

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

      4. *-commutative 53.3%

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

   5. Simplified 53.3%

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

   6. Taylor expanded in j around 0 41.6%

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

      1. mul-1-neg 41.6%

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

      2. *-commutative 41.6%

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

      3. distribute-rgt-neg-in 41.6%

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

      4. distribute-rgt-neg-in 41.6%

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

   8. Simplified 41.6%

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

   if -0.94999999999999996 < b < -1.02e-113 or -4.4999999999999999e-211 < b < 5.20000000000000034e-242

   1. Initial program 75.5%

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

   3. Taylor expanded in j around inf 65.8%

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

   4. Taylor expanded in a around inf 43.7%

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

   if 2.7999999999999998e-46 < b < 1.26000000000000001e39

   1. Initial program 71.1%

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

   3. Taylor expanded in j around inf 67.0%

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

   4. Taylor expanded in a around 0 42.1%

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

      1. neg-mul-1 42.1%

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

      2. distribute-rgt-neg-in 42.1%

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

   6. Simplified 42.1%

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

4. Final simplification 46.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+221}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+206}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -0.95:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq -1.02 \cdot 10^{-113}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-211}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-242}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;b \leq 1.26 \cdot 10^{+39}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.75 \cdot 10^{+79}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -14.5:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-228}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -2.75e+79)
     t_3
     (if (<= b -14.5)
       t_2
       (if (<= b -2.5e-22)
         t_3
         (if (<= b -2.2e-153)
           t_1
           (if (<= b -3.1e-228)
             t_2
             (if (<= b 9e-236)
               t_1
               (if (<= b 2.5e-49) t_2 (if (<= b 7.8e+45) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.75e+79) {
		tmp = t_3;
	} else if (b <= -14.5) {
		tmp = t_2;
	} else if (b <= -2.5e-22) {
		tmp = t_3;
	} else if (b <= -2.2e-153) {
		tmp = t_1;
	} else if (b <= -3.1e-228) {
		tmp = t_2;
	} else if (b <= 9e-236) {
		tmp = t_1;
	} else if (b <= 2.5e-49) {
		tmp = t_2;
	} else if (b <= 7.8e+45) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = x * ((y * z) - (t * a))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-2.75d+79)) then
        tmp = t_3
    else if (b <= (-14.5d0)) then
        tmp = t_2
    else if (b <= (-2.5d-22)) then
        tmp = t_3
    else if (b <= (-2.2d-153)) then
        tmp = t_1
    else if (b <= (-3.1d-228)) then
        tmp = t_2
    else if (b <= 9d-236) then
        tmp = t_1
    else if (b <= 2.5d-49) then
        tmp = t_2
    else if (b <= 7.8d+45) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.75e+79) {
		tmp = t_3;
	} else if (b <= -14.5) {
		tmp = t_2;
	} else if (b <= -2.5e-22) {
		tmp = t_3;
	} else if (b <= -2.2e-153) {
		tmp = t_1;
	} else if (b <= -3.1e-228) {
		tmp = t_2;
	} else if (b <= 9e-236) {
		tmp = t_1;
	} else if (b <= 2.5e-49) {
		tmp = t_2;
	} else if (b <= 7.8e+45) {
		tmp = t_1;
	} 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 = x * ((y * z) - (t * a))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -2.75e+79:
		tmp = t_3
	elif b <= -14.5:
		tmp = t_2
	elif b <= -2.5e-22:
		tmp = t_3
	elif b <= -2.2e-153:
		tmp = t_1
	elif b <= -3.1e-228:
		tmp = t_2
	elif b <= 9e-236:
		tmp = t_1
	elif b <= 2.5e-49:
		tmp = t_2
	elif b <= 7.8e+45:
		tmp = t_1
	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(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.75e+79)
		tmp = t_3;
	elseif (b <= -14.5)
		tmp = t_2;
	elseif (b <= -2.5e-22)
		tmp = t_3;
	elseif (b <= -2.2e-153)
		tmp = t_1;
	elseif (b <= -3.1e-228)
		tmp = t_2;
	elseif (b <= 9e-236)
		tmp = t_1;
	elseif (b <= 2.5e-49)
		tmp = t_2;
	elseif (b <= 7.8e+45)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = x * ((y * z) - (t * a));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.75e+79)
		tmp = t_3;
	elseif (b <= -14.5)
		tmp = t_2;
	elseif (b <= -2.5e-22)
		tmp = t_3;
	elseif (b <= -2.2e-153)
		tmp = t_1;
	elseif (b <= -3.1e-228)
		tmp = t_2;
	elseif (b <= 9e-236)
		tmp = t_1;
	elseif (b <= 2.5e-49)
		tmp = t_2;
	elseif (b <= 7.8e+45)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.75e+79], t$95$3, If[LessEqual[b, -14.5], t$95$2, If[LessEqual[b, -2.5e-22], t$95$3, If[LessEqual[b, -2.2e-153], t$95$1, If[LessEqual[b, -3.1e-228], t$95$2, If[LessEqual[b, 9e-236], t$95$1, If[LessEqual[b, 2.5e-49], t$95$2, If[LessEqual[b, 7.8e+45], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.75000000000000003e79 or -14.5 < b < -2.49999999999999977e-22 or 7.7999999999999999e45 < b

   1. Initial program 69.5%

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

   3. Taylor expanded in b around inf 68.3%

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

   if -2.75000000000000003e79 < b < -14.5 or -2.20000000000000001e-153 < b < -3.0999999999999998e-228 or 8.99999999999999997e-236 < b < 2.4999999999999999e-49

   1. Initial program 74.0%

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

   3. Taylor expanded in x around inf 60.7%

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

   if -2.49999999999999977e-22 < b < -2.20000000000000001e-153 or -3.0999999999999998e-228 < b < 8.99999999999999997e-236 or 2.4999999999999999e-49 < b < 7.7999999999999999e45

   1. Initial program 74.3%

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

   3. Taylor expanded in j around inf 68.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.75 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -14.5:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -2.2 \cdot 10^{-153}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{-228}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{-49}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 29.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ t_3 := \left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{if}\;b \leq -3.6 \cdot 10^{+229}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+203}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-213}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-239}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-178}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* b (* z (- c)))) (t_3 (* (* t a) (- x))))
   (if (<= b -3.6e+229)
     t_2
     (if (<= b -1.8e+203)
       t_1
       (if (<= b -3.1e+79)
         t_2
         (if (<= b -1.65e-213)
           t_3
           (if (<= b 1.7e-239)
             (* j (* a c))
             (if (<= b 2.8e-178)
               t_3
               (if (<= b 3e-86)
                 (* z (* x y))
                 (if (<= b 2.25e+36) (* j (* i (- y))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = b * (z * -c);
	double t_3 = (t * a) * -x;
	double tmp;
	if (b <= -3.6e+229) {
		tmp = t_2;
	} else if (b <= -1.8e+203) {
		tmp = t_1;
	} else if (b <= -3.1e+79) {
		tmp = t_2;
	} else if (b <= -1.65e-213) {
		tmp = t_3;
	} else if (b <= 1.7e-239) {
		tmp = j * (a * c);
	} else if (b <= 2.8e-178) {
		tmp = t_3;
	} else if (b <= 3e-86) {
		tmp = z * (x * y);
	} else if (b <= 2.25e+36) {
		tmp = j * (i * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = b * (z * -c)
    t_3 = (t * a) * -x
    if (b <= (-3.6d+229)) then
        tmp = t_2
    else if (b <= (-1.8d+203)) then
        tmp = t_1
    else if (b <= (-3.1d+79)) then
        tmp = t_2
    else if (b <= (-1.65d-213)) then
        tmp = t_3
    else if (b <= 1.7d-239) then
        tmp = j * (a * c)
    else if (b <= 2.8d-178) then
        tmp = t_3
    else if (b <= 3d-86) then
        tmp = z * (x * y)
    else if (b <= 2.25d+36) then
        tmp = j * (i * -y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = b * (z * -c);
	double t_3 = (t * a) * -x;
	double tmp;
	if (b <= -3.6e+229) {
		tmp = t_2;
	} else if (b <= -1.8e+203) {
		tmp = t_1;
	} else if (b <= -3.1e+79) {
		tmp = t_2;
	} else if (b <= -1.65e-213) {
		tmp = t_3;
	} else if (b <= 1.7e-239) {
		tmp = j * (a * c);
	} else if (b <= 2.8e-178) {
		tmp = t_3;
	} else if (b <= 3e-86) {
		tmp = z * (x * y);
	} else if (b <= 2.25e+36) {
		tmp = j * (i * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = b * (z * -c)
	t_3 = (t * a) * -x
	tmp = 0
	if b <= -3.6e+229:
		tmp = t_2
	elif b <= -1.8e+203:
		tmp = t_1
	elif b <= -3.1e+79:
		tmp = t_2
	elif b <= -1.65e-213:
		tmp = t_3
	elif b <= 1.7e-239:
		tmp = j * (a * c)
	elif b <= 2.8e-178:
		tmp = t_3
	elif b <= 3e-86:
		tmp = z * (x * y)
	elif b <= 2.25e+36:
		tmp = j * (i * -y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(b * Float64(z * Float64(-c)))
	t_3 = Float64(Float64(t * a) * Float64(-x))
	tmp = 0.0
	if (b <= -3.6e+229)
		tmp = t_2;
	elseif (b <= -1.8e+203)
		tmp = t_1;
	elseif (b <= -3.1e+79)
		tmp = t_2;
	elseif (b <= -1.65e-213)
		tmp = t_3;
	elseif (b <= 1.7e-239)
		tmp = Float64(j * Float64(a * c));
	elseif (b <= 2.8e-178)
		tmp = t_3;
	elseif (b <= 3e-86)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 2.25e+36)
		tmp = Float64(j * Float64(i * Float64(-y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = b * (z * -c);
	t_3 = (t * a) * -x;
	tmp = 0.0;
	if (b <= -3.6e+229)
		tmp = t_2;
	elseif (b <= -1.8e+203)
		tmp = t_1;
	elseif (b <= -3.1e+79)
		tmp = t_2;
	elseif (b <= -1.65e-213)
		tmp = t_3;
	elseif (b <= 1.7e-239)
		tmp = j * (a * c);
	elseif (b <= 2.8e-178)
		tmp = t_3;
	elseif (b <= 3e-86)
		tmp = z * (x * y);
	elseif (b <= 2.25e+36)
		tmp = j * (i * -y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[b, -3.6e+229], t$95$2, If[LessEqual[b, -1.8e+203], t$95$1, If[LessEqual[b, -3.1e+79], t$95$2, If[LessEqual[b, -1.65e-213], t$95$3, If[LessEqual[b, 1.7e-239], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.8e-178], t$95$3, If[LessEqual[b, 3e-86], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.25e+36], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -3.59999999999999986e229 or -1.79999999999999991e203 < b < -3.0999999999999999e79

   1. Initial program 60.2%

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

   3. Taylor expanded in y around -inf 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in a around 0 65.5%

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

   7. Taylor expanded in c around inf 49.0%

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

      1. mul-1-neg 49.0%

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

      2. *-commutative 49.0%

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

   9. Simplified 49.0%

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

   if -3.59999999999999986e229 < b < -1.79999999999999991e203 or 2.24999999999999998e36 < b

   1. Initial program 79.2%

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

   3. Taylor expanded in y around -inf 82.5%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in a around 0 86.1%

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

   7. Taylor expanded in t around inf 54.3%

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

   if -3.0999999999999999e79 < b < -1.65000000000000016e-213 or 1.7e-239 < b < 2.80000000000000019e-178

   1. Initial program 73.6%

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

   3. Taylor expanded in y around -inf 65.9%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in x around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. +-commutative 54.6%

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

      3. *-commutative 54.6%

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

      4. sub-neg 54.6%

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

   8. Simplified 54.6%

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

   9. Taylor expanded in z around 0 43.1%

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

       1. mul-1-neg 43.1%

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

       2. distribute-lft-neg-out 43.1%

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

       3. *-commutative 43.1%

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

   11. Simplified 43.1%

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

   if -1.65000000000000016e-213 < b < 1.7e-239

   1. Initial program 76.1%

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

   3. Taylor expanded in j around inf 70.2%

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

   4. Taylor expanded in a around inf 46.8%

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

   if 2.80000000000000019e-178 < b < 3.0000000000000001e-86

   1. Initial program 71.2%

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

   3. Taylor expanded in y around -inf 55.1%

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

      1. mul-1-neg 55.1%

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

      2. *-commutative 55.1%

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

      3. distribute-rgt-neg-in 55.1%

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

      4. +-commutative 55.1%

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

      5. mul-1-neg 55.1%

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

      6. unsub-neg 55.1%

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

      7. *-commutative 55.1%

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

      8. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in j around 0 30.7%

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

      1. mul-1-neg 30.7%

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

      2. distribute-rgt-neg-in 30.7%

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

   8. Simplified 30.7%

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

   9. Taylor expanded in x around 0 34.0%

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

       1. *-commutative 34.0%

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

       2. *-commutative 34.0%

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

       3. associate-*r* 34.2%

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

   11. Simplified 34.2%

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

   if 3.0000000000000001e-86 < b < 2.24999999999999998e36

   1. Initial program 72.3%

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

   3. Taylor expanded in j around inf 56.9%

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

   4. Taylor expanded in a around 0 40.2%

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

      1. neg-mul-1 40.2%

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

      2. distribute-rgt-neg-in 40.2%

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

   6. Simplified 40.2%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+229}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -1.8 \cdot 10^{+203}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -1.65 \cdot 10^{-213}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-239}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-178}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-86}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.25 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 29.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_3 := \left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+223}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-204}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-178}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* z (* b (- c)))) (t_3 (* (* t a) (- x))))
   (if (<= b -2.2e+223)
     t_2
     (if (<= b -1.55e+204)
       t_1
       (if (<= b -2.7e+79)
         t_2
         (if (<= b -1.08e-204)
           t_3
           (if (<= b 2.8e-240)
             (* j (* a c))
             (if (<= b 3.7e-178)
               t_3
               (if (<= b 8.4e-88)
                 (* z (* x y))
                 (if (<= b 2.5e+36) (* j (* i (- y))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = z * (b * -c);
	double t_3 = (t * a) * -x;
	double tmp;
	if (b <= -2.2e+223) {
		tmp = t_2;
	} else if (b <= -1.55e+204) {
		tmp = t_1;
	} else if (b <= -2.7e+79) {
		tmp = t_2;
	} else if (b <= -1.08e-204) {
		tmp = t_3;
	} else if (b <= 2.8e-240) {
		tmp = j * (a * c);
	} else if (b <= 3.7e-178) {
		tmp = t_3;
	} else if (b <= 8.4e-88) {
		tmp = z * (x * y);
	} else if (b <= 2.5e+36) {
		tmp = j * (i * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = z * (b * -c)
    t_3 = (t * a) * -x
    if (b <= (-2.2d+223)) then
        tmp = t_2
    else if (b <= (-1.55d+204)) then
        tmp = t_1
    else if (b <= (-2.7d+79)) then
        tmp = t_2
    else if (b <= (-1.08d-204)) then
        tmp = t_3
    else if (b <= 2.8d-240) then
        tmp = j * (a * c)
    else if (b <= 3.7d-178) then
        tmp = t_3
    else if (b <= 8.4d-88) then
        tmp = z * (x * y)
    else if (b <= 2.5d+36) then
        tmp = j * (i * -y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = z * (b * -c);
	double t_3 = (t * a) * -x;
	double tmp;
	if (b <= -2.2e+223) {
		tmp = t_2;
	} else if (b <= -1.55e+204) {
		tmp = t_1;
	} else if (b <= -2.7e+79) {
		tmp = t_2;
	} else if (b <= -1.08e-204) {
		tmp = t_3;
	} else if (b <= 2.8e-240) {
		tmp = j * (a * c);
	} else if (b <= 3.7e-178) {
		tmp = t_3;
	} else if (b <= 8.4e-88) {
		tmp = z * (x * y);
	} else if (b <= 2.5e+36) {
		tmp = j * (i * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = z * (b * -c)
	t_3 = (t * a) * -x
	tmp = 0
	if b <= -2.2e+223:
		tmp = t_2
	elif b <= -1.55e+204:
		tmp = t_1
	elif b <= -2.7e+79:
		tmp = t_2
	elif b <= -1.08e-204:
		tmp = t_3
	elif b <= 2.8e-240:
		tmp = j * (a * c)
	elif b <= 3.7e-178:
		tmp = t_3
	elif b <= 8.4e-88:
		tmp = z * (x * y)
	elif b <= 2.5e+36:
		tmp = j * (i * -y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(z * Float64(b * Float64(-c)))
	t_3 = Float64(Float64(t * a) * Float64(-x))
	tmp = 0.0
	if (b <= -2.2e+223)
		tmp = t_2;
	elseif (b <= -1.55e+204)
		tmp = t_1;
	elseif (b <= -2.7e+79)
		tmp = t_2;
	elseif (b <= -1.08e-204)
		tmp = t_3;
	elseif (b <= 2.8e-240)
		tmp = Float64(j * Float64(a * c));
	elseif (b <= 3.7e-178)
		tmp = t_3;
	elseif (b <= 8.4e-88)
		tmp = Float64(z * Float64(x * y));
	elseif (b <= 2.5e+36)
		tmp = Float64(j * Float64(i * Float64(-y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = z * (b * -c);
	t_3 = (t * a) * -x;
	tmp = 0.0;
	if (b <= -2.2e+223)
		tmp = t_2;
	elseif (b <= -1.55e+204)
		tmp = t_1;
	elseif (b <= -2.7e+79)
		tmp = t_2;
	elseif (b <= -1.08e-204)
		tmp = t_3;
	elseif (b <= 2.8e-240)
		tmp = j * (a * c);
	elseif (b <= 3.7e-178)
		tmp = t_3;
	elseif (b <= 8.4e-88)
		tmp = z * (x * y);
	elseif (b <= 2.5e+36)
		tmp = j * (i * -y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[b, -2.2e+223], t$95$2, If[LessEqual[b, -1.55e+204], t$95$1, If[LessEqual[b, -2.7e+79], t$95$2, If[LessEqual[b, -1.08e-204], t$95$3, If[LessEqual[b, 2.8e-240], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e-178], t$95$3, If[LessEqual[b, 8.4e-88], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.5e+36], N[(j * N[(i * (-y)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.2e223 or -1.5500000000000001e204 < b < -2.7e79

   1. Initial program 60.2%

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

   3. Taylor expanded in y around -inf 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in a around 0 65.5%

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

   7. Taylor expanded in c around inf 49.0%

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

      1. associate-*r* 50.8%

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

      2. associate-*r* 50.8%

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

      3. *-commutative 50.8%

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

      4. mul-1-neg 50.8%

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

      5. distribute-rgt-neg-in 50.8%

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

   9. Simplified 50.8%

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

   if -2.2e223 < b < -1.5500000000000001e204 or 2.49999999999999988e36 < b

   1. Initial program 79.2%

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

   3. Taylor expanded in y around -inf 82.5%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in a around 0 86.1%

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

   7. Taylor expanded in t around inf 54.3%

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

   if -2.7e79 < b < -1.08e-204 or 2.7999999999999999e-240 < b < 3.70000000000000004e-178

   1. Initial program 73.6%

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

   3. Taylor expanded in y around -inf 65.9%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in x around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. +-commutative 54.6%

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

      3. *-commutative 54.6%

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

      4. sub-neg 54.6%

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

   8. Simplified 54.6%

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

   9. Taylor expanded in z around 0 43.1%

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

       1. mul-1-neg 43.1%

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

       2. distribute-lft-neg-out 43.1%

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

       3. *-commutative 43.1%

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

   11. Simplified 43.1%

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

   if -1.08e-204 < b < 2.7999999999999999e-240

   1. Initial program 76.1%

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

   3. Taylor expanded in j around inf 70.2%

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

   4. Taylor expanded in a around inf 46.8%

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

   if 3.70000000000000004e-178 < b < 8.3999999999999998e-88

   1. Initial program 71.2%

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

   3. Taylor expanded in y around -inf 55.1%

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

      1. mul-1-neg 55.1%

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

      2. *-commutative 55.1%

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

      3. distribute-rgt-neg-in 55.1%

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

      4. +-commutative 55.1%

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

      5. mul-1-neg 55.1%

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

      6. unsub-neg 55.1%

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

      7. *-commutative 55.1%

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

      8. *-commutative 55.1%

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

   5. Simplified 55.1%

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

   6. Taylor expanded in j around 0 30.7%

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

      1. mul-1-neg 30.7%

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

      2. distribute-rgt-neg-in 30.7%

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

   8. Simplified 30.7%

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

   9. Taylor expanded in x around 0 34.0%

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

       1. *-commutative 34.0%

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

       2. *-commutative 34.0%

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

       3. associate-*r* 34.2%

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

   11. Simplified 34.2%

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

   if 8.3999999999999998e-88 < b < 2.49999999999999988e36

   1. Initial program 72.3%

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

   3. Taylor expanded in j around inf 56.9%

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

   4. Taylor expanded in a around 0 40.2%

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

      1. neg-mul-1 40.2%

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

      2. distribute-rgt-neg-in 40.2%

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

   6. Simplified 40.2%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+223}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -1.55 \cdot 10^{+204}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -1.08 \cdot 10^{-204}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 2.8 \cdot 10^{-240}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-178}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 8.4 \cdot 10^{-88}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq 2.5 \cdot 10^{+36}:\\ \;\;\;\;j \cdot \left(i \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 29.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ t_3 := \left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+221}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -7 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-214}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-242}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-178}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* z (* b (- c)))) (t_3 (* (* t a) (- x))))
   (if (<= b -2.6e+221)
     t_2
     (if (<= b -7e+201)
       t_1
       (if (<= b -2.55e+79)
         t_2
         (if (<= b -4.2e-214)
           t_3
           (if (<= b 1.1e-242)
             (* j (* a c))
             (if (<= b 3.3e-178)
               t_3
               (if (<= b 7.2e-140)
                 (* a (* c j))
                 (if (<= b 1.6e+42) (* i (* j (- y))) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = z * (b * -c);
	double t_3 = (t * a) * -x;
	double tmp;
	if (b <= -2.6e+221) {
		tmp = t_2;
	} else if (b <= -7e+201) {
		tmp = t_1;
	} else if (b <= -2.55e+79) {
		tmp = t_2;
	} else if (b <= -4.2e-214) {
		tmp = t_3;
	} else if (b <= 1.1e-242) {
		tmp = j * (a * c);
	} else if (b <= 3.3e-178) {
		tmp = t_3;
	} else if (b <= 7.2e-140) {
		tmp = a * (c * j);
	} else if (b <= 1.6e+42) {
		tmp = i * (j * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = z * (b * -c)
    t_3 = (t * a) * -x
    if (b <= (-2.6d+221)) then
        tmp = t_2
    else if (b <= (-7d+201)) then
        tmp = t_1
    else if (b <= (-2.55d+79)) then
        tmp = t_2
    else if (b <= (-4.2d-214)) then
        tmp = t_3
    else if (b <= 1.1d-242) then
        tmp = j * (a * c)
    else if (b <= 3.3d-178) then
        tmp = t_3
    else if (b <= 7.2d-140) then
        tmp = a * (c * j)
    else if (b <= 1.6d+42) then
        tmp = i * (j * -y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = z * (b * -c);
	double t_3 = (t * a) * -x;
	double tmp;
	if (b <= -2.6e+221) {
		tmp = t_2;
	} else if (b <= -7e+201) {
		tmp = t_1;
	} else if (b <= -2.55e+79) {
		tmp = t_2;
	} else if (b <= -4.2e-214) {
		tmp = t_3;
	} else if (b <= 1.1e-242) {
		tmp = j * (a * c);
	} else if (b <= 3.3e-178) {
		tmp = t_3;
	} else if (b <= 7.2e-140) {
		tmp = a * (c * j);
	} else if (b <= 1.6e+42) {
		tmp = i * (j * -y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = z * (b * -c)
	t_3 = (t * a) * -x
	tmp = 0
	if b <= -2.6e+221:
		tmp = t_2
	elif b <= -7e+201:
		tmp = t_1
	elif b <= -2.55e+79:
		tmp = t_2
	elif b <= -4.2e-214:
		tmp = t_3
	elif b <= 1.1e-242:
		tmp = j * (a * c)
	elif b <= 3.3e-178:
		tmp = t_3
	elif b <= 7.2e-140:
		tmp = a * (c * j)
	elif b <= 1.6e+42:
		tmp = i * (j * -y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(z * Float64(b * Float64(-c)))
	t_3 = Float64(Float64(t * a) * Float64(-x))
	tmp = 0.0
	if (b <= -2.6e+221)
		tmp = t_2;
	elseif (b <= -7e+201)
		tmp = t_1;
	elseif (b <= -2.55e+79)
		tmp = t_2;
	elseif (b <= -4.2e-214)
		tmp = t_3;
	elseif (b <= 1.1e-242)
		tmp = Float64(j * Float64(a * c));
	elseif (b <= 3.3e-178)
		tmp = t_3;
	elseif (b <= 7.2e-140)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 1.6e+42)
		tmp = Float64(i * Float64(j * Float64(-y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = z * (b * -c);
	t_3 = (t * a) * -x;
	tmp = 0.0;
	if (b <= -2.6e+221)
		tmp = t_2;
	elseif (b <= -7e+201)
		tmp = t_1;
	elseif (b <= -2.55e+79)
		tmp = t_2;
	elseif (b <= -4.2e-214)
		tmp = t_3;
	elseif (b <= 1.1e-242)
		tmp = j * (a * c);
	elseif (b <= 3.3e-178)
		tmp = t_3;
	elseif (b <= 7.2e-140)
		tmp = a * (c * j);
	elseif (b <= 1.6e+42)
		tmp = i * (j * -y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t * a), $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[b, -2.6e+221], t$95$2, If[LessEqual[b, -7e+201], t$95$1, If[LessEqual[b, -2.55e+79], t$95$2, If[LessEqual[b, -4.2e-214], t$95$3, If[LessEqual[b, 1.1e-242], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e-178], t$95$3, If[LessEqual[b, 7.2e-140], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e+42], N[(i * N[(j * (-y)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.60000000000000004e221 or -7.0000000000000004e201 < b < -2.5500000000000001e79

   1. Initial program 60.2%

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

   3. Taylor expanded in y around -inf 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in a around 0 65.5%

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

   7. Taylor expanded in c around inf 49.0%

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

      1. associate-*r* 50.8%

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

      2. associate-*r* 50.8%

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

      3. *-commutative 50.8%

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

      4. mul-1-neg 50.8%

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

      5. distribute-rgt-neg-in 50.8%

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

   9. Simplified 50.8%

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

   if -2.60000000000000004e221 < b < -7.0000000000000004e201 or 1.60000000000000001e42 < b

   1. Initial program 79.2%

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

   3. Taylor expanded in y around -inf 82.5%

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

   5. Simplified 84.2%

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

   6. Taylor expanded in a around 0 86.1%

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

   7. Taylor expanded in t around inf 54.3%

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

   if -2.5500000000000001e79 < b < -4.19999999999999984e-214 or 1.10000000000000001e-242 < b < 3.3000000000000002e-178

   1. Initial program 73.6%

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

   3. Taylor expanded in y around -inf 65.9%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in x around inf 54.6%

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

      1. mul-1-neg 54.6%

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

      2. +-commutative 54.6%

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

      3. *-commutative 54.6%

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

      4. sub-neg 54.6%

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

   8. Simplified 54.6%

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

   9. Taylor expanded in z around 0 43.1%

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

       1. mul-1-neg 43.1%

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

       2. distribute-lft-neg-out 43.1%

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

       3. *-commutative 43.1%

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

   11. Simplified 43.1%

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

   if -4.19999999999999984e-214 < b < 1.10000000000000001e-242

   1. Initial program 76.1%

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

   3. Taylor expanded in j around inf 70.2%

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

   4. Taylor expanded in a around inf 46.8%

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

   if 3.3000000000000002e-178 < b < 7.2000000000000001e-140

   1. Initial program 72.9%

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

   3. Taylor expanded in a around inf 44.5%

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

      1. +-commutative 44.5%

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

      2. mul-1-neg 44.5%

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

      3. unsub-neg 44.5%

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

      4. *-commutative 44.5%

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

   5. Simplified 44.5%

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

   6. Taylor expanded in j around inf 44.0%

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

   if 7.2000000000000001e-140 < b < 1.60000000000000001e42

   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 y around -inf 49.1%

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

      1. mul-1-neg 49.1%

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

      2. *-commutative 49.1%

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

      3. distribute-rgt-neg-in 49.1%

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

      4. +-commutative 49.1%

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

      5. mul-1-neg 49.1%

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

      6. unsub-neg 49.1%

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

      7. *-commutative 49.1%

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

      8. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in j around inf 39.3%

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

      1. associate-*r* 39.3%

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

      2. neg-mul-1 39.3%

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

      3. *-commutative 39.3%

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

   8. Simplified 39.3%

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

4. Final simplification 47.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+221}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{+201}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -2.55 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -4.2 \cdot 10^{-214}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-242}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-178}:\\ \;\;\;\;\left(t \cdot a\right) \cdot \left(-x\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-140}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+42}:\\ \;\;\;\;i \cdot \left(j \cdot \left(-y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -2.45 \cdot 10^{+79}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-8}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-153}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-210}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* t (- (* b i) (* x a))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -2.45e+79)
     t_3
     (if (<= b -3.5e-8)
       t_2
       (if (<= b -4e-153)
         t_1
         (if (<= b -1.32e-210)
           t_2
           (if (<= b 1.4e-236)
             t_1
             (if (<= b 1.15e-48)
               (* x (- (* y z) (* t a)))
               (if (<= b 8.2e+45) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.45e+79) {
		tmp = t_3;
	} else if (b <= -3.5e-8) {
		tmp = t_2;
	} else if (b <= -4e-153) {
		tmp = t_1;
	} else if (b <= -1.32e-210) {
		tmp = t_2;
	} else if (b <= 1.4e-236) {
		tmp = t_1;
	} else if (b <= 1.15e-48) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 8.2e+45) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-2.45d+79)) then
        tmp = t_3
    else if (b <= (-3.5d-8)) then
        tmp = t_2
    else if (b <= (-4d-153)) then
        tmp = t_1
    else if (b <= (-1.32d-210)) then
        tmp = t_2
    else if (b <= 1.4d-236) then
        tmp = t_1
    else if (b <= 1.15d-48) then
        tmp = x * ((y * z) - (t * a))
    else if (b <= 8.2d+45) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -2.45e+79) {
		tmp = t_3;
	} else if (b <= -3.5e-8) {
		tmp = t_2;
	} else if (b <= -4e-153) {
		tmp = t_1;
	} else if (b <= -1.32e-210) {
		tmp = t_2;
	} else if (b <= 1.4e-236) {
		tmp = t_1;
	} else if (b <= 1.15e-48) {
		tmp = x * ((y * z) - (t * a));
	} else if (b <= 8.2e+45) {
		tmp = t_1;
	} 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 * ((b * i) - (x * a))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -2.45e+79:
		tmp = t_3
	elif b <= -3.5e-8:
		tmp = t_2
	elif b <= -4e-153:
		tmp = t_1
	elif b <= -1.32e-210:
		tmp = t_2
	elif b <= 1.4e-236:
		tmp = t_1
	elif b <= 1.15e-48:
		tmp = x * ((y * z) - (t * a))
	elif b <= 8.2e+45:
		tmp = t_1
	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 * Float64(Float64(b * i) - Float64(x * a)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -2.45e+79)
		tmp = t_3;
	elseif (b <= -3.5e-8)
		tmp = t_2;
	elseif (b <= -4e-153)
		tmp = t_1;
	elseif (b <= -1.32e-210)
		tmp = t_2;
	elseif (b <= 1.4e-236)
		tmp = t_1;
	elseif (b <= 1.15e-48)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (b <= 8.2e+45)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -2.45e+79)
		tmp = t_3;
	elseif (b <= -3.5e-8)
		tmp = t_2;
	elseif (b <= -4e-153)
		tmp = t_1;
	elseif (b <= -1.32e-210)
		tmp = t_2;
	elseif (b <= 1.4e-236)
		tmp = t_1;
	elseif (b <= 1.15e-48)
		tmp = x * ((y * z) - (t * a));
	elseif (b <= 8.2e+45)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.45e+79], t$95$3, If[LessEqual[b, -3.5e-8], t$95$2, If[LessEqual[b, -4e-153], t$95$1, If[LessEqual[b, -1.32e-210], t$95$2, If[LessEqual[b, 1.4e-236], t$95$1, If[LessEqual[b, 1.15e-48], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8.2e+45], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.4499999999999999e79 or 8.20000000000000025e45 < b

   1. Initial program 69.7%

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

   3. Taylor expanded in b around inf 68.4%

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

   if -2.4499999999999999e79 < b < -3.50000000000000024e-8 or -4.00000000000000016e-153 < b < -1.3200000000000001e-210

   1. Initial program 81.8%

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

   3. Taylor expanded in y around -inf 77.6%

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

   5. Simplified 77.6%

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

   6. Taylor expanded in t around -inf 77.2%

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

      1. mul-1-neg 77.2%

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

      2. distribute-rgt-neg-in 77.2%

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

      3. +-commutative 77.2%

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

      4. mul-1-neg 77.2%

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

      5. unsub-neg 77.2%

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

   8. Simplified 77.2%

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

   if -3.50000000000000024e-8 < b < -4.00000000000000016e-153 or -1.3200000000000001e-210 < b < 1.39999999999999993e-236 or 1.15e-48 < b < 8.20000000000000025e45

   1. Initial program 73.2%

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

   3. Taylor expanded in j around inf 65.4%

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

   if 1.39999999999999993e-236 < b < 1.15e-48

   1. Initial program 71.1%

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

   3. Taylor expanded in x around inf 59.4%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.45 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-153}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq -1.32 \cdot 10^{-210}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-236}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 58.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 - i \cdot \left(y \cdot j\right)\\ t_3 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{+79}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-296}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+44}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (- t_1 (* i (* y j))))
        (t_3 (* b (- (* t i) (* z c)))))
   (if (<= b -3e+79)
     t_3
     (if (<= b 4e-296)
       (+ t_1 (* j (* a c)))
       (if (<= b 1.65e-48)
         t_2
         (if (<= b 1.18e-8)
           (* j (- (* a c) (* y i)))
           (if (<= b 3.7e+44) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (i * (y * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3e+79) {
		tmp = t_3;
	} else if (b <= 4e-296) {
		tmp = t_1 + (j * (a * c));
	} else if (b <= 1.65e-48) {
		tmp = t_2;
	} else if (b <= 1.18e-8) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 3.7e+44) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = t_1 - (i * (y * j))
    t_3 = b * ((t * i) - (z * c))
    if (b <= (-3d+79)) then
        tmp = t_3
    else if (b <= 4d-296) then
        tmp = t_1 + (j * (a * c))
    else if (b <= 1.65d-48) then
        tmp = t_2
    else if (b <= 1.18d-8) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 3.7d+44) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = t_1 - (i * (y * j));
	double t_3 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3e+79) {
		tmp = t_3;
	} else if (b <= 4e-296) {
		tmp = t_1 + (j * (a * c));
	} else if (b <= 1.65e-48) {
		tmp = t_2;
	} else if (b <= 1.18e-8) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 3.7e+44) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = t_1 - (i * (y * j))
	t_3 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -3e+79:
		tmp = t_3
	elif b <= 4e-296:
		tmp = t_1 + (j * (a * c))
	elif b <= 1.65e-48:
		tmp = t_2
	elif b <= 1.18e-8:
		tmp = j * ((a * c) - (y * i))
	elif b <= 3.7e+44:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(t_1 - Float64(i * Float64(y * j)))
	t_3 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -3e+79)
		tmp = t_3;
	elseif (b <= 4e-296)
		tmp = Float64(t_1 + Float64(j * Float64(a * c)));
	elseif (b <= 1.65e-48)
		tmp = t_2;
	elseif (b <= 1.18e-8)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 3.7e+44)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = t_1 - (i * (y * j));
	t_3 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3e+79)
		tmp = t_3;
	elseif (b <= 4e-296)
		tmp = t_1 + (j * (a * c));
	elseif (b <= 1.65e-48)
		tmp = t_2;
	elseif (b <= 1.18e-8)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 3.7e+44)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+79], t$95$3, If[LessEqual[b, 4e-296], N[(t$95$1 + N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.65e-48], t$95$2, If[LessEqual[b, 1.18e-8], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+44], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.99999999999999974e79 or 3.7000000000000001e44 < b

   1. Initial program 69.7%

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

   3. Taylor expanded in b around inf 68.4%

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

   if -2.99999999999999974e79 < b < 4e-296

   1. Initial program 80.1%

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

   3. Taylor expanded in b around 0 74.8%

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

   4. Taylor expanded in a around inf 62.8%

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

   if 4e-296 < b < 1.65e-48 or 1.18e-8 < b < 3.7000000000000001e44

   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 b around 0 73.3%

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

   4. Taylor expanded in c around 0 71.5%

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

      1. +-commutative 71.5%

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

      2. *-commutative 71.5%

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

      3. mul-1-neg 71.5%

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

      4. unsub-neg 71.5%

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

      5. *-commutative 71.5%

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

   6. Simplified 71.5%

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

   if 1.65e-48 < b < 1.18e-8

   1. Initial program 50.4%

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

   3. Taylor expanded in j around inf 78.6%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-296}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;b \leq 1.65 \cdot 10^{-48}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;b \leq 1.18 \cdot 10^{-8}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 69.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right) + t\_2\\ \mathbf{if}\;b \leq -2.9 \cdot 10^{+208}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{+94}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq -2.95 \cdot 10^{-22}:\\ \;\;\;\;\left(t\_2 + y \cdot \left(x \cdot z\right)\right) + t\_3\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+33}:\\ \;\;\;\;t\_1 + t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (* j (- (* a c) (* y i))))
        (t_4 (+ (* y (- (* x z) (* i j))) t_2)))
   (if (<= b -2.9e+208)
     t_4
     (if (<= b -4.1e+94)
       (+ t_2 t_1)
       (if (<= b -2.95e-22)
         (+ (+ t_2 (* y (* x z))) t_3)
         (if (<= b 8.6e+33) (+ t_1 t_3) t_4))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = (y * ((x * z) - (i * j))) + t_2;
	double tmp;
	if (b <= -2.9e+208) {
		tmp = t_4;
	} else if (b <= -4.1e+94) {
		tmp = t_2 + t_1;
	} else if (b <= -2.95e-22) {
		tmp = (t_2 + (y * (x * z))) + t_3;
	} else if (b <= 8.6e+33) {
		tmp = t_1 + t_3;
	} else {
		tmp = t_4;
	}
	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 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    t_3 = j * ((a * c) - (y * i))
    t_4 = (y * ((x * z) - (i * j))) + t_2
    if (b <= (-2.9d+208)) then
        tmp = t_4
    else if (b <= (-4.1d+94)) then
        tmp = t_2 + t_1
    else if (b <= (-2.95d-22)) then
        tmp = (t_2 + (y * (x * z))) + t_3
    else if (b <= 8.6d+33) then
        tmp = t_1 + t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = j * ((a * c) - (y * i));
	double t_4 = (y * ((x * z) - (i * j))) + t_2;
	double tmp;
	if (b <= -2.9e+208) {
		tmp = t_4;
	} else if (b <= -4.1e+94) {
		tmp = t_2 + t_1;
	} else if (b <= -2.95e-22) {
		tmp = (t_2 + (y * (x * z))) + t_3;
	} else if (b <= 8.6e+33) {
		tmp = t_1 + t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((t * i) - (z * c))
	t_3 = j * ((a * c) - (y * i))
	t_4 = (y * ((x * z) - (i * j))) + t_2
	tmp = 0
	if b <= -2.9e+208:
		tmp = t_4
	elif b <= -4.1e+94:
		tmp = t_2 + t_1
	elif b <= -2.95e-22:
		tmp = (t_2 + (y * (x * z))) + t_3
	elif b <= 8.6e+33:
		tmp = t_1 + t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_4 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_2)
	tmp = 0.0
	if (b <= -2.9e+208)
		tmp = t_4;
	elseif (b <= -4.1e+94)
		tmp = Float64(t_2 + t_1);
	elseif (b <= -2.95e-22)
		tmp = Float64(Float64(t_2 + Float64(y * Float64(x * z))) + t_3);
	elseif (b <= 8.6e+33)
		tmp = Float64(t_1 + t_3);
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((t * i) - (z * c));
	t_3 = j * ((a * c) - (y * i));
	t_4 = (y * ((x * z) - (i * j))) + t_2;
	tmp = 0.0;
	if (b <= -2.9e+208)
		tmp = t_4;
	elseif (b <= -4.1e+94)
		tmp = t_2 + t_1;
	elseif (b <= -2.95e-22)
		tmp = (t_2 + (y * (x * z))) + t_3;
	elseif (b <= 8.6e+33)
		tmp = t_1 + t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[b, -2.9e+208], t$95$4, If[LessEqual[b, -4.1e+94], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, -2.95e-22], N[(N[(t$95$2 + N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision], If[LessEqual[b, 8.6e+33], N[(t$95$1 + t$95$3), $MachinePrecision], t$95$4]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.90000000000000008e208 or 8.60000000000000057e33 < b

   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 y around -inf 75.7%

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

   5. Simplified 77.0%

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

   6. Taylor expanded in a around 0 80.9%

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

   if -2.90000000000000008e208 < b < -4.10000000000000031e94

   1. Initial program 58.8%

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

   3. Taylor expanded in j around 0 76.1%

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

   if -4.10000000000000031e94 < b < -2.95000000000000004e-22

   1. Initial program 73.3%

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

   3. Taylor expanded in y around inf 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*l* 73.1%

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

   5. Simplified 73.1%

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

   if -2.95000000000000004e-22 < b < 8.60000000000000057e33

   1. Initial program 74.1%

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

   3. Taylor expanded in b around 0 76.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.9 \cdot 10^{+208}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{+94}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -2.95 \cdot 10^{-22}:\\ \;\;\;\;\left(b \cdot \left(t \cdot i - z \cdot c\right) + y \cdot \left(x \cdot z\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 8.6 \cdot 10^{+33}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+201}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -9.4 \cdot 10^{+80} \lor \neg \left(b \leq 2.2 \cdot 10^{+47}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -7.5e+229)
   (- (* y (- (* x z) (* i j))) (* b (* z c)))
   (if (<= b -1.45e+201)
     (* i (- (* t b) (* y j)))
     (if (or (<= b -9.4e+80) (not (<= b 2.2e+47)))
       (* b (- (* t i) (* z c)))
       (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7.5e+229) {
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	} else if (b <= -1.45e+201) {
		tmp = i * ((t * b) - (y * j));
	} else if ((b <= -9.4e+80) || !(b <= 2.2e+47)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-7.5d+229)) then
        tmp = (y * ((x * z) - (i * j))) - (b * (z * c))
    else if (b <= (-1.45d+201)) then
        tmp = i * ((t * b) - (y * j))
    else if ((b <= (-9.4d+80)) .or. (.not. (b <= 2.2d+47))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -7.5e+229) {
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	} else if (b <= -1.45e+201) {
		tmp = i * ((t * b) - (y * j));
	} else if ((b <= -9.4e+80) || !(b <= 2.2e+47)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -7.5e+229:
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c))
	elif b <= -1.45e+201:
		tmp = i * ((t * b) - (y * j))
	elif (b <= -9.4e+80) or not (b <= 2.2e+47):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -7.5e+229)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(z * c)));
	elseif (b <= -1.45e+201)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif ((b <= -9.4e+80) || !(b <= 2.2e+47))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -7.5e+229)
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	elseif (b <= -1.45e+201)
		tmp = i * ((t * b) - (y * j));
	elseif ((b <= -9.4e+80) || ~((b <= 2.2e+47)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -7.5e+229], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.45e+201], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -9.4e+80], N[Not[LessEqual[b, 2.2e+47]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -7.50000000000000021e229

   1. Initial program 57.4%

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

   3. Taylor expanded in y around -inf 61.8%

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

   5. Simplified 61.8%

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

   6. Taylor expanded in a around 0 66.6%

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

   7. Taylor expanded in t around 0 71.7%

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

      1. distribute-lft-out 71.7%

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

      2. *-commutative 71.7%

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

   9. Simplified 71.7%

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

   if -7.50000000000000021e229 < b < -1.4500000000000001e201

   1. Initial program 56.9%

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

   3. Taylor expanded in y around -inf 85.0%

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

   5. Simplified 85.0%

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

   6. Taylor expanded in i around -inf 99.6%

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

      1. mul-1-neg 99.6%

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

      2. *-commutative 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. +-commutative 99.6%

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

      5. mul-1-neg 99.6%

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

      6. unsub-neg 99.6%

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

      7. *-commutative 99.6%

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

      8. *-commutative 99.6%

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

   8. Simplified 99.6%

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

   if -1.4500000000000001e201 < b < -9.40000000000000019e80 or 2.1999999999999999e47 < b

   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 b around inf 71.6%

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

   if -9.40000000000000019e80 < b < 2.1999999999999999e47

   1. Initial program 74.1%

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

   3. Taylor expanded in b around 0 74.4%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.5 \cdot 10^{+229}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{+201}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;b \leq -9.4 \cdot 10^{+80} \lor \neg \left(b \leq 2.2 \cdot 10^{+47}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 68.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_3 := y \cdot \left(x \cdot z - i \cdot j\right) + t\_2\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+208}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+94}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-22} \lor \neg \left(b \leq 1.5 \cdot 10^{+34}\right):\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a))))
        (t_2 (* b (- (* t i) (* z c))))
        (t_3 (+ (* y (- (* x z) (* i j))) t_2)))
   (if (<= b -1.05e+208)
     t_3
     (if (<= b -4e+94)
       (+ t_2 t_1)
       (if (or (<= b -2.7e-22) (not (<= b 1.5e+34)))
         t_3
         (+ t_1 (* j (- (* a c) (* y i)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = (y * ((x * z) - (i * j))) + t_2;
	double tmp;
	if (b <= -1.05e+208) {
		tmp = t_3;
	} else if (b <= -4e+94) {
		tmp = t_2 + t_1;
	} else if ((b <= -2.7e-22) || !(b <= 1.5e+34)) {
		tmp = t_3;
	} else {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    t_3 = (y * ((x * z) - (i * j))) + t_2
    if (b <= (-1.05d+208)) then
        tmp = t_3
    else if (b <= (-4d+94)) then
        tmp = t_2 + t_1
    else if ((b <= (-2.7d-22)) .or. (.not. (b <= 1.5d+34))) then
        tmp = t_3
    else
        tmp = t_1 + (j * ((a * c) - (y * i)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double t_3 = (y * ((x * z) - (i * j))) + t_2;
	double tmp;
	if (b <= -1.05e+208) {
		tmp = t_3;
	} else if (b <= -4e+94) {
		tmp = t_2 + t_1;
	} else if ((b <= -2.7e-22) || !(b <= 1.5e+34)) {
		tmp = t_3;
	} else {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((t * i) - (z * c))
	t_3 = (y * ((x * z) - (i * j))) + t_2
	tmp = 0
	if b <= -1.05e+208:
		tmp = t_3
	elif b <= -4e+94:
		tmp = t_2 + t_1
	elif (b <= -2.7e-22) or not (b <= 1.5e+34):
		tmp = t_3
	else:
		tmp = t_1 + (j * ((a * c) - (y * i)))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_3 = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) + t_2)
	tmp = 0.0
	if (b <= -1.05e+208)
		tmp = t_3;
	elseif (b <= -4e+94)
		tmp = Float64(t_2 + t_1);
	elseif ((b <= -2.7e-22) || !(b <= 1.5e+34))
		tmp = t_3;
	else
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((t * i) - (z * c));
	t_3 = (y * ((x * z) - (i * j))) + t_2;
	tmp = 0.0;
	if (b <= -1.05e+208)
		tmp = t_3;
	elseif (b <= -4e+94)
		tmp = t_2 + t_1;
	elseif ((b <= -2.7e-22) || ~((b <= 1.5e+34)))
		tmp = t_3;
	else
		tmp = t_1 + (j * ((a * c) - (y * i)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[b, -1.05e+208], t$95$3, If[LessEqual[b, -4e+94], N[(t$95$2 + t$95$1), $MachinePrecision], If[Or[LessEqual[b, -2.7e-22], N[Not[LessEqual[b, 1.5e+34]], $MachinePrecision]], t$95$3, N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.0499999999999999e208 or -4.0000000000000001e94 < b < -2.7000000000000002e-22 or 1.50000000000000009e34 < b

   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 y around -inf 76.0%

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

   5. Simplified 77.9%

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

   6. Taylor expanded in a around 0 77.6%

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

   if -1.0499999999999999e208 < b < -4.0000000000000001e94

   1. Initial program 58.8%

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

   3. Taylor expanded in j around 0 76.1%

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

   if -2.7000000000000002e-22 < b < 1.50000000000000009e34

   1. Initial program 74.1%

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

   3. Taylor expanded in b around 0 76.8%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+208}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{+94}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq -2.7 \cdot 10^{-22} \lor \neg \left(b \leq 1.5 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 57.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -3 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-150}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))))
   (if (<= b -3e+79)
     t_1
     (if (<= b -6.5e-8)
       (* t (- (* b i) (* x a)))
       (if (<= b -7.6e-150)
         (* j (- (* a c) (* y i)))
         (if (<= b 2.65e+45)
           (+ (* x (- (* y z) (* t a))) (* j (* a 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3e+79) {
		tmp = t_1;
	} else if (b <= -6.5e-8) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= -7.6e-150) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 2.65e+45) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * 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 = b * ((t * i) - (z * c))
    if (b <= (-3d+79)) then
        tmp = t_1
    else if (b <= (-6.5d-8)) then
        tmp = t * ((b * i) - (x * a))
    else if (b <= (-7.6d-150)) then
        tmp = j * ((a * c) - (y * i))
    else if (b <= 2.65d+45) then
        tmp = (x * ((y * z) - (t * a))) + (j * (a * 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 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -3e+79) {
		tmp = t_1;
	} else if (b <= -6.5e-8) {
		tmp = t * ((b * i) - (x * a));
	} else if (b <= -7.6e-150) {
		tmp = j * ((a * c) - (y * i));
	} else if (b <= 2.65e+45) {
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c));
	} 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 <= -3e+79:
		tmp = t_1
	elif b <= -6.5e-8:
		tmp = t * ((b * i) - (x * a))
	elif b <= -7.6e-150:
		tmp = j * ((a * c) - (y * i))
	elif b <= 2.65e+45:
		tmp = (x * ((y * z) - (t * a))) + (j * (a * c))
	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 <= -3e+79)
		tmp = t_1;
	elseif (b <= -6.5e-8)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (b <= -7.6e-150)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (b <= 2.65e+45)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(a * 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 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -3e+79)
		tmp = t_1;
	elseif (b <= -6.5e-8)
		tmp = t * ((b * i) - (x * a));
	elseif (b <= -7.6e-150)
		tmp = j * ((a * c) - (y * i));
	elseif (b <= 2.65e+45)
		tmp = (x * ((y * z) - (t * a))) + (j * (a * 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[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3e+79], t$95$1, If[LessEqual[b, -6.5e-8], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.6e-150], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.65e+45], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.99999999999999974e79 or 2.64999999999999996e45 < b

   1. Initial program 69.7%

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

   3. Taylor expanded in b around inf 68.4%

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

   if -2.99999999999999974e79 < b < -6.49999999999999997e-8

   1. Initial program 75.2%

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

   3. Taylor expanded in y around -inf 74.8%

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

   5. Simplified 74.8%

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

   6. Taylor expanded in t around -inf 69.0%

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

      1. mul-1-neg 69.0%

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

      2. distribute-rgt-neg-in 69.0%

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

      3. +-commutative 69.0%

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

      4. mul-1-neg 69.0%

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

      5. unsub-neg 69.0%

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

   8. Simplified 69.0%

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

   if -6.49999999999999997e-8 < b < -7.5999999999999997e-150

   1. Initial program 75.6%

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

   3. Taylor expanded in j around inf 61.7%

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

   if -7.5999999999999997e-150 < b < 2.64999999999999996e45

   1. Initial program 73.2%

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

   3. Taylor expanded in b around 0 77.4%

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

   4. Taylor expanded in a around inf 62.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-8}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;b \leq -7.6 \cdot 10^{-150}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.65 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 65.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.4 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-22}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+46}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1.4e+219)
     (- (* y (- (* x z) (* i j))) (* b (* z c)))
     (if (<= b -1.25e-22)
       (+ t_2 t_1)
       (if (<= b 8.2e+46) (+ t_1 (* j (- (* a c) (* y i)))) t_2)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.4e+219) {
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	} else if (b <= -1.25e-22) {
		tmp = t_2 + t_1;
	} else if (b <= 8.2e+46) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1.4d+219)) then
        tmp = (y * ((x * z) - (i * j))) - (b * (z * c))
    else if (b <= (-1.25d-22)) then
        tmp = t_2 + t_1
    else if (b <= 8.2d+46) then
        tmp = t_1 + (j * ((a * c) - (y * i)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.4e+219) {
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	} else if (b <= -1.25e-22) {
		tmp = t_2 + t_1;
	} else if (b <= 8.2e+46) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.4e+219:
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c))
	elif b <= -1.25e-22:
		tmp = t_2 + t_1
	elif b <= 8.2e+46:
		tmp = t_1 + (j * ((a * c) - (y * i)))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.4e+219)
		tmp = Float64(Float64(y * Float64(Float64(x * z) - Float64(i * j))) - Float64(b * Float64(z * c)));
	elseif (b <= -1.25e-22)
		tmp = Float64(t_2 + t_1);
	elseif (b <= 8.2e+46)
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.4e+219)
		tmp = (y * ((x * z) - (i * j))) - (b * (z * c));
	elseif (b <= -1.25e-22)
		tmp = t_2 + t_1;
	elseif (b <= 8.2e+46)
		tmp = t_1 + (j * ((a * c) - (y * i)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.4e+219], N[(N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -1.25e-22], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[b, 8.2e+46], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.40000000000000008e219

   1. Initial program 52.4%

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

   3. Taylor expanded in y around -inf 65.1%

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

   5. Simplified 65.1%

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

   6. Taylor expanded in a around 0 69.4%

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

   7. Taylor expanded in t around 0 69.8%

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

      1. distribute-lft-out 69.8%

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

      2. *-commutative 69.8%

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

   9. Simplified 69.8%

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

   if -1.40000000000000008e219 < b < -1.24999999999999988e-22

   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 j around 0 68.4%

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

   if -1.24999999999999988e-22 < b < 8.19999999999999999e46

   1. Initial program 74.5%

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

   3. Taylor expanded in b around 0 77.1%

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

   if 8.19999999999999999e46 < b

   1. Initial program 80.3%

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

   3. Taylor expanded in b around inf 74.8%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.4 \cdot 10^{+219}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-22}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) + x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 26.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+170}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-8} \lor \neg \left(b \leq 1.32 \cdot 10^{+35}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= b -2.8e+253)
     (* x (* y z))
     (if (<= b -5.2e+170)
       t_1
       (if (<= b -4.7e+73)
         (* z (* x y))
         (if (or (<= b -8e-8) (not (<= b 1.32e+35))) t_1 (* j (* a c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (b <= -2.8e+253) {
		tmp = x * (y * z);
	} else if (b <= -5.2e+170) {
		tmp = t_1;
	} else if (b <= -4.7e+73) {
		tmp = z * (x * y);
	} else if ((b <= -8e-8) || !(b <= 1.32e+35)) {
		tmp = t_1;
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (b <= (-2.8d+253)) then
        tmp = x * (y * z)
    else if (b <= (-5.2d+170)) then
        tmp = t_1
    else if (b <= (-4.7d+73)) then
        tmp = z * (x * y)
    else if ((b <= (-8d-8)) .or. (.not. (b <= 1.32d+35))) then
        tmp = t_1
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (b <= -2.8e+253) {
		tmp = x * (y * z);
	} else if (b <= -5.2e+170) {
		tmp = t_1;
	} else if (b <= -4.7e+73) {
		tmp = z * (x * y);
	} else if ((b <= -8e-8) || !(b <= 1.32e+35)) {
		tmp = t_1;
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if b <= -2.8e+253:
		tmp = x * (y * z)
	elif b <= -5.2e+170:
		tmp = t_1
	elif b <= -4.7e+73:
		tmp = z * (x * y)
	elif (b <= -8e-8) or not (b <= 1.32e+35):
		tmp = t_1
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (b <= -2.8e+253)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -5.2e+170)
		tmp = t_1;
	elseif (b <= -4.7e+73)
		tmp = Float64(z * Float64(x * y));
	elseif ((b <= -8e-8) || !(b <= 1.32e+35))
		tmp = t_1;
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (b <= -2.8e+253)
		tmp = x * (y * z);
	elseif (b <= -5.2e+170)
		tmp = t_1;
	elseif (b <= -4.7e+73)
		tmp = z * (x * y);
	elseif ((b <= -8e-8) || ~((b <= 1.32e+35)))
		tmp = t_1;
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.8e+253], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.2e+170], t$95$1, If[LessEqual[b, -4.7e+73], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -8e-8], N[Not[LessEqual[b, 1.32e+35]], $MachinePrecision]], t$95$1, N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.8e253

   1. Initial program 47.1%

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

   3. Taylor expanded in y around -inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. *-commutative 60.7%

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

      3. distribute-rgt-neg-in 60.7%

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

      4. +-commutative 60.7%

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

      5. mul-1-neg 60.7%

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

      6. unsub-neg 60.7%

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

      7. *-commutative 60.7%

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

      8. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in j around 0 47.9%

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

      1. *-commutative 47.9%

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

   8. Simplified 47.9%

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

   if -2.8e253 < b < -5.1999999999999996e170 or -4.7000000000000002e73 < b < -8.0000000000000002e-8 or 1.31999999999999995e35 < b

   1. Initial program 75.5%

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

   3. Taylor expanded in y around -inf 77.7%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in a around 0 80.7%

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

   7. Taylor expanded in t around inf 48.7%

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

   if -5.1999999999999996e170 < b < -4.7000000000000002e73

   1. Initial program 69.1%

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

   3. Taylor expanded in y around -inf 33.9%

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

      1. mul-1-neg 33.9%

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

      2. *-commutative 33.9%

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

      3. distribute-rgt-neg-in 33.9%

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

      4. +-commutative 33.9%

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

      5. mul-1-neg 33.9%

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

      6. unsub-neg 33.9%

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

      7. *-commutative 33.9%

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

      8. *-commutative 33.9%

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

   5. Simplified 33.9%

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

   6. Taylor expanded in j around 0 27.5%

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

      1. mul-1-neg 27.5%

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

      2. distribute-rgt-neg-in 27.5%

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

   8. Simplified 27.5%

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

   9. Taylor expanded in x around 0 22.5%

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

       1. *-commutative 22.5%

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

       2. *-commutative 22.5%

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

       3. associate-*r* 27.1%

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

   11. Simplified 27.1%

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

   if -8.0000000000000002e-8 < b < 1.31999999999999995e35

   1. Initial program 73.3%

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

   3. Taylor expanded in j around inf 55.1%

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

   4. Taylor expanded in a around inf 34.1%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.8 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -5.2 \cdot 10^{+170}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -4.7 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;b \leq -8 \cdot 10^{-8} \lor \neg \left(b \leq 1.32 \cdot 10^{+35}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 26.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+169}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.38 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-7} \lor \neg \left(b \leq 3.3 \cdot 10^{+35}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= b -2.4e+253)
     (* x (* y z))
     (if (<= b -7.5e+169)
       t_1
       (if (<= b -1.38e+78)
         (* y (* x z))
         (if (or (<= b -1e-7) (not (<= b 3.3e+35))) t_1 (* j (* a c))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (b <= -2.4e+253) {
		tmp = x * (y * z);
	} else if (b <= -7.5e+169) {
		tmp = t_1;
	} else if (b <= -1.38e+78) {
		tmp = y * (x * z);
	} else if ((b <= -1e-7) || !(b <= 3.3e+35)) {
		tmp = t_1;
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (b <= (-2.4d+253)) then
        tmp = x * (y * z)
    else if (b <= (-7.5d+169)) then
        tmp = t_1
    else if (b <= (-1.38d+78)) then
        tmp = y * (x * z)
    else if ((b <= (-1d-7)) .or. (.not. (b <= 3.3d+35))) then
        tmp = t_1
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (b <= -2.4e+253) {
		tmp = x * (y * z);
	} else if (b <= -7.5e+169) {
		tmp = t_1;
	} else if (b <= -1.38e+78) {
		tmp = y * (x * z);
	} else if ((b <= -1e-7) || !(b <= 3.3e+35)) {
		tmp = t_1;
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if b <= -2.4e+253:
		tmp = x * (y * z)
	elif b <= -7.5e+169:
		tmp = t_1
	elif b <= -1.38e+78:
		tmp = y * (x * z)
	elif (b <= -1e-7) or not (b <= 3.3e+35):
		tmp = t_1
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (b <= -2.4e+253)
		tmp = Float64(x * Float64(y * z));
	elseif (b <= -7.5e+169)
		tmp = t_1;
	elseif (b <= -1.38e+78)
		tmp = Float64(y * Float64(x * z));
	elseif ((b <= -1e-7) || !(b <= 3.3e+35))
		tmp = t_1;
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (b <= -2.4e+253)
		tmp = x * (y * z);
	elseif (b <= -7.5e+169)
		tmp = t_1;
	elseif (b <= -1.38e+78)
		tmp = y * (x * z);
	elseif ((b <= -1e-7) || ~((b <= 3.3e+35)))
		tmp = t_1;
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.4e+253], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -7.5e+169], t$95$1, If[LessEqual[b, -1.38e+78], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1e-7], N[Not[LessEqual[b, 3.3e+35]], $MachinePrecision]], t$95$1, N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.39999999999999991e253

   1. Initial program 47.1%

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

   3. Taylor expanded in y around -inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. *-commutative 60.7%

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

      3. distribute-rgt-neg-in 60.7%

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

      4. +-commutative 60.7%

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

      5. mul-1-neg 60.7%

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

      6. unsub-neg 60.7%

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

      7. *-commutative 60.7%

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

      8. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in j around 0 47.9%

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

      1. *-commutative 47.9%

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

   8. Simplified 47.9%

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

   if -2.39999999999999991e253 < b < -7.49999999999999992e169 or -1.37999999999999992e78 < b < -9.9999999999999995e-8 or 3.3000000000000002e35 < b

   1. Initial program 75.5%

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

   3. Taylor expanded in y around -inf 77.7%

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

   5. Simplified 78.8%

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

   6. Taylor expanded in a around 0 80.7%

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

   7. Taylor expanded in t around inf 48.7%

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

   if -7.49999999999999992e169 < b < -1.37999999999999992e78

   1. Initial program 69.1%

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

   3. Taylor expanded in y around -inf 33.9%

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

      1. mul-1-neg 33.9%

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

      2. *-commutative 33.9%

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

      3. distribute-rgt-neg-in 33.9%

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

      4. +-commutative 33.9%

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

      5. mul-1-neg 33.9%

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

      6. unsub-neg 33.9%

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

      7. *-commutative 33.9%

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

      8. *-commutative 33.9%

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

   5. Simplified 33.9%

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

   6. Taylor expanded in j around 0 27.5%

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

      1. mul-1-neg 27.5%

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

      2. distribute-rgt-neg-in 27.5%

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

   8. Simplified 27.5%

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

   9. Taylor expanded in x around 0 22.5%

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

       1. *-commutative 22.5%

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

       2. associate-*r* 27.5%

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

       3. *-commutative 27.5%

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

   11. Simplified 27.5%

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

   if -9.9999999999999995e-8 < b < 3.3000000000000002e35

   1. Initial program 73.3%

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

   3. Taylor expanded in j around inf 55.1%

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

   4. Taylor expanded in a around inf 34.1%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{+169}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -1.38 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;b \leq -1 \cdot 10^{-7} \lor \neg \left(b \leq 3.3 \cdot 10^{+35}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 40.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+223}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* z (* b (- c)))))
   (if (<= b -1.5e+223)
     t_2
     (if (<= b -6.5e+201)
       t_1
       (if (<= b -3.1e+79)
         t_2
         (if (<= b 1.55e+35) (* a (- (* c j) (* x t))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = z * (b * -c);
	double tmp;
	if (b <= -1.5e+223) {
		tmp = t_2;
	} else if (b <= -6.5e+201) {
		tmp = t_1;
	} else if (b <= -3.1e+79) {
		tmp = t_2;
	} else if (b <= 1.55e+35) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = z * (b * -c)
    if (b <= (-1.5d+223)) then
        tmp = t_2
    else if (b <= (-6.5d+201)) then
        tmp = t_1
    else if (b <= (-3.1d+79)) then
        tmp = t_2
    else if (b <= 1.55d+35) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = z * (b * -c);
	double tmp;
	if (b <= -1.5e+223) {
		tmp = t_2;
	} else if (b <= -6.5e+201) {
		tmp = t_1;
	} else if (b <= -3.1e+79) {
		tmp = t_2;
	} else if (b <= 1.55e+35) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = z * (b * -c)
	tmp = 0
	if b <= -1.5e+223:
		tmp = t_2
	elif b <= -6.5e+201:
		tmp = t_1
	elif b <= -3.1e+79:
		tmp = t_2
	elif b <= 1.55e+35:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(z * Float64(b * Float64(-c)))
	tmp = 0.0
	if (b <= -1.5e+223)
		tmp = t_2;
	elseif (b <= -6.5e+201)
		tmp = t_1;
	elseif (b <= -3.1e+79)
		tmp = t_2;
	elseif (b <= 1.55e+35)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = z * (b * -c);
	tmp = 0.0;
	if (b <= -1.5e+223)
		tmp = t_2;
	elseif (b <= -6.5e+201)
		tmp = t_1;
	elseif (b <= -3.1e+79)
		tmp = t_2;
	elseif (b <= 1.55e+35)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(b * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.5e+223], t$95$2, If[LessEqual[b, -6.5e+201], t$95$1, If[LessEqual[b, -3.1e+79], t$95$2, If[LessEqual[b, 1.55e+35], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.50000000000000001e223 or -6.5000000000000004e201 < b < -3.0999999999999999e79

   1. Initial program 60.2%

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

   3. Taylor expanded in y around -inf 60.2%

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

   5. Simplified 60.2%

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

   6. Taylor expanded in a around 0 65.5%

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

   7. Taylor expanded in c around inf 49.0%

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

      1. associate-*r* 50.8%

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

      2. associate-*r* 50.8%

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

      3. *-commutative 50.8%

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

      4. mul-1-neg 50.8%

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

      5. distribute-rgt-neg-in 50.8%

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

   9. Simplified 50.8%

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

   if -1.50000000000000001e223 < b < -6.5000000000000004e201 or 1.54999999999999993e35 < b

   1. Initial program 79.5%

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

   3. Taylor expanded in y around -inf 81.1%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in a around 0 86.3%

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

   7. Taylor expanded in t around inf 53.5%

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

   if -3.0999999999999999e79 < b < 1.54999999999999993e35

   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 a around inf 50.0%

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

      1. +-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

      4. *-commutative 50.0%

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

   5. Simplified 50.0%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.5 \cdot 10^{+223}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{+201}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -3.1 \cdot 10^{+79}:\\ \;\;\;\;z \cdot \left(b \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+35}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{if}\;b \leq -1.04 \cdot 10^{+80}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-256}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+45}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* b (- (* t i) (* z c)))))
   (if (<= b -1.04e+80)
     t_2
     (if (<= b 1.8e-256)
       t_1
       (if (<= b 2.6e-46)
         (* a (- (* c j) (* x t)))
         (if (<= b 3.3e+45) 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 * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.04e+80) {
		tmp = t_2;
	} else if (b <= 1.8e-256) {
		tmp = t_1;
	} else if (b <= 2.6e-46) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 3.3e+45) {
		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 = j * ((a * c) - (y * i))
    t_2 = b * ((t * i) - (z * c))
    if (b <= (-1.04d+80)) then
        tmp = t_2
    else if (b <= 1.8d-256) then
        tmp = t_1
    else if (b <= 2.6d-46) then
        tmp = a * ((c * j) - (x * t))
    else if (b <= 3.3d+45) 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 = j * ((a * c) - (y * i));
	double t_2 = b * ((t * i) - (z * c));
	double tmp;
	if (b <= -1.04e+80) {
		tmp = t_2;
	} else if (b <= 1.8e-256) {
		tmp = t_1;
	} else if (b <= 2.6e-46) {
		tmp = a * ((c * j) - (x * t));
	} else if (b <= 3.3e+45) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = b * ((t * i) - (z * c))
	tmp = 0
	if b <= -1.04e+80:
		tmp = t_2
	elif b <= 1.8e-256:
		tmp = t_1
	elif b <= 2.6e-46:
		tmp = a * ((c * j) - (x * t))
	elif b <= 3.3e+45:
		tmp = 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(a * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	tmp = 0.0
	if (b <= -1.04e+80)
		tmp = t_2;
	elseif (b <= 1.8e-256)
		tmp = t_1;
	elseif (b <= 2.6e-46)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (b <= 3.3e+45)
		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 = j * ((a * c) - (y * i));
	t_2 = b * ((t * i) - (z * c));
	tmp = 0.0;
	if (b <= -1.04e+80)
		tmp = t_2;
	elseif (b <= 1.8e-256)
		tmp = t_1;
	elseif (b <= 2.6e-46)
		tmp = a * ((c * j) - (x * t));
	elseif (b <= 3.3e+45)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.04e+80], t$95$2, If[LessEqual[b, 1.8e-256], t$95$1, If[LessEqual[b, 2.6e-46], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.3e+45], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.04000000000000006e80 or 3.3000000000000001e45 < b

   1. Initial program 69.4%

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

   3. Taylor expanded in b around inf 69.0%

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

   if -1.04000000000000006e80 < b < 1.8000000000000001e-256 or 2.6000000000000002e-46 < b < 3.3000000000000001e45

   1. Initial program 78.1%

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

   3. Taylor expanded in j around inf 56.6%

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

   if 1.8000000000000001e-256 < b < 2.6000000000000002e-46

   1. Initial program 65.8%

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

   3. Taylor expanded in a around inf 54.0%

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

      1. +-commutative 54.0%

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

      2. mul-1-neg 54.0%

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

      3. unsub-neg 54.0%

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

      4. *-commutative 54.0%

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

   5. Simplified 54.0%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.04 \cdot 10^{+80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{-256}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-46}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{+45}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 29.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{if}\;b \leq -3.4 \cdot 10^{+229}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+204}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+79}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+33}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* b (* z (- c)))))
   (if (<= b -3.4e+229)
     t_2
     (if (<= b -1.05e+204)
       t_1
       (if (<= b -1.6e+79) t_2 (if (<= b 5.5e+33) (* j (* a 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 = b * (t * i);
	double t_2 = b * (z * -c);
	double tmp;
	if (b <= -3.4e+229) {
		tmp = t_2;
	} else if (b <= -1.05e+204) {
		tmp = t_1;
	} else if (b <= -1.6e+79) {
		tmp = t_2;
	} else if (b <= 5.5e+33) {
		tmp = j * (a * 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) :: t_2
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = b * (z * -c)
    if (b <= (-3.4d+229)) then
        tmp = t_2
    else if (b <= (-1.05d+204)) then
        tmp = t_1
    else if (b <= (-1.6d+79)) then
        tmp = t_2
    else if (b <= 5.5d+33) then
        tmp = j * (a * 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 = b * (t * i);
	double t_2 = b * (z * -c);
	double tmp;
	if (b <= -3.4e+229) {
		tmp = t_2;
	} else if (b <= -1.05e+204) {
		tmp = t_1;
	} else if (b <= -1.6e+79) {
		tmp = t_2;
	} else if (b <= 5.5e+33) {
		tmp = j * (a * c);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = b * (z * -c)
	tmp = 0
	if b <= -3.4e+229:
		tmp = t_2
	elif b <= -1.05e+204:
		tmp = t_1
	elif b <= -1.6e+79:
		tmp = t_2
	elif b <= 5.5e+33:
		tmp = j * (a * c)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(b * Float64(z * Float64(-c)))
	tmp = 0.0
	if (b <= -3.4e+229)
		tmp = t_2;
	elseif (b <= -1.05e+204)
		tmp = t_1;
	elseif (b <= -1.6e+79)
		tmp = t_2;
	elseif (b <= 5.5e+33)
		tmp = Float64(j * Float64(a * 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 = b * (t * i);
	t_2 = b * (z * -c);
	tmp = 0.0;
	if (b <= -3.4e+229)
		tmp = t_2;
	elseif (b <= -1.05e+204)
		tmp = t_1;
	elseif (b <= -1.6e+79)
		tmp = t_2;
	elseif (b <= 5.5e+33)
		tmp = j * (a * 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[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -3.4e+229], t$95$2, If[LessEqual[b, -1.05e+204], t$95$1, If[LessEqual[b, -1.6e+79], t$95$2, If[LessEqual[b, 5.5e+33], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.4000000000000001e229 or -1.05e204 < b < -1.60000000000000001e79

   1. Initial program 59.1%

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

   3. Taylor expanded in y around -inf 59.1%

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

   5. Simplified 59.1%

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

   6. Taylor expanded in a around 0 64.4%

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

   7. Taylor expanded in c around inf 48.2%

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

      1. mul-1-neg 48.2%

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

      2. *-commutative 48.2%

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

   9. Simplified 48.2%

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

   if -3.4000000000000001e229 < b < -1.05e204 or 5.5000000000000006e33 < b

   1. Initial program 79.5%

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

   3. Taylor expanded in y around -inf 81.1%

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

   5. Simplified 82.8%

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

   6. Taylor expanded in a around 0 86.3%

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

   7. Taylor expanded in t around inf 53.5%

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

   if -1.60000000000000001e79 < b < 5.5000000000000006e33

   1. Initial program 74.0%

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

   3. Taylor expanded in j around inf 52.9%

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

   4. Taylor expanded in a around inf 32.1%

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

4. Final simplification 40.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.4 \cdot 10^{+229}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{+204}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -1.6 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{+33}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 29.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-92}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -1.1e-57)
   (* a (* t (- x)))
   (if (<= a 1.36e-92)
     (* t (* b i))
     (if (<= a 1.02e+100) (* b (* z (- c))) (* j (* a c))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.1e-57) {
		tmp = a * (t * -x);
	} else if (a <= 1.36e-92) {
		tmp = t * (b * i);
	} else if (a <= 1.02e+100) {
		tmp = b * (z * -c);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (a <= (-1.1d-57)) then
        tmp = a * (t * -x)
    else if (a <= 1.36d-92) then
        tmp = t * (b * i)
    else if (a <= 1.02d+100) then
        tmp = b * (z * -c)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (a <= -1.1e-57) {
		tmp = a * (t * -x);
	} else if (a <= 1.36e-92) {
		tmp = t * (b * i);
	} else if (a <= 1.02e+100) {
		tmp = b * (z * -c);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -1.1e-57:
		tmp = a * (t * -x)
	elif a <= 1.36e-92:
		tmp = t * (b * i)
	elif a <= 1.02e+100:
		tmp = b * (z * -c)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -1.1e-57)
		tmp = Float64(a * Float64(t * Float64(-x)));
	elseif (a <= 1.36e-92)
		tmp = Float64(t * Float64(b * i));
	elseif (a <= 1.02e+100)
		tmp = Float64(b * Float64(z * Float64(-c)));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (a <= -1.1e-57)
		tmp = a * (t * -x);
	elseif (a <= 1.36e-92)
		tmp = t * (b * i);
	elseif (a <= 1.02e+100)
		tmp = b * (z * -c);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -1.1e-57], N[(a * N[(t * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.36e-92], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+100], N[(b * N[(z * (-c)), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.09999999999999999e-57

   1. Initial program 63.3%

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

   3. Taylor expanded in a around inf 56.5%

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

      1. +-commutative 56.5%

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

      2. mul-1-neg 56.5%

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

      3. unsub-neg 56.5%

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

      4. *-commutative 56.5%

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

   5. Simplified 56.5%

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

   6. Taylor expanded in j around 0 37.3%

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

      1. mul-1-neg 37.3%

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

      2. *-commutative 37.3%

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

      3. distribute-rgt-neg-in 37.3%

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

      4. distribute-rgt-neg-in 37.3%

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

   8. Simplified 37.3%

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

   if -1.09999999999999999e-57 < a < 1.36e-92

   1. Initial program 78.1%

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

   3. Taylor expanded in y around -inf 67.5%

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

   5. Simplified 67.5%

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

   6. Taylor expanded in a around 0 70.1%

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

   7. Taylor expanded in t around inf 31.8%

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

      1. associate-*r* 33.9%

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

   9. Simplified 33.9%

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

   if 1.36e-92 < a < 1.0199999999999999e100

   1. Initial program 76.3%

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

   3. Taylor expanded in y around -inf 78.3%

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

   5. Simplified 78.3%

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

   6. Taylor expanded in a around 0 65.6%

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

   7. Taylor expanded in c around inf 31.7%

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

      1. mul-1-neg 31.7%

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

      2. *-commutative 31.7%

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

   9. Simplified 31.7%

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

   if 1.0199999999999999e100 < a

   1. Initial program 70.8%

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

   3. Taylor expanded in j around inf 58.8%

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

   4. Taylor expanded in a around inf 48.6%

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

4. Final simplification 37.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.1 \cdot 10^{-57}:\\ \;\;\;\;a \cdot \left(t \cdot \left(-x\right)\right)\\ \mathbf{elif}\;a \leq 1.36 \cdot 10^{-92}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+100}:\\ \;\;\;\;b \cdot \left(z \cdot \left(-c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 27.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-7} \lor \neg \left(b \leq 1.2 \cdot 10^{+35}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2.6e+253)
   (* x (* y z))
   (if (or (<= b -1.1e-7) (not (<= b 1.2e+35))) (* b (* t i)) (* j (* a c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.6e+253) {
		tmp = x * (y * z);
	} else if ((b <= -1.1e-7) || !(b <= 1.2e+35)) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-2.6d+253)) then
        tmp = x * (y * z)
    else if ((b <= (-1.1d-7)) .or. (.not. (b <= 1.2d+35))) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.6e+253) {
		tmp = x * (y * z);
	} else if ((b <= -1.1e-7) || !(b <= 1.2e+35)) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -2.6e+253:
		tmp = x * (y * z)
	elif (b <= -1.1e-7) or not (b <= 1.2e+35):
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -2.6e+253)
		tmp = Float64(x * Float64(y * z));
	elseif ((b <= -1.1e-7) || !(b <= 1.2e+35))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -2.6e+253)
		tmp = x * (y * z);
	elseif ((b <= -1.1e-7) || ~((b <= 1.2e+35)))
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -2.6e+253], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, -1.1e-7], N[Not[LessEqual[b, 1.2e+35]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6e253

   1. Initial program 47.1%

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

   3. Taylor expanded in y around -inf 60.7%

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

      1. mul-1-neg 60.7%

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

      2. *-commutative 60.7%

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

      3. distribute-rgt-neg-in 60.7%

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

      4. +-commutative 60.7%

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

      5. mul-1-neg 60.7%

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

      6. unsub-neg 60.7%

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

      7. *-commutative 60.7%

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

      8. *-commutative 60.7%

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

   5. Simplified 60.7%

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

   6. Taylor expanded in j around 0 47.9%

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

      1. *-commutative 47.9%

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

   8. Simplified 47.9%

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

   if -2.6e253 < b < -1.1000000000000001e-7 or 1.20000000000000007e35 < b

   1. Initial program 73.9%

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

   3. Taylor expanded in y around -inf 73.8%

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

   5. Simplified 74.7%

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

   6. Taylor expanded in a around 0 76.0%

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

   7. Taylor expanded in t around inf 39.3%

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

   if -1.1000000000000001e-7 < b < 1.20000000000000007e35

   1. Initial program 73.3%

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

   3. Taylor expanded in j around inf 55.1%

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

   4. Taylor expanded in a around inf 34.1%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+253}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-7} \lor \neg \left(b \leq 1.2 \cdot 10^{+35}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 51.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+79} \lor \neg \left(b \leq 1.7 \cdot 10^{+35}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -2.5e+79) (not (<= b 1.7e+35)))
   (* b (- (* t i) (* z c)))
   (* a (- (* c j) (* x t)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.5e+79) || !(b <= 1.7e+35)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-2.5d+79)) .or. (.not. (b <= 1.7d+35))) then
        tmp = b * ((t * i) - (z * c))
    else
        tmp = a * ((c * j) - (x * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -2.5e+79) || !(b <= 1.7e+35)) {
		tmp = b * ((t * i) - (z * c));
	} else {
		tmp = a * ((c * j) - (x * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -2.5e+79) or not (b <= 1.7e+35):
		tmp = b * ((t * i) - (z * c))
	else:
		tmp = a * ((c * j) - (x * t))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -2.5e+79) || !(b <= 1.7e+35))
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	else
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -2.5e+79) || ~((b <= 1.7e+35)))
		tmp = b * ((t * i) - (z * c));
	else
		tmp = a * ((c * j) - (x * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -2.5e+79], N[Not[LessEqual[b, 1.7e+35]], $MachinePrecision]], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.5e79 or 1.7000000000000001e35 < b

   1. Initial program 70.2%

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

   3. Taylor expanded in b around inf 67.2%

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

   if -2.5e79 < b < 1.7000000000000001e35

   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 a around inf 50.0%

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

      1. +-commutative 50.0%

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

      2. mul-1-neg 50.0%

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

      3. unsub-neg 50.0%

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

      4. *-commutative 50.0%

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

   5. Simplified 50.0%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+79} \lor \neg \left(b \leq 1.7 \cdot 10^{+35}\right):\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-8} \lor \neg \left(b \leq 6 \cdot 10^{+33}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -6.2e-8) (not (<= b 6e+33))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -6.2e-8) || !(b <= 6e+33)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-6.2d-8)) .or. (.not. (b <= 6d+33))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -6.2e-8) || !(b <= 6e+33)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -6.2e-8) or not (b <= 6e+33):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -6.2e-8) || !(b <= 6e+33))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -6.2e-8) || ~((b <= 6e+33)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -6.2e-8], N[Not[LessEqual[b, 6e+33]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.2e-8 or 5.99999999999999967e33 < b

   1. Initial program 70.8%

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

   3. Taylor expanded in y around -inf 71.4%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in a around 0 74.2%

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

   7. Taylor expanded in t around inf 37.2%

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

   if -6.2e-8 < b < 5.99999999999999967e33

   1. Initial program 73.3%

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

   3. Taylor expanded in a around inf 49.9%

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

      1. +-commutative 49.9%

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

      2. mul-1-neg 49.9%

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

      3. unsub-neg 49.9%

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

      4. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in j around inf 29.0%

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

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{-8} \lor \neg \left(b \leq 6 \cdot 10^{+33}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 28.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-7} \lor \neg \left(b \leq 1.1 \cdot 10^{+34}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= b -1.1e-7) (not (<= b 1.1e+34))) (* b (* t i)) (* j (* a c))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.1e-7) || !(b <= 1.1e+34)) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((b <= (-1.1d-7)) .or. (.not. (b <= 1.1d+34))) then
        tmp = b * (t * i)
    else
        tmp = j * (a * c)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((b <= -1.1e-7) || !(b <= 1.1e+34)) {
		tmp = b * (t * i);
	} else {
		tmp = j * (a * c);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (b <= -1.1e-7) or not (b <= 1.1e+34):
		tmp = b * (t * i)
	else:
		tmp = j * (a * c)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((b <= -1.1e-7) || !(b <= 1.1e+34))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(j * Float64(a * c));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((b <= -1.1e-7) || ~((b <= 1.1e+34)))
		tmp = b * (t * i);
	else
		tmp = j * (a * c);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[b, -1.1e-7], N[Not[LessEqual[b, 1.1e+34]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.1000000000000001e-7 or 1.1000000000000001e34 < b

   1. Initial program 70.8%

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

   3. Taylor expanded in y around -inf 71.4%

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

   5. Simplified 72.2%

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

   6. Taylor expanded in a around 0 74.2%

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

   7. Taylor expanded in t around inf 37.2%

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

   if -1.1000000000000001e-7 < b < 1.1000000000000001e34

   1. Initial program 73.3%

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

   3. Taylor expanded in j around inf 55.1%

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

   4. Taylor expanded in a around inf 34.1%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{-7} \lor \neg \left(b \leq 1.1 \cdot 10^{+34}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 22.8% 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 72.0%

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

3. Taylor expanded in a around inf 38.6%

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

   1. +-commutative 38.6%

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

   2. mul-1-neg 38.6%

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

   3. unsub-neg 38.6%

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

   4. *-commutative 38.6%

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

5. Simplified 38.6%

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

6. Taylor expanded in j around inf 20.1%

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

7. Final simplification 20.1%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
8. Add Preprocessing

Developer target: 60.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024036 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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