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

Percentage Accurate: 73.6% → 81.7%

Time: 27.3s

Alternatives: 26

Speedup: 0.5×

• 57.6% 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: 73.6% 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: 81.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 93.7%

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

   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 t around inf 52.7%

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

      1. distribute-lft-out-- 52.7%

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

      2. *-commutative 52.7%

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

      3. *-commutative 52.7%

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

   5. Simplified 52.7%

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

4. Final simplification 85.1%

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

Alternative 2: 49.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -4.6 \cdot 10^{+126}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(i \cdot \left(t - j \cdot \frac{y}{b}\right)\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{-50}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+61} \lor \neg \left(a \leq 2 \cdot 10^{+169}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \frac{y \cdot z - t \cdot a}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -4.6e+126)
     t_1
     (if (<= a -1.05e-148)
       (* b (* i (- t (* j (/ y b)))))
       (if (<= a 3.2e-118)
         (* y (- (* x z) (* i j)))
         (if (<= a 6.2e-86)
           (* b (- (* t i) (* z c)))
           (if (<= a 3.65e-50)
             (* i (- (* t b) (* y j)))
             (if (or (<= a 7e+61) (not (<= a 2e+169)))
               t_1
               (* b (* x (/ (- (* y z) (* t a)) b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.6e+126) {
		tmp = t_1;
	} else if (a <= -1.05e-148) {
		tmp = b * (i * (t - (j * (y / b))));
	} else if (a <= 3.2e-118) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 6.2e-86) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 3.65e-50) {
		tmp = i * ((t * b) - (y * j));
	} else if ((a <= 7e+61) || !(a <= 2e+169)) {
		tmp = t_1;
	} else {
		tmp = b * (x * (((y * z) - (t * a)) / b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-4.6d+126)) then
        tmp = t_1
    else if (a <= (-1.05d-148)) then
        tmp = b * (i * (t - (j * (y / b))))
    else if (a <= 3.2d-118) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 6.2d-86) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 3.65d-50) then
        tmp = i * ((t * b) - (y * j))
    else if ((a <= 7d+61) .or. (.not. (a <= 2d+169))) then
        tmp = t_1
    else
        tmp = b * (x * (((y * z) - (t * a)) / b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -4.6e+126) {
		tmp = t_1;
	} else if (a <= -1.05e-148) {
		tmp = b * (i * (t - (j * (y / b))));
	} else if (a <= 3.2e-118) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 6.2e-86) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 3.65e-50) {
		tmp = i * ((t * b) - (y * j));
	} else if ((a <= 7e+61) || !(a <= 2e+169)) {
		tmp = t_1;
	} else {
		tmp = b * (x * (((y * z) - (t * a)) / b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -4.6e+126:
		tmp = t_1
	elif a <= -1.05e-148:
		tmp = b * (i * (t - (j * (y / b))))
	elif a <= 3.2e-118:
		tmp = y * ((x * z) - (i * j))
	elif a <= 6.2e-86:
		tmp = b * ((t * i) - (z * c))
	elif a <= 3.65e-50:
		tmp = i * ((t * b) - (y * j))
	elif (a <= 7e+61) or not (a <= 2e+169):
		tmp = t_1
	else:
		tmp = b * (x * (((y * z) - (t * a)) / b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -4.6e+126)
		tmp = t_1;
	elseif (a <= -1.05e-148)
		tmp = Float64(b * Float64(i * Float64(t - Float64(j * Float64(y / b)))));
	elseif (a <= 3.2e-118)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 6.2e-86)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 3.65e-50)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif ((a <= 7e+61) || !(a <= 2e+169))
		tmp = t_1;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(Float64(y * z) - Float64(t * a)) / b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -4.6e+126)
		tmp = t_1;
	elseif (a <= -1.05e-148)
		tmp = b * (i * (t - (j * (y / b))));
	elseif (a <= 3.2e-118)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 6.2e-86)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 3.65e-50)
		tmp = i * ((t * b) - (y * j));
	elseif ((a <= 7e+61) || ~((a <= 2e+169)))
		tmp = t_1;
	else
		tmp = b * (x * (((y * z) - (t * a)) / b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -4.6e+126], t$95$1, If[LessEqual[a, -1.05e-148], N[(b * N[(i * N[(t - N[(j * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-118], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.2e-86], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.65e-50], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 7e+61], N[Not[LessEqual[a, 2e+169]], $MachinePrecision]], t$95$1, N[(b * N[(x * N[(N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -4.6000000000000001e126 or 3.65000000000000018e-50 < a < 7.00000000000000036e61 or 1.99999999999999987e169 < a

   1. Initial program 58.4%

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

   3. Taylor expanded in a around inf 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. *-commutative 72.9%

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

      5. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   if -4.6000000000000001e126 < a < -1.05e-148

   1. Initial program 82.4%

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

   3. Taylor expanded in b around inf 69.2%

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

      1. fma-define 72.7%

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

      2. associate-/l* 72.8%

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

      3. *-commutative 72.8%

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

      4. associate-/l* 74.5%

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

      5. *-commutative 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in i around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. distribute-rgt-neg-in 53.0%

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

      4. neg-mul-1 53.0%

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

      5. +-commutative 53.0%

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

      6. unsub-neg 53.0%

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

      7. associate-/l* 54.7%

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

   8. Simplified 54.7%

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

   if -1.05e-148 < a < 3.20000000000000004e-118

   1. Initial program 81.5%

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

   3. Taylor expanded in y around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

   5. Simplified 60.6%

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

   if 3.20000000000000004e-118 < a < 6.19999999999999977e-86

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 81.7%

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

      1. *-commutative 81.7%

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

      2. *-commutative 81.7%

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

   5. Simplified 81.7%

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

   if 6.19999999999999977e-86 < a < 3.65000000000000018e-50

   1. Initial program 84.3%

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

   3. Taylor expanded in i around inf 68.7%

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

      1. distribute-lft-out-- 68.7%

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

      2. *-commutative 68.7%

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

      3. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in i around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. *-commutative 68.7%

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

      3. *-commutative 68.7%

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

      4. *-commutative 68.7%

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

      5. distribute-rgt-neg-in 68.7%

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

      6. *-commutative 68.7%

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

   8. Simplified 68.7%

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

   if 7.00000000000000036e61 < a < 1.99999999999999987e169

   1. Initial program 82.5%

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

   3. Taylor expanded in b around inf 82.4%

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

      1. fma-define 82.4%

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

      2. associate-/l* 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-/l* 82.5%

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

      5. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around inf 69.9%

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

      1. div-sub 74.4%

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

   8. Simplified 74.4%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{+126}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(i \cdot \left(t - j \cdot \frac{y}{b}\right)\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-118}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{-86}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{-50}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+61} \lor \neg \left(a \leq 2 \cdot 10^{+169}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \frac{y \cdot z - t \cdot a}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.8 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(i \cdot \left(t - j \cdot \frac{y}{b}\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(\frac{t \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+56} \lor \neg \left(a \leq 7.2 \cdot 10^{+169}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \frac{y \cdot z - t \cdot a}{b}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -3.8e+124)
     t_1
     (if (<= a -1.5e-148)
       (* b (* i (- t (* j (/ y b)))))
       (if (<= a 9.5e-117)
         (* y (- (* x z) (* i j)))
         (if (<= a 6.8e-85)
           (* b (- (* t i) (* z c)))
           (if (<= a 4.5e-48)
             (* y (- (/ (* t (* b i)) y) (* i j)))
             (if (or (<= a 1.25e+56) (not (<= a 7.2e+169)))
               t_1
               (* b (* x (/ (- (* y z) (* t a)) b)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.8e+124) {
		tmp = t_1;
	} else if (a <= -1.5e-148) {
		tmp = b * (i * (t - (j * (y / b))));
	} else if (a <= 9.5e-117) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 6.8e-85) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4.5e-48) {
		tmp = y * (((t * (b * i)) / y) - (i * j));
	} else if ((a <= 1.25e+56) || !(a <= 7.2e+169)) {
		tmp = t_1;
	} else {
		tmp = b * (x * (((y * z) - (t * a)) / b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-3.8d+124)) then
        tmp = t_1
    else if (a <= (-1.5d-148)) then
        tmp = b * (i * (t - (j * (y / b))))
    else if (a <= 9.5d-117) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 6.8d-85) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 4.5d-48) then
        tmp = y * (((t * (b * i)) / y) - (i * j))
    else if ((a <= 1.25d+56) .or. (.not. (a <= 7.2d+169))) then
        tmp = t_1
    else
        tmp = b * (x * (((y * z) - (t * a)) / b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.8e+124) {
		tmp = t_1;
	} else if (a <= -1.5e-148) {
		tmp = b * (i * (t - (j * (y / b))));
	} else if (a <= 9.5e-117) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 6.8e-85) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 4.5e-48) {
		tmp = y * (((t * (b * i)) / y) - (i * j));
	} else if ((a <= 1.25e+56) || !(a <= 7.2e+169)) {
		tmp = t_1;
	} else {
		tmp = b * (x * (((y * z) - (t * a)) / b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.8e+124:
		tmp = t_1
	elif a <= -1.5e-148:
		tmp = b * (i * (t - (j * (y / b))))
	elif a <= 9.5e-117:
		tmp = y * ((x * z) - (i * j))
	elif a <= 6.8e-85:
		tmp = b * ((t * i) - (z * c))
	elif a <= 4.5e-48:
		tmp = y * (((t * (b * i)) / y) - (i * j))
	elif (a <= 1.25e+56) or not (a <= 7.2e+169):
		tmp = t_1
	else:
		tmp = b * (x * (((y * z) - (t * a)) / b))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.8e+124)
		tmp = t_1;
	elseif (a <= -1.5e-148)
		tmp = Float64(b * Float64(i * Float64(t - Float64(j * Float64(y / b)))));
	elseif (a <= 9.5e-117)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 6.8e-85)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 4.5e-48)
		tmp = Float64(y * Float64(Float64(Float64(t * Float64(b * i)) / y) - Float64(i * j)));
	elseif ((a <= 1.25e+56) || !(a <= 7.2e+169))
		tmp = t_1;
	else
		tmp = Float64(b * Float64(x * Float64(Float64(Float64(y * z) - Float64(t * a)) / b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.8e+124)
		tmp = t_1;
	elseif (a <= -1.5e-148)
		tmp = b * (i * (t - (j * (y / b))));
	elseif (a <= 9.5e-117)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 6.8e-85)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 4.5e-48)
		tmp = y * (((t * (b * i)) / y) - (i * j));
	elseif ((a <= 1.25e+56) || ~((a <= 7.2e+169)))
		tmp = t_1;
	else
		tmp = b * (x * (((y * z) - (t * a)) / b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.8e+124], t$95$1, If[LessEqual[a, -1.5e-148], N[(b * N[(i * N[(t - N[(j * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9.5e-117], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e-85], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.5e-48], N[(y * N[(N[(N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[a, 1.25e+56], N[Not[LessEqual[a, 7.2e+169]], $MachinePrecision]], t$95$1, N[(b * N[(x * N[(N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if a < -3.7999999999999998e124 or 4.49999999999999988e-48 < a < 1.25000000000000006e56 or 7.20000000000000019e169 < a

   1. Initial program 58.4%

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

   3. Taylor expanded in a around inf 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. *-commutative 72.9%

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

      5. *-commutative 72.9%

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

   5. Simplified 72.9%

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

   if -3.7999999999999998e124 < a < -1.49999999999999999e-148

   1. Initial program 82.4%

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

   3. Taylor expanded in b around inf 69.2%

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

      1. fma-define 72.7%

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

      2. associate-/l* 72.8%

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

      3. *-commutative 72.8%

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

      4. associate-/l* 74.5%

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

      5. *-commutative 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in i around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. distribute-rgt-neg-in 53.0%

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

      4. neg-mul-1 53.0%

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

      5. +-commutative 53.0%

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

      6. unsub-neg 53.0%

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

      7. associate-/l* 54.7%

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

   8. Simplified 54.7%

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

   if -1.49999999999999999e-148 < a < 9.5000000000000004e-117

   1. Initial program 81.5%

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

   3. Taylor expanded in y around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

   5. Simplified 60.6%

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

   if 9.5000000000000004e-117 < a < 6.8e-85

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 81.7%

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

      1. *-commutative 81.7%

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

      2. *-commutative 81.7%

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

   5. Simplified 81.7%

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

   if 6.8e-85 < a < 4.49999999999999988e-48

   1. Initial program 84.3%

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

   3. Taylor expanded in i around inf 68.7%

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

      1. distribute-lft-out-- 68.7%

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

      2. *-commutative 68.7%

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

      3. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in y around inf 83.8%

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

      1. +-commutative 83.8%

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

      2. mul-1-neg 83.8%

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

      3. unsub-neg 83.8%

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

      4. associate-*r* 83.8%

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

      5. *-commutative 83.8%

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

      6. *-commutative 83.8%

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

   8. Simplified 83.8%

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

   if 1.25000000000000006e56 < a < 7.20000000000000019e169

   1. Initial program 82.5%

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

   3. Taylor expanded in b around inf 82.4%

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

      1. fma-define 82.4%

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

      2. associate-/l* 82.4%

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

      3. *-commutative 82.4%

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

      4. associate-/l* 82.5%

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

      5. *-commutative 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in x around inf 69.9%

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

      1. div-sub 74.4%

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

   8. Simplified 74.4%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(i \cdot \left(t - j \cdot \frac{y}{b}\right)\right)\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-117}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{-48}:\\ \;\;\;\;y \cdot \left(\frac{t \cdot \left(b \cdot i\right)}{y} - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+56} \lor \neg \left(a \leq 7.2 \cdot 10^{+169}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(x \cdot \frac{y \cdot z - t \cdot a}{b}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 55.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{+96}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-192}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -3.65 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -1.25e+96)
     t_1
     (if (<= i -9.5e+18)
       (* t (- (* a (* c (/ j t))) (* x a)))
       (if (<= i -3.5e-75)
         (- (* i (* t b)) (* x (- (* t a) (* y z))))
         (if (<= i -7.5e-192)
           (* a (- (* c j) (* x t)))
           (if (<= i -3.65e-218)
             (+ (* x (* y z)) (* b (- (* t i) (* z c))))
             (if (<= i 2.3e-43)
               (- (* x (- (* y z) (* t a))) (* c (* z b)))
               t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.25e+96) {
		tmp = t_1;
	} else if (i <= -9.5e+18) {
		tmp = t * ((a * (c * (j / t))) - (x * a));
	} else if (i <= -3.5e-75) {
		tmp = (i * (t * b)) - (x * ((t * a) - (y * z)));
	} else if (i <= -7.5e-192) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= -3.65e-218) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else if (i <= 2.3e-43) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-1.25d+96)) then
        tmp = t_1
    else if (i <= (-9.5d+18)) then
        tmp = t * ((a * (c * (j / t))) - (x * a))
    else if (i <= (-3.5d-75)) then
        tmp = (i * (t * b)) - (x * ((t * a) - (y * z)))
    else if (i <= (-7.5d-192)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= (-3.65d-218)) then
        tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
    else if (i <= 2.3d-43) then
        tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.25e+96) {
		tmp = t_1;
	} else if (i <= -9.5e+18) {
		tmp = t * ((a * (c * (j / t))) - (x * a));
	} else if (i <= -3.5e-75) {
		tmp = (i * (t * b)) - (x * ((t * a) - (y * z)));
	} else if (i <= -7.5e-192) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= -3.65e-218) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else if (i <= 2.3e-43) {
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.25e+96:
		tmp = t_1
	elif i <= -9.5e+18:
		tmp = t * ((a * (c * (j / t))) - (x * a))
	elif i <= -3.5e-75:
		tmp = (i * (t * b)) - (x * ((t * a) - (y * z)))
	elif i <= -7.5e-192:
		tmp = a * ((c * j) - (x * t))
	elif i <= -3.65e-218:
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
	elif i <= 2.3e-43:
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.25e+96)
		tmp = t_1;
	elseif (i <= -9.5e+18)
		tmp = Float64(t * Float64(Float64(a * Float64(c * Float64(j / t))) - Float64(x * a)));
	elseif (i <= -3.5e-75)
		tmp = Float64(Float64(i * Float64(t * b)) - Float64(x * Float64(Float64(t * a) - Float64(y * z))));
	elseif (i <= -7.5e-192)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= -3.65e-218)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (i <= 2.3e-43)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(c * Float64(z * b)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.25e+96)
		tmp = t_1;
	elseif (i <= -9.5e+18)
		tmp = t * ((a * (c * (j / t))) - (x * a));
	elseif (i <= -3.5e-75)
		tmp = (i * (t * b)) - (x * ((t * a) - (y * z)));
	elseif (i <= -7.5e-192)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= -3.65e-218)
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	elseif (i <= 2.3e-43)
		tmp = (x * ((y * z) - (t * a))) - (c * (z * b));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.25e+96], t$95$1, If[LessEqual[i, -9.5e+18], N[(t * N[(N[(a * N[(c * N[(j / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.5e-75], N[(N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision] - N[(x * N[(N[(t * a), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -7.5e-192], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -3.65e-218], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.3e-43], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(c * N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.2500000000000001e96 or 2.2999999999999999e-43 < i

   1. Initial program 64.1%

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

   3. Taylor expanded in i around inf 69.0%

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

      1. distribute-lft-out-- 69.0%

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

      2. *-commutative 69.0%

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

      3. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in i around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. *-commutative 69.0%

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

      3. *-commutative 69.0%

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

      4. *-commutative 69.0%

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

      5. distribute-rgt-neg-in 69.0%

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

      6. *-commutative 69.0%

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

   8. Simplified 69.0%

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

   if -1.2500000000000001e96 < i < -9.5e18

   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 a around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

      5. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in t around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

      4. associate-/l* 67.6%

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

      5. associate-/l* 74.0%

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

   8. Simplified 74.0%

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

   if -9.5e18 < i < -3.49999999999999985e-75

   1. Initial program 85.7%

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

   3. Taylor expanded in j around 0 67.1%

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

   4. Taylor expanded in c around inf 62.7%

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

      1. associate-*r/ 62.7%

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

      2. mul-1-neg 62.7%

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

      3. distribute-lft-neg-out 62.7%

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

      4. *-commutative 62.7%

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

   6. Simplified 62.7%

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

   7. Taylor expanded in c around 0 67.5%

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

      1. associate-*r* 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*r* 63.1%

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

      4. associate-*r* 63.1%

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

      5. *-commutative 63.1%

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

      6. mul-1-neg 63.1%

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

      7. *-commutative 63.1%

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

      8. distribute-rgt-neg-in 63.1%

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

   9. Simplified 63.1%

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

   if -3.49999999999999985e-75 < i < -7.5000000000000001e-192

   1. Initial program 87.9%

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

   3. Taylor expanded in a around inf 70.8%

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

      1. +-commutative 70.8%

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

      2. mul-1-neg 70.8%

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

      3. unsub-neg 70.8%

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

      4. *-commutative 70.8%

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

      5. *-commutative 70.8%

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

   5. Simplified 70.8%

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

   if -7.5000000000000001e-192 < i < -3.6499999999999999e-218

   1. Initial program 87.9%

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

   3. Taylor expanded in j around 0 99.1%

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

   4. Taylor expanded in a around 0 78.3%

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

      1. *-commutative 78.3%

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

      2. cancel-sign-sub-inv 78.3%

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

      3. +-commutative 78.3%

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

      4. +-commutative 78.3%

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

      5. cancel-sign-sub-inv 78.3%

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

      6. *-commutative 78.3%

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

      7. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   if -3.6499999999999999e-218 < i < 2.2999999999999999e-43

   1. Initial program 82.1%

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

   3. Taylor expanded in j around 0 65.9%

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

   4. Taylor expanded in c around inf 64.7%

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

      1. associate-*r/ 64.7%

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

      2. mul-1-neg 64.7%

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

      3. distribute-lft-neg-out 64.7%

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

      4. *-commutative 64.7%

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

   6. Simplified 64.7%

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

   7. Taylor expanded in c around inf 63.1%

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

      1. associate-*r* 63.7%

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

      2. *-commutative 63.7%

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

      3. associate-*r* 63.2%

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

   9. Simplified 63.2%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+96}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -9.5 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)\\ \mathbf{elif}\;i \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;i \cdot \left(t \cdot b\right) - x \cdot \left(t \cdot a - y \cdot z\right)\\ \mathbf{elif}\;i \leq -7.5 \cdot 10^{-192}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq -3.65 \cdot 10^{-218}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 2.3 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - c \cdot \left(z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 55.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -1.25 \cdot 10^{+96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-50}:\\ \;\;\;\;t\_1 + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.22 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(z \cdot \left(\frac{a \cdot j}{z} - b\right)\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{-43}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))) (t_2 (* i (- (* t b) (* y j)))))
   (if (<= i -1.25e+96)
     t_2
     (if (<= i -1.5e+18)
       (* t (- (* a (* c (/ j t))) (* x a)))
       (if (<= i -1.7e-50)
         (+ t_1 (* t (* b i)))
         (if (<= i -1.22e-105)
           (* c (* z (- (/ (* a j) z) b)))
           (if (<= i -8e-204)
             (* a (- (* c j) (* x t)))
             (if (<= i 1.75e-43) (- t_1 (* b (* z c))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.25e+96) {
		tmp = t_2;
	} else if (i <= -1.5e+18) {
		tmp = t * ((a * (c * (j / t))) - (x * a));
	} else if (i <= -1.7e-50) {
		tmp = t_1 + (t * (b * i));
	} else if (i <= -1.22e-105) {
		tmp = c * (z * (((a * j) / z) - b));
	} else if (i <= -8e-204) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.75e-43) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * ((y * z) - (t * a))
    t_2 = i * ((t * b) - (y * j))
    if (i <= (-1.25d+96)) then
        tmp = t_2
    else if (i <= (-1.5d+18)) then
        tmp = t * ((a * (c * (j / t))) - (x * a))
    else if (i <= (-1.7d-50)) then
        tmp = t_1 + (t * (b * i))
    else if (i <= (-1.22d-105)) then
        tmp = c * (z * (((a * j) / z) - b))
    else if (i <= (-8d-204)) then
        tmp = a * ((c * j) - (x * t))
    else if (i <= 1.75d-43) then
        tmp = t_1 - (b * (z * c))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = x * ((y * z) - (t * a));
	double t_2 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -1.25e+96) {
		tmp = t_2;
	} else if (i <= -1.5e+18) {
		tmp = t * ((a * (c * (j / t))) - (x * a));
	} else if (i <= -1.7e-50) {
		tmp = t_1 + (t * (b * i));
	} else if (i <= -1.22e-105) {
		tmp = c * (z * (((a * j) / z) - b));
	} else if (i <= -8e-204) {
		tmp = a * ((c * j) - (x * t));
	} else if (i <= 1.75e-43) {
		tmp = t_1 - (b * (z * c));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = x * ((y * z) - (t * a))
	t_2 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -1.25e+96:
		tmp = t_2
	elif i <= -1.5e+18:
		tmp = t * ((a * (c * (j / t))) - (x * a))
	elif i <= -1.7e-50:
		tmp = t_1 + (t * (b * i))
	elif i <= -1.22e-105:
		tmp = c * (z * (((a * j) / z) - b))
	elif i <= -8e-204:
		tmp = a * ((c * j) - (x * t))
	elif i <= 1.75e-43:
		tmp = t_1 - (b * (z * c))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_2 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -1.25e+96)
		tmp = t_2;
	elseif (i <= -1.5e+18)
		tmp = Float64(t * Float64(Float64(a * Float64(c * Float64(j / t))) - Float64(x * a)));
	elseif (i <= -1.7e-50)
		tmp = Float64(t_1 + Float64(t * Float64(b * i)));
	elseif (i <= -1.22e-105)
		tmp = Float64(c * Float64(z * Float64(Float64(Float64(a * j) / z) - b)));
	elseif (i <= -8e-204)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (i <= 1.75e-43)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = x * ((y * z) - (t * a));
	t_2 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -1.25e+96)
		tmp = t_2;
	elseif (i <= -1.5e+18)
		tmp = t * ((a * (c * (j / t))) - (x * a));
	elseif (i <= -1.7e-50)
		tmp = t_1 + (t * (b * i));
	elseif (i <= -1.22e-105)
		tmp = c * (z * (((a * j) / z) - b));
	elseif (i <= -8e-204)
		tmp = a * ((c * j) - (x * t));
	elseif (i <= 1.75e-43)
		tmp = t_1 - (b * (z * c));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.25e+96], t$95$2, If[LessEqual[i, -1.5e+18], N[(t * N[(N[(a * N[(c * N[(j / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.7e-50], N[(t$95$1 + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -1.22e-105], N[(c * N[(z * N[(N[(N[(a * j), $MachinePrecision] / z), $MachinePrecision] - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -8e-204], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.75e-43], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -1.2500000000000001e96 or 1.74999999999999999e-43 < i

   1. Initial program 64.1%

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

   3. Taylor expanded in i around inf 69.0%

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

      1. distribute-lft-out-- 69.0%

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

      2. *-commutative 69.0%

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

      3. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in i around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. *-commutative 69.0%

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

      3. *-commutative 69.0%

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

      4. *-commutative 69.0%

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

      5. distribute-rgt-neg-in 69.0%

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

      6. *-commutative 69.0%

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

   8. Simplified 69.0%

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

   if -1.2500000000000001e96 < i < -1.5e18

   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 a around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

      5. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in t around inf 67.6%

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

      1. +-commutative 67.6%

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

      2. mul-1-neg 67.6%

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

      3. unsub-neg 67.6%

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

      4. associate-/l* 67.6%

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

      5. associate-/l* 74.0%

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

   8. Simplified 74.0%

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

   if -1.5e18 < i < -1.70000000000000007e-50

   1. Initial program 89.4%

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

   3. Taylor expanded in j around 0 68.9%

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

   4. Taylor expanded in c around 0 69.3%

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

      1. mul-1-neg 69.3%

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

      2. associate-*r* 69.3%

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

      3. distribute-lft-neg-in 69.3%

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

      4. distribute-rgt-neg-in 69.3%

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

   6. Simplified 69.3%

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

   if -1.70000000000000007e-50 < i < -1.22000000000000001e-105

   1. Initial program 79.7%

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

   3. Taylor expanded in z around inf 60.0%

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

   4. Taylor expanded in c around inf 80.4%

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

   if -1.22000000000000001e-105 < i < -8.00000000000000001e-204

   1. Initial program 89.4%

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

   3. Taylor expanded in a around inf 73.5%

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

      1. +-commutative 73.5%

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

      2. mul-1-neg 73.5%

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

      3. unsub-neg 73.5%

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

      4. *-commutative 73.5%

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

      5. *-commutative 73.5%

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

   5. Simplified 73.5%

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

   if -8.00000000000000001e-204 < i < 1.74999999999999999e-43

   1. Initial program 81.5%

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

   3. Taylor expanded in j around 0 67.2%

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

   4. Taylor expanded in c around inf 64.6%

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

      1. *-commutative 64.6%

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

   6. Simplified 64.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+96}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -1.5 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(a \cdot \left(c \cdot \frac{j}{t}\right) - x \cdot a\right)\\ \mathbf{elif}\;i \leq -1.7 \cdot 10^{-50}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq -1.22 \cdot 10^{-105}:\\ \;\;\;\;c \cdot \left(z \cdot \left(\frac{a \cdot j}{z} - b\right)\right)\\ \mathbf{elif}\;i \leq -8 \cdot 10^{-204}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;i \leq 1.75 \cdot 10^{-43}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.6 \cdot 10^{+82}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-58}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -2.6e+82)
     t_2
     (if (<= a -1.05e+15)
       (* x (- (* y z) (* t a)))
       (if (<= a -2.3e-159)
         t_1
         (if (<= a 1.8e-120)
           (* y (- (* x z) (* i j)))
           (if (<= a 3.2e-58) t_1 (if (<= a 1.42e-56) (* z (* x y)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.6e+82) {
		tmp = t_2;
	} else if (a <= -1.05e+15) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -2.3e-159) {
		tmp = t_1;
	} else if (a <= 1.8e-120) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 3.2e-58) {
		tmp = t_1;
	} else if (a <= 1.42e-56) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-2.6d+82)) then
        tmp = t_2
    else if (a <= (-1.05d+15)) then
        tmp = x * ((y * z) - (t * a))
    else if (a <= (-2.3d-159)) then
        tmp = t_1
    else if (a <= 1.8d-120) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 3.2d-58) then
        tmp = t_1
    else if (a <= 1.42d-56) then
        tmp = z * (x * y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.6e+82) {
		tmp = t_2;
	} else if (a <= -1.05e+15) {
		tmp = x * ((y * z) - (t * a));
	} else if (a <= -2.3e-159) {
		tmp = t_1;
	} else if (a <= 1.8e-120) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 3.2e-58) {
		tmp = t_1;
	} else if (a <= 1.42e-56) {
		tmp = z * (x * y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.6e+82:
		tmp = t_2
	elif a <= -1.05e+15:
		tmp = x * ((y * z) - (t * a))
	elif a <= -2.3e-159:
		tmp = t_1
	elif a <= 1.8e-120:
		tmp = y * ((x * z) - (i * j))
	elif a <= 3.2e-58:
		tmp = t_1
	elif a <= 1.42e-56:
		tmp = z * (x * y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.6e+82)
		tmp = t_2;
	elseif (a <= -1.05e+15)
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	elseif (a <= -2.3e-159)
		tmp = t_1;
	elseif (a <= 1.8e-120)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 3.2e-58)
		tmp = t_1;
	elseif (a <= 1.42e-56)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.6e+82)
		tmp = t_2;
	elseif (a <= -1.05e+15)
		tmp = x * ((y * z) - (t * a));
	elseif (a <= -2.3e-159)
		tmp = t_1;
	elseif (a <= 1.8e-120)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 3.2e-58)
		tmp = t_1;
	elseif (a <= 1.42e-56)
		tmp = z * (x * y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.6e+82], t$95$2, If[LessEqual[a, -1.05e+15], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -2.3e-159], t$95$1, If[LessEqual[a, 1.8e-120], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 3.2e-58], t$95$1, If[LessEqual[a, 1.42e-56], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -2.5999999999999998e82 or 1.42e-56 < a

   1. Initial program 65.3%

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

   3. Taylor expanded in a around inf 65.0%

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

      1. +-commutative 65.0%

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

      2. mul-1-neg 65.0%

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

      3. unsub-neg 65.0%

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

      4. *-commutative 65.0%

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

      5. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   if -2.5999999999999998e82 < a < -1.05e15

   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 inf 75.4%

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

      1. fma-define 81.7%

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

      2. associate-/l* 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-/l* 81.6%

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

      5. *-commutative 81.6%

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

   5. Simplified 81.6%

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

   6. Taylor expanded in x around -inf 63.4%

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

   if -1.05e15 < a < -2.29999999999999978e-159 or 1.8000000000000001e-120 < a < 3.2000000000000001e-58

   1. Initial program 83.9%

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

   3. Taylor expanded in b around inf 57.3%

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

      1. *-commutative 57.3%

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

      2. *-commutative 57.3%

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

   5. Simplified 57.3%

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

   if -2.29999999999999978e-159 < a < 1.8000000000000001e-120

   1. Initial program 80.6%

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

   3. Taylor expanded in y around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. mul-1-neg 60.3%

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

      3. unsub-neg 60.3%

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

      4. *-commutative 60.3%

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

   5. Simplified 60.3%

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

   if 3.2000000000000001e-58 < a < 1.42e-56

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+82}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-159}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-58}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{-56}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_2 := t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ t_3 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;i \leq -2.25 \cdot 10^{-191}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-278}:\\ \;\;\;\;t\_1 - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{+84}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

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 (* j (- (* a c) (* y i)))))
        (t_3 (* i (- (* t b) (* y j)))))
   (if (<= i -9.5e+95)
     t_3
     (if (<= i -2.25e-191)
       t_2
       (if (<= i -6.2e-278)
         (- t_1 (* b (* z c)))
         (if (<= i 7.6e+84) 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 + (j * ((a * c) - (y * i)));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -9.5e+95) {
		tmp = t_3;
	} else if (i <= -2.25e-191) {
		tmp = t_2;
	} else if (i <= -6.2e-278) {
		tmp = t_1 - (b * (z * c));
	} else if (i <= 7.6e+84) {
		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 + (j * ((a * c) - (y * i)))
    t_3 = i * ((t * b) - (y * j))
    if (i <= (-9.5d+95)) then
        tmp = t_3
    else if (i <= (-2.25d-191)) then
        tmp = t_2
    else if (i <= (-6.2d-278)) then
        tmp = t_1 - (b * (z * c))
    else if (i <= 7.6d+84) 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 + (j * ((a * c) - (y * i)));
	double t_3 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -9.5e+95) {
		tmp = t_3;
	} else if (i <= -2.25e-191) {
		tmp = t_2;
	} else if (i <= -6.2e-278) {
		tmp = t_1 - (b * (z * c));
	} else if (i <= 7.6e+84) {
		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 + (j * ((a * c) - (y * i)))
	t_3 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -9.5e+95:
		tmp = t_3
	elif i <= -2.25e-191:
		tmp = t_2
	elif i <= -6.2e-278:
		tmp = t_1 - (b * (z * c))
	elif i <= 7.6e+84:
		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(j * Float64(Float64(a * c) - Float64(y * i))))
	t_3 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -9.5e+95)
		tmp = t_3;
	elseif (i <= -2.25e-191)
		tmp = t_2;
	elseif (i <= -6.2e-278)
		tmp = Float64(t_1 - Float64(b * Float64(z * c)));
	elseif (i <= 7.6e+84)
		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 + (j * ((a * c) - (y * i)));
	t_3 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -9.5e+95)
		tmp = t_3;
	elseif (i <= -2.25e-191)
		tmp = t_2;
	elseif (i <= -6.2e-278)
		tmp = t_1 - (b * (z * c));
	elseif (i <= 7.6e+84)
		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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -9.5e+95], t$95$3, If[LessEqual[i, -2.25e-191], t$95$2, If[LessEqual[i, -6.2e-278], N[(t$95$1 - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7.6e+84], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if i < -9.5000000000000004e95 or 7.6000000000000002e84 < i

   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 i around inf 75.8%

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

      1. distribute-lft-out-- 75.8%

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

      2. *-commutative 75.8%

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

      3. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in i around 0 75.8%

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

      1. mul-1-neg 75.8%

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

      2. *-commutative 75.8%

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

      3. *-commutative 75.8%

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

      4. *-commutative 75.8%

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

      5. distribute-rgt-neg-in 75.8%

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

      6. *-commutative 75.8%

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

   8. Simplified 75.8%

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

   if -9.5000000000000004e95 < i < -2.25000000000000004e-191 or -6.19999999999999983e-278 < i < 7.6000000000000002e84

   1. Initial program 80.9%

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

   3. Taylor expanded in b around 0 69.0%

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

   if -2.25000000000000004e-191 < i < -6.19999999999999983e-278

   1. Initial program 89.7%

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

   3. Taylor expanded in j around 0 94.7%

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

   4. Taylor expanded in c around inf 80.9%

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

      1. *-commutative 80.9%

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

   6. Simplified 80.9%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -9.5 \cdot 10^{+95}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq -2.25 \cdot 10^{-191}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;i \leq -6.2 \cdot 10^{-278}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 7.6 \cdot 10^{+84}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -6.6 \cdot 10^{+124}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-187}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -6.6e+124)
     t_2
     (if (<= a -1.08e-187)
       t_1
       (if (<= a 5.3e-120)
         (* y (- (* x z) (* i j)))
         (if (<= a 1.95e-84)
           (* b (- (* t i) (* z c)))
           (if (<= a 1.26e-55) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.6e+124) {
		tmp = t_2;
	} else if (a <= -1.08e-187) {
		tmp = t_1;
	} else if (a <= 5.3e-120) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.95e-84) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.26e-55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-6.6d+124)) then
        tmp = t_2
    else if (a <= (-1.08d-187)) then
        tmp = t_1
    else if (a <= 5.3d-120) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 1.95d-84) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 1.26d-55) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -6.6e+124) {
		tmp = t_2;
	} else if (a <= -1.08e-187) {
		tmp = t_1;
	} else if (a <= 5.3e-120) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 1.95e-84) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.26e-55) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -6.6e+124:
		tmp = t_2
	elif a <= -1.08e-187:
		tmp = t_1
	elif a <= 5.3e-120:
		tmp = y * ((x * z) - (i * j))
	elif a <= 1.95e-84:
		tmp = b * ((t * i) - (z * c))
	elif a <= 1.26e-55:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -6.6e+124)
		tmp = t_2;
	elseif (a <= -1.08e-187)
		tmp = t_1;
	elseif (a <= 5.3e-120)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 1.95e-84)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 1.26e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -6.6e+124)
		tmp = t_2;
	elseif (a <= -1.08e-187)
		tmp = t_1;
	elseif (a <= 5.3e-120)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 1.95e-84)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 1.26e-55)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.6e+124], t$95$2, If[LessEqual[a, -1.08e-187], t$95$1, If[LessEqual[a, 5.3e-120], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.95e-84], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.26e-55], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -6.60000000000000029e124 or 1.2599999999999999e-55 < a

   1. Initial program 63.2%

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

   3. Taylor expanded in a around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

      5. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   if -6.60000000000000029e124 < a < -1.08e-187 or 1.95000000000000011e-84 < a < 1.2599999999999999e-55

   1. Initial program 82.0%

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

   3. Taylor expanded in i around inf 54.8%

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

      1. distribute-lft-out-- 54.8%

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

      2. *-commutative 54.8%

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

      3. *-commutative 54.8%

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

   5. Simplified 54.8%

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

   6. Taylor expanded in i around 0 54.8%

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

      1. mul-1-neg 54.8%

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

      2. *-commutative 54.8%

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

      3. *-commutative 54.8%

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

      4. *-commutative 54.8%

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

      5. distribute-rgt-neg-in 54.8%

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

      6. *-commutative 54.8%

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

   8. Simplified 54.8%

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

   if -1.08e-187 < a < 5.29999999999999997e-120

   1. Initial program 82.0%

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

   3. Taylor expanded in y around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if 5.29999999999999997e-120 < a < 1.95000000000000011e-84

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 81.7%

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

      1. *-commutative 81.7%

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

      2. *-commutative 81.7%

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

   5. Simplified 81.7%

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

4. Final simplification 62.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.6 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.08 \cdot 10^{-187}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 1.95 \cdot 10^{-84}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.26 \cdot 10^{-55}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 50.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -3.6 \cdot 10^{+124}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(i \cdot \left(t - j \cdot \frac{y}{b}\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-49}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= a -3.6e+124)
     t_1
     (if (<= a -1.05e-148)
       (* b (* i (- t (* j (/ y b)))))
       (if (<= a 1.7e-120)
         (* y (- (* x z) (* i j)))
         (if (<= a 9e-85)
           (* b (- (* t i) (* z c)))
           (if (<= a 1.35e-49) (* i (- (* t b) (* y j))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.6e+124) {
		tmp = t_1;
	} else if (a <= -1.05e-148) {
		tmp = b * (i * (t - (j * (y / b))));
	} else if (a <= 1.7e-120) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 9e-85) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.35e-49) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (a <= (-3.6d+124)) then
        tmp = t_1
    else if (a <= (-1.05d-148)) then
        tmp = b * (i * (t - (j * (y / b))))
    else if (a <= 1.7d-120) then
        tmp = y * ((x * z) - (i * j))
    else if (a <= 9d-85) then
        tmp = b * ((t * i) - (z * c))
    else if (a <= 1.35d-49) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -3.6e+124) {
		tmp = t_1;
	} else if (a <= -1.05e-148) {
		tmp = b * (i * (t - (j * (y / b))));
	} else if (a <= 1.7e-120) {
		tmp = y * ((x * z) - (i * j));
	} else if (a <= 9e-85) {
		tmp = b * ((t * i) - (z * c));
	} else if (a <= 1.35e-49) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -3.6e+124:
		tmp = t_1
	elif a <= -1.05e-148:
		tmp = b * (i * (t - (j * (y / b))))
	elif a <= 1.7e-120:
		tmp = y * ((x * z) - (i * j))
	elif a <= 9e-85:
		tmp = b * ((t * i) - (z * c))
	elif a <= 1.35e-49:
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -3.6e+124)
		tmp = t_1;
	elseif (a <= -1.05e-148)
		tmp = Float64(b * Float64(i * Float64(t - Float64(j * Float64(y / b)))));
	elseif (a <= 1.7e-120)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (a <= 9e-85)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (a <= 1.35e-49)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -3.6e+124)
		tmp = t_1;
	elseif (a <= -1.05e-148)
		tmp = b * (i * (t - (j * (y / b))));
	elseif (a <= 1.7e-120)
		tmp = y * ((x * z) - (i * j));
	elseif (a <= 9e-85)
		tmp = b * ((t * i) - (z * c));
	elseif (a <= 1.35e-49)
		tmp = i * ((t * b) - (y * j));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.6e+124], t$95$1, If[LessEqual[a, -1.05e-148], N[(b * N[(i * N[(t - N[(j * N[(y / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.7e-120], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e-85], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e-49], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -3.59999999999999986e124 or 1.35e-49 < a

   1. Initial program 63.2%

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

   3. Taylor expanded in a around inf 67.8%

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

      1. +-commutative 67.8%

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

      2. mul-1-neg 67.8%

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

      3. unsub-neg 67.8%

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

      4. *-commutative 67.8%

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

      5. *-commutative 67.8%

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

   5. Simplified 67.8%

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

   if -3.59999999999999986e124 < a < -1.05e-148

   1. Initial program 82.4%

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

   3. Taylor expanded in b around inf 69.2%

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

      1. fma-define 72.7%

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

      2. associate-/l* 72.8%

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

      3. *-commutative 72.8%

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

      4. associate-/l* 74.5%

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

      5. *-commutative 74.5%

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

   5. Simplified 74.5%

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

   6. Taylor expanded in i around -inf 53.0%

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

      1. mul-1-neg 53.0%

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

      2. *-commutative 53.0%

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

      3. distribute-rgt-neg-in 53.0%

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

      4. neg-mul-1 53.0%

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

      5. +-commutative 53.0%

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

      6. unsub-neg 53.0%

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

      7. associate-/l* 54.7%

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

   8. Simplified 54.7%

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

   if -1.05e-148 < a < 1.70000000000000005e-120

   1. Initial program 81.5%

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

   3. Taylor expanded in y around inf 60.6%

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

      1. +-commutative 60.6%

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

      2. mul-1-neg 60.6%

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

      3. unsub-neg 60.6%

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

      4. *-commutative 60.6%

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

   5. Simplified 60.6%

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

   if 1.70000000000000005e-120 < a < 9.00000000000000008e-85

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 81.7%

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

      1. *-commutative 81.7%

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

      2. *-commutative 81.7%

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

   5. Simplified 81.7%

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

   if 9.00000000000000008e-85 < a < 1.35e-49

   1. Initial program 84.3%

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

   3. Taylor expanded in i around inf 68.7%

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

      1. distribute-lft-out-- 68.7%

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

      2. *-commutative 68.7%

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

      3. *-commutative 68.7%

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

   5. Simplified 68.7%

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

   6. Taylor expanded in i around 0 68.7%

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

      1. mul-1-neg 68.7%

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

      2. *-commutative 68.7%

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

      3. *-commutative 68.7%

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

      4. *-commutative 68.7%

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

      5. distribute-rgt-neg-in 68.7%

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

      6. *-commutative 68.7%

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

   8. Simplified 68.7%

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

4. Final simplification 63.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-148}:\\ \;\;\;\;b \cdot \left(i \cdot \left(t - j \cdot \frac{y}{b}\right)\right)\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-120}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-85}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{-49}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 58.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{if}\;i \leq -5.2 \cdot 10^{+95}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (- (* t b) (* y j)))))
   (if (<= i -5.2e+95)
     t_1
     (if (<= i 4.3e-41)
       (- (* x (- (* y z) (* t a))) (* b (* z c)))
       (if (<= i 1.15e+32)
         (+ (* x (* y z)) (* b (- (* t i) (* z c))))
         (if (<= i 1.4e+73)
           (* t (- (* b i) (* x a)))
           (if (<= i 7e+98) (* j (- (* a c) (* y i))) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -5.2e+95) {
		tmp = t_1;
	} else if (i <= 4.3e-41) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (i <= 1.15e+32) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else if (i <= 1.4e+73) {
		tmp = t * ((b * i) - (x * a));
	} else if (i <= 7e+98) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = i * ((t * b) - (y * j))
    if (i <= (-5.2d+95)) then
        tmp = t_1
    else if (i <= 4.3d-41) then
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    else if (i <= 1.15d+32) then
        tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
    else if (i <= 1.4d+73) then
        tmp = t * ((b * i) - (x * a))
    else if (i <= 7d+98) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * ((t * b) - (y * j));
	double tmp;
	if (i <= -5.2e+95) {
		tmp = t_1;
	} else if (i <= 4.3e-41) {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	} else if (i <= 1.15e+32) {
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	} else if (i <= 1.4e+73) {
		tmp = t * ((b * i) - (x * a));
	} else if (i <= 7e+98) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * ((t * b) - (y * j))
	tmp = 0
	if i <= -5.2e+95:
		tmp = t_1
	elif i <= 4.3e-41:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	elif i <= 1.15e+32:
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)))
	elif i <= 1.4e+73:
		tmp = t * ((b * i) - (x * a))
	elif i <= 7e+98:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(Float64(t * b) - Float64(y * j)))
	tmp = 0.0
	if (i <= -5.2e+95)
		tmp = t_1;
	elseif (i <= 4.3e-41)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	elseif (i <= 1.15e+32)
		tmp = Float64(Float64(x * Float64(y * z)) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (i <= 1.4e+73)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (i <= 7e+98)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * ((t * b) - (y * j));
	tmp = 0.0;
	if (i <= -5.2e+95)
		tmp = t_1;
	elseif (i <= 4.3e-41)
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	elseif (i <= 1.15e+32)
		tmp = (x * (y * z)) + (b * ((t * i) - (z * c)));
	elseif (i <= 1.4e+73)
		tmp = t * ((b * i) - (x * a));
	elseif (i <= 7e+98)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -5.2e+95], t$95$1, If[LessEqual[i, 4.3e-41], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.15e+32], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.4e+73], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 7e+98], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -5.19999999999999981e95 or 7e98 < i

   1. Initial program 59.3%

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

   3. Taylor expanded in i around inf 75.2%

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

      1. distribute-lft-out-- 75.2%

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

      2. *-commutative 75.2%

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

      3. *-commutative 75.2%

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

   5. Simplified 75.2%

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

   6. Taylor expanded in i around 0 75.2%

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

      1. mul-1-neg 75.2%

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

      2. *-commutative 75.2%

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

      3. *-commutative 75.2%

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

      4. *-commutative 75.2%

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

      5. distribute-rgt-neg-in 75.2%

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

      6. *-commutative 75.2%

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

   8. Simplified 75.2%

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

   if -5.19999999999999981e95 < i < 4.2999999999999999e-41

   1. Initial program 83.0%

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

   3. Taylor expanded in j around 0 64.2%

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

   4. Taylor expanded in c around inf 60.0%

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

      1. *-commutative 60.0%

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

   6. Simplified 60.0%

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

   if 4.2999999999999999e-41 < i < 1.15e32

   1. Initial program 74.7%

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

   3. Taylor expanded in j around 0 56.9%

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

   4. Taylor expanded in a around 0 63.2%

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

      1. *-commutative 63.2%

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

      2. cancel-sign-sub-inv 63.2%

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

      3. +-commutative 63.2%

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

      4. +-commutative 63.2%

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

      5. cancel-sign-sub-inv 63.2%

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

      6. *-commutative 63.2%

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

      7. *-commutative 63.2%

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

   6. Simplified 63.2%

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

   if 1.15e32 < i < 1.40000000000000004e73

   1. Initial program 71.4%

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

   3. Taylor expanded in t around inf 71.4%

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

      1. distribute-lft-out-- 71.4%

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

      2. *-commutative 71.4%

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

      3. *-commutative 71.4%

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

   5. Simplified 71.4%

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

   if 1.40000000000000004e73 < i < 7e98

   1. Initial program 100.0%

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

   3. Taylor expanded in b around inf 100.0%

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

      1. fma-define 100.0%

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

      2. associate-/l* 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

      5. *-commutative 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in j around -inf 80.3%

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

      1. sub-neg 80.3%

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

      2. *-commutative 80.3%

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

      3. sub-neg 80.3%

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

   8. Simplified 80.3%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.2 \cdot 10^{+95}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;i \leq 4.3 \cdot 10^{-41}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.15 \cdot 10^{+32}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;i \leq 1.4 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;i \leq 7 \cdot 10^{+98}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 29.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := t \cdot \left(x \cdot \left(-a\right)\right)\\ t_3 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;x \leq -1 \cdot 10^{-48}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-255}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-175}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* t (* x (- a)))) (t_3 (* b (* t i))))
   (if (<= x -1e-48)
     t_2
     (if (<= x -1.8e-255)
       t_1
       (if (<= x 3.7e-175)
         t_3
         (if (<= x 2.1e-123) t_1 (if (<= x 5.8e+14) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = t * (x * -a);
	double t_3 = b * (t * i);
	double tmp;
	if (x <= -1e-48) {
		tmp = t_2;
	} else if (x <= -1.8e-255) {
		tmp = t_1;
	} else if (x <= 3.7e-175) {
		tmp = t_3;
	} else if (x <= 2.1e-123) {
		tmp = t_1;
	} else if (x <= 5.8e+14) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = i * (y * -j)
    t_2 = t * (x * -a)
    t_3 = b * (t * i)
    if (x <= (-1d-48)) then
        tmp = t_2
    else if (x <= (-1.8d-255)) then
        tmp = t_1
    else if (x <= 3.7d-175) then
        tmp = t_3
    else if (x <= 2.1d-123) then
        tmp = t_1
    else if (x <= 5.8d+14) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = t * (x * -a);
	double t_3 = b * (t * i);
	double tmp;
	if (x <= -1e-48) {
		tmp = t_2;
	} else if (x <= -1.8e-255) {
		tmp = t_1;
	} else if (x <= 3.7e-175) {
		tmp = t_3;
	} else if (x <= 2.1e-123) {
		tmp = t_1;
	} else if (x <= 5.8e+14) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = t * (x * -a)
	t_3 = b * (t * i)
	tmp = 0
	if x <= -1e-48:
		tmp = t_2
	elif x <= -1.8e-255:
		tmp = t_1
	elif x <= 3.7e-175:
		tmp = t_3
	elif x <= 2.1e-123:
		tmp = t_1
	elif x <= 5.8e+14:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	t_2 = Float64(t * Float64(x * Float64(-a)))
	t_3 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (x <= -1e-48)
		tmp = t_2;
	elseif (x <= -1.8e-255)
		tmp = t_1;
	elseif (x <= 3.7e-175)
		tmp = t_3;
	elseif (x <= 2.1e-123)
		tmp = t_1;
	elseif (x <= 5.8e+14)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	t_2 = t * (x * -a);
	t_3 = b * (t * i);
	tmp = 0.0;
	if (x <= -1e-48)
		tmp = t_2;
	elseif (x <= -1.8e-255)
		tmp = t_1;
	elseif (x <= 3.7e-175)
		tmp = t_3;
	elseif (x <= 2.1e-123)
		tmp = t_1;
	elseif (x <= 5.8e+14)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1e-48], t$95$2, If[LessEqual[x, -1.8e-255], t$95$1, If[LessEqual[x, 3.7e-175], t$95$3, If[LessEqual[x, 2.1e-123], t$95$1, If[LessEqual[x, 5.8e+14], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.9999999999999997e-49 or 5.8e14 < x

   1. Initial program 72.6%

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

   3. Taylor expanded in a around inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

      5. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in t around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

      4. associate-/l* 48.6%

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

      5. associate-/l* 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in c around 0 43.0%

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

       1. neg-mul-1 43.0%

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

       2. distribute-lft-neg-in 43.0%

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

       3. *-commutative 43.0%

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

   11. Simplified 43.0%

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

   if -9.9999999999999997e-49 < x < -1.8000000000000001e-255 or 3.69999999999999998e-175 < x < 2.0999999999999999e-123

   1. Initial program 74.7%

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

   3. Taylor expanded in i around inf 49.6%

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

      1. distribute-lft-out-- 49.6%

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

      2. *-commutative 49.6%

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

      3. *-commutative 49.6%

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

   5. Simplified 49.6%

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

   6. Taylor expanded in y around inf 41.9%

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

      1. mul-1-neg 41.9%

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

      2. *-commutative 41.9%

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

      3. distribute-rgt-neg-in 41.9%

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

      4. distribute-rgt-neg-out 41.9%

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

   8. Simplified 41.9%

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

   if -1.8000000000000001e-255 < x < 3.69999999999999998e-175 or 2.0999999999999999e-123 < x < 5.8e14

   1. Initial program 76.4%

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

   3. Taylor expanded in j around 0 63.7%

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

   4. Taylor expanded in i around inf 39.5%

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

      1. *-commutative 39.5%

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

   6. Simplified 39.5%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -1.8 \cdot 10^{-255}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-175}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-123}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+14}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+198}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-88}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-224}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.66 \cdot 10^{+103}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -1e+198)
   (* b (* t i))
   (if (<= b -3.9e+39)
     (* z (* c (- b)))
     (if (<= b -3.3e-88)
       (* (* x t) (- a))
       (if (<= b 1.05e-224)
         (* a (* c j))
         (if (<= b 1.66e+103) (* i (* y (- j))) (* t (* b i))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1e+198) {
		tmp = b * (t * i);
	} else if (b <= -3.9e+39) {
		tmp = z * (c * -b);
	} else if (b <= -3.3e-88) {
		tmp = (x * t) * -a;
	} else if (b <= 1.05e-224) {
		tmp = a * (c * j);
	} else if (b <= 1.66e+103) {
		tmp = i * (y * -j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-1d+198)) then
        tmp = b * (t * i)
    else if (b <= (-3.9d+39)) then
        tmp = z * (c * -b)
    else if (b <= (-3.3d-88)) then
        tmp = (x * t) * -a
    else if (b <= 1.05d-224) then
        tmp = a * (c * j)
    else if (b <= 1.66d+103) then
        tmp = i * (y * -j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -1e+198) {
		tmp = b * (t * i);
	} else if (b <= -3.9e+39) {
		tmp = z * (c * -b);
	} else if (b <= -3.3e-88) {
		tmp = (x * t) * -a;
	} else if (b <= 1.05e-224) {
		tmp = a * (c * j);
	} else if (b <= 1.66e+103) {
		tmp = i * (y * -j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -1e+198:
		tmp = b * (t * i)
	elif b <= -3.9e+39:
		tmp = z * (c * -b)
	elif b <= -3.3e-88:
		tmp = (x * t) * -a
	elif b <= 1.05e-224:
		tmp = a * (c * j)
	elif b <= 1.66e+103:
		tmp = i * (y * -j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -1e+198)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= -3.9e+39)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (b <= -3.3e-88)
		tmp = Float64(Float64(x * t) * Float64(-a));
	elseif (b <= 1.05e-224)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 1.66e+103)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -1e+198)
		tmp = b * (t * i);
	elseif (b <= -3.9e+39)
		tmp = z * (c * -b);
	elseif (b <= -3.3e-88)
		tmp = (x * t) * -a;
	elseif (b <= 1.05e-224)
		tmp = a * (c * j);
	elseif (b <= 1.66e+103)
		tmp = i * (y * -j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -1e+198], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.9e+39], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -3.3e-88], N[(N[(x * t), $MachinePrecision] * (-a)), $MachinePrecision], If[LessEqual[b, 1.05e-224], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.66e+103], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -1.00000000000000002e198

   1. Initial program 60.1%

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

   3. Taylor expanded in j around 0 73.4%

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

   4. Taylor expanded in i around inf 53.8%

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

      1. *-commutative 53.8%

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

   6. Simplified 53.8%

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

   if -1.00000000000000002e198 < b < -3.9000000000000001e39

   1. Initial program 73.4%

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

   3. Taylor expanded in z around inf 50.6%

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

      1. *-commutative 50.6%

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

   5. Simplified 50.6%

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

   6. Taylor expanded in x around 0 44.1%

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

      1. neg-mul-1 44.1%

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

      2. distribute-rgt-neg-in 44.1%

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

   8. Simplified 44.1%

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

   if -3.9000000000000001e39 < b < -3.29999999999999994e-88

   1. Initial program 75.6%

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

   3. Taylor expanded in a around inf 42.1%

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

      1. +-commutative 42.1%

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

      2. mul-1-neg 42.1%

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

      3. unsub-neg 42.1%

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

      4. *-commutative 42.1%

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

      5. *-commutative 42.1%

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

   5. Simplified 42.1%

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

   6. Taylor expanded in j around 0 36.7%

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

      1. mul-1-neg 36.7%

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

      2. *-commutative 36.7%

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

      3. distribute-rgt-neg-in 36.7%

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

   8. Simplified 36.7%

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

   if -3.29999999999999994e-88 < b < 1.05000000000000003e-224

   1. Initial program 80.4%

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

   3. Taylor expanded in a around inf 51.3%

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

      1. +-commutative 51.3%

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

      2. mul-1-neg 51.3%

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

      3. unsub-neg 51.3%

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

      4. *-commutative 51.3%

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

      5. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in j around inf 39.4%

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

      1. *-commutative 39.4%

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

   8. Simplified 39.4%

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

   if 1.05000000000000003e-224 < b < 1.6600000000000001e103

   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 i around inf 49.1%

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

      1. distribute-lft-out-- 49.1%

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

      2. *-commutative 49.1%

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

      3. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in y around inf 38.5%

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

      1. mul-1-neg 38.5%

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

      2. *-commutative 38.5%

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

      3. distribute-rgt-neg-in 38.5%

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

      4. distribute-rgt-neg-out 38.5%

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

   8. Simplified 38.5%

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

   if 1.6600000000000001e103 < b

   1. Initial program 80.9%

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

   3. Taylor expanded in j around 0 78.5%

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

   4. Taylor expanded in i around inf 41.2%

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

      1. associate-*r* 46.1%

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

   6. Simplified 46.1%

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

4. Final simplification 41.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{+198}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq -3.9 \cdot 10^{+39}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;b \leq -3.3 \cdot 10^{-88}:\\ \;\;\;\;\left(x \cdot t\right) \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-224}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 1.66 \cdot 10^{+103}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 29.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := t \cdot \left(x \cdot \left(-a\right)\right)\\ t_3 := i \cdot \left(t \cdot b\right)\\ \mathbf{if}\;x \leq -7.5 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-260}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-174}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-110}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+14}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* t (* x (- a)))) (t_3 (* i (* t b))))
   (if (<= x -7.5e-52)
     t_2
     (if (<= x -4.8e-260)
       t_1
       (if (<= x 2.3e-174)
         t_3
         (if (<= x 2.3e-110) t_1 (if (<= x 1.85e+14) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = t * (x * -a);
	double t_3 = i * (t * b);
	double tmp;
	if (x <= -7.5e-52) {
		tmp = t_2;
	} else if (x <= -4.8e-260) {
		tmp = t_1;
	} else if (x <= 2.3e-174) {
		tmp = t_3;
	} else if (x <= 2.3e-110) {
		tmp = t_1;
	} else if (x <= 1.85e+14) {
		tmp = t_3;
	} 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) :: t_3
    real(8) :: tmp
    t_1 = i * (y * -j)
    t_2 = t * (x * -a)
    t_3 = i * (t * b)
    if (x <= (-7.5d-52)) then
        tmp = t_2
    else if (x <= (-4.8d-260)) then
        tmp = t_1
    else if (x <= 2.3d-174) then
        tmp = t_3
    else if (x <= 2.3d-110) then
        tmp = t_1
    else if (x <= 1.85d+14) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = t * (x * -a);
	double t_3 = i * (t * b);
	double tmp;
	if (x <= -7.5e-52) {
		tmp = t_2;
	} else if (x <= -4.8e-260) {
		tmp = t_1;
	} else if (x <= 2.3e-174) {
		tmp = t_3;
	} else if (x <= 2.3e-110) {
		tmp = t_1;
	} else if (x <= 1.85e+14) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = t * (x * -a)
	t_3 = i * (t * b)
	tmp = 0
	if x <= -7.5e-52:
		tmp = t_2
	elif x <= -4.8e-260:
		tmp = t_1
	elif x <= 2.3e-174:
		tmp = t_3
	elif x <= 2.3e-110:
		tmp = t_1
	elif x <= 1.85e+14:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	t_2 = Float64(t * Float64(x * Float64(-a)))
	t_3 = Float64(i * Float64(t * b))
	tmp = 0.0
	if (x <= -7.5e-52)
		tmp = t_2;
	elseif (x <= -4.8e-260)
		tmp = t_1;
	elseif (x <= 2.3e-174)
		tmp = t_3;
	elseif (x <= 2.3e-110)
		tmp = t_1;
	elseif (x <= 1.85e+14)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	t_2 = t * (x * -a);
	t_3 = i * (t * b);
	tmp = 0.0;
	if (x <= -7.5e-52)
		tmp = t_2;
	elseif (x <= -4.8e-260)
		tmp = t_1;
	elseif (x <= 2.3e-174)
		tmp = t_3;
	elseif (x <= 2.3e-110)
		tmp = t_1;
	elseif (x <= 1.85e+14)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(x * (-a)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.5e-52], t$95$2, If[LessEqual[x, -4.8e-260], t$95$1, If[LessEqual[x, 2.3e-174], t$95$3, If[LessEqual[x, 2.3e-110], t$95$1, If[LessEqual[x, 1.85e+14], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.50000000000000006e-52 or 1.85e14 < x

   1. Initial program 72.6%

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

   3. Taylor expanded in a around inf 53.6%

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

      1. +-commutative 53.6%

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

      2. mul-1-neg 53.6%

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

      3. unsub-neg 53.6%

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

      4. *-commutative 53.6%

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

      5. *-commutative 53.6%

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

   5. Simplified 53.6%

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

   6. Taylor expanded in t around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

      4. associate-/l* 48.6%

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

      5. associate-/l* 50.0%

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

   8. Simplified 50.0%

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

   9. Taylor expanded in c around 0 43.0%

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

       1. neg-mul-1 43.0%

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

       2. distribute-lft-neg-in 43.0%

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

       3. *-commutative 43.0%

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

   11. Simplified 43.0%

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

   if -7.50000000000000006e-52 < x < -4.8000000000000001e-260 or 2.2999999999999999e-174 < x < 2.3000000000000001e-110

   1. Initial program 76.0%

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

   3. Taylor expanded in i around inf 47.5%

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

      1. distribute-lft-out-- 47.5%

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

      2. *-commutative 47.5%

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

      3. *-commutative 47.5%

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

   5. Simplified 47.5%

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

   6. Taylor expanded in y around inf 40.1%

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

      1. mul-1-neg 40.1%

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

      2. *-commutative 40.1%

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

      3. distribute-rgt-neg-in 40.1%

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

      4. distribute-rgt-neg-out 40.1%

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

   8. Simplified 40.1%

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

   if -4.8000000000000001e-260 < x < 2.2999999999999999e-174 or 2.3000000000000001e-110 < x < 1.85e14

   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 i around inf 54.1%

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

      1. distribute-lft-out-- 54.1%

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

      2. *-commutative 54.1%

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

      3. *-commutative 54.1%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in y around 0 41.5%

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

      1. mul-1-neg 41.5%

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

      2. *-commutative 41.5%

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

      3. distribute-rgt-neg-in 41.5%

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

   8. Simplified 41.5%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.5 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-260}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-174}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-110}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{+14}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(x \cdot \left(-a\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{-39}:\\ \;\;\;\;t\_1 + b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(t\_1 + t \cdot \left(b \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= b -1e-39)
     (+ t_1 (* b (* c (- (/ (* t i) c) z))))
     (+ (+ t_1 (* t (* b i))) (* 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 tmp;
	if (b <= -1e-39) {
		tmp = t_1 + (b * (c * (((t * i) / c) - z)));
	} else {
		tmp = (t_1 + (t * (b * i))) + (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) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (b <= (-1d-39)) then
        tmp = t_1 + (b * (c * (((t * i) / c) - z)))
    else
        tmp = (t_1 + (t * (b * i))) + (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 tmp;
	if (b <= -1e-39) {
		tmp = t_1 + (b * (c * (((t * i) / c) - z)));
	} else {
		tmp = (t_1 + (t * (b * i))) + (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))
	tmp = 0
	if b <= -1e-39:
		tmp = t_1 + (b * (c * (((t * i) / c) - z)))
	else:
		tmp = (t_1 + (t * (b * i))) + (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)))
	tmp = 0.0
	if (b <= -1e-39)
		tmp = Float64(t_1 + Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - z))));
	else
		tmp = Float64(Float64(t_1 + Float64(t * Float64(b * i))) + 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));
	tmp = 0.0;
	if (b <= -1e-39)
		tmp = t_1 + (b * (c * (((t * i) / c) - z)));
	else
		tmp = (t_1 + (t * (b * i))) + (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]}, If[LessEqual[b, -1e-39], N[(t$95$1 + N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 + N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.99999999999999929e-40

   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 j around 0 70.2%

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

   4. Taylor expanded in c around inf 70.5%

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

      1. associate-*r/ 70.5%

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

      2. mul-1-neg 70.5%

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

      3. distribute-lft-neg-out 70.5%

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

      4. *-commutative 70.5%

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

   6. Simplified 70.5%

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

   if -9.99999999999999929e-40 < b

   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 c around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. *-commutative 73.8%

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

      3. associate-*r* 76.2%

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

      4. distribute-rgt-neg-out 76.2%

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

      5. *-commutative 76.2%

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

      6. associate-*l* 76.7%

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

   5. Simplified 76.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1 \cdot 10^{-39}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) + t \cdot \left(b \cdot i\right)\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{-76} \lor \neg \left(b \leq 4.4 \cdot 10^{+103}\right):\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (or (<= b -1.2e-76) (not (<= b 4.4e+103)))
     (+ t_1 (* b (- (* t i) (* z c))))
     (+ 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 tmp;
	if ((b <= -1.2e-76) || !(b <= 4.4e+103)) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} 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) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if ((b <= (-1.2d-76)) .or. (.not. (b <= 4.4d+103))) then
        tmp = t_1 + (b * ((t * i) - (z * c)))
    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 tmp;
	if ((b <= -1.2e-76) || !(b <= 4.4e+103)) {
		tmp = t_1 + (b * ((t * i) - (z * c)));
	} 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))
	tmp = 0
	if (b <= -1.2e-76) or not (b <= 4.4e+103):
		tmp = t_1 + (b * ((t * i) - (z * c)))
	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)))
	tmp = 0.0
	if ((b <= -1.2e-76) || !(b <= 4.4e+103))
		tmp = Float64(t_1 + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	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));
	tmp = 0.0;
	if ((b <= -1.2e-76) || ~((b <= 4.4e+103)))
		tmp = t_1 + (b * ((t * i) - (z * c)));
	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]}, If[Or[LessEqual[b, -1.2e-76], N[Not[LessEqual[b, 4.4e+103]], $MachinePrecision]], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -1.20000000000000007e-76 or 4.39999999999999985e103 < b

   1. Initial program 73.8%

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

   3. Taylor expanded in j around 0 73.1%

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

   if -1.20000000000000007e-76 < b < 4.39999999999999985e103

   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 74.6%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.2 \cdot 10^{-76} \lor \neg \left(b \leq 4.4 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \left(y \cdot z - t \cdot a\right)\\ \mathbf{if}\;b \leq -3.15 \cdot 10^{-84}:\\ \;\;\;\;t\_1 + b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;t\_1 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1 + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* x (- (* y z) (* t a)))))
   (if (<= b -3.15e-84)
     (+ t_1 (* b (* c (- (/ (* t i) c) z))))
     (if (<= b 2.1e+103)
       (+ t_1 (* j (- (* a c) (* y i))))
       (+ t_1 (* 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 tmp;
	if (b <= -3.15e-84) {
		tmp = t_1 + (b * (c * (((t * i) / c) - z)));
	} else if (b <= 2.1e+103) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1 + (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) :: tmp
    t_1 = x * ((y * z) - (t * a))
    if (b <= (-3.15d-84)) then
        tmp = t_1 + (b * (c * (((t * i) / c) - z)))
    else if (b <= 2.1d+103) then
        tmp = t_1 + (j * ((a * c) - (y * i)))
    else
        tmp = t_1 + (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 tmp;
	if (b <= -3.15e-84) {
		tmp = t_1 + (b * (c * (((t * i) / c) - z)));
	} else if (b <= 2.1e+103) {
		tmp = t_1 + (j * ((a * c) - (y * i)));
	} else {
		tmp = t_1 + (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))
	tmp = 0
	if b <= -3.15e-84:
		tmp = t_1 + (b * (c * (((t * i) / c) - z)))
	elif b <= 2.1e+103:
		tmp = t_1 + (j * ((a * c) - (y * i)))
	else:
		tmp = t_1 + (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)))
	tmp = 0.0
	if (b <= -3.15e-84)
		tmp = Float64(t_1 + Float64(b * Float64(c * Float64(Float64(Float64(t * i) / c) - z))));
	elseif (b <= 2.1e+103)
		tmp = Float64(t_1 + Float64(j * Float64(Float64(a * c) - Float64(y * i))));
	else
		tmp = Float64(t_1 + 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));
	tmp = 0.0;
	if (b <= -3.15e-84)
		tmp = t_1 + (b * (c * (((t * i) / c) - z)));
	elseif (b <= 2.1e+103)
		tmp = t_1 + (j * ((a * c) - (y * i)));
	else
		tmp = t_1 + (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]}, If[LessEqual[b, -3.15e-84], N[(t$95$1 + N[(b * N[(c * N[(N[(N[(t * i), $MachinePrecision] / c), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+103], N[(t$95$1 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -3.1500000000000002e-84

   1. Initial program 70.9%

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

   3. Taylor expanded in j around 0 69.8%

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

   4. Taylor expanded in c around inf 71.1%

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

      1. associate-*r/ 71.1%

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

      2. mul-1-neg 71.1%

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

      3. distribute-lft-neg-out 71.1%

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

      4. *-commutative 71.1%

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

   6. Simplified 71.1%

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

   if -3.1500000000000002e-84 < b < 2.1000000000000002e103

   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 b around 0 74.8%

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

   if 2.1000000000000002e103 < b

   1. Initial program 80.9%

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

   3. Taylor expanded in j around 0 78.5%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.15 \cdot 10^{-84}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(c \cdot \left(\frac{t \cdot i}{c} - z\right)\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 39.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := i \cdot \left(y \cdot \left(-j\right)\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;y \leq 78000:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+171}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+238}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* i (* y (- j)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= y 78000.0)
     t_2
     (if (<= y 2.7e+52)
       t_1
       (if (<= y 7.5e+171) t_2 (if (<= y 1.65e+238) t_1 (* x (* y z))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= 78000.0) {
		tmp = t_2;
	} else if (y <= 2.7e+52) {
		tmp = t_1;
	} else if (y <= 7.5e+171) {
		tmp = t_2;
	} else if (y <= 1.65e+238) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = i * (y * -j)
    t_2 = a * ((c * j) - (x * t))
    if (y <= 78000.0d0) then
        tmp = t_2
    else if (y <= 2.7d+52) then
        tmp = t_1
    else if (y <= 7.5d+171) then
        tmp = t_2
    else if (y <= 1.65d+238) then
        tmp = t_1
    else
        tmp = x * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = i * (y * -j);
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (y <= 78000.0) {
		tmp = t_2;
	} else if (y <= 2.7e+52) {
		tmp = t_1;
	} else if (y <= 7.5e+171) {
		tmp = t_2;
	} else if (y <= 1.65e+238) {
		tmp = t_1;
	} else {
		tmp = x * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = i * (y * -j)
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if y <= 78000.0:
		tmp = t_2
	elif y <= 2.7e+52:
		tmp = t_1
	elif y <= 7.5e+171:
		tmp = t_2
	elif y <= 1.65e+238:
		tmp = t_1
	else:
		tmp = x * (y * z)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(i * Float64(y * Float64(-j)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (y <= 78000.0)
		tmp = t_2;
	elseif (y <= 2.7e+52)
		tmp = t_1;
	elseif (y <= 7.5e+171)
		tmp = t_2;
	elseif (y <= 1.65e+238)
		tmp = t_1;
	else
		tmp = Float64(x * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = i * (y * -j);
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (y <= 78000.0)
		tmp = t_2;
	elseif (y <= 2.7e+52)
		tmp = t_1;
	elseif (y <= 7.5e+171)
		tmp = t_2;
	elseif (y <= 1.65e+238)
		tmp = t_1;
	else
		tmp = x * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 78000.0], t$95$2, If[LessEqual[y, 2.7e+52], t$95$1, If[LessEqual[y, 7.5e+171], t$95$2, If[LessEqual[y, 1.65e+238], t$95$1, N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < 78000 or 2.7e52 < y < 7.4999999999999998e171

   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 a around inf 48.6%

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

      1. +-commutative 48.6%

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

      2. mul-1-neg 48.6%

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

      3. unsub-neg 48.6%

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

      4. *-commutative 48.6%

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

      5. *-commutative 48.6%

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

   5. Simplified 48.6%

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

   if 78000 < y < 2.7e52 or 7.4999999999999998e171 < y < 1.65e238

   1. Initial program 61.5%

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

   3. Taylor expanded in i around inf 72.6%

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

      1. distribute-lft-out-- 72.6%

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

      2. *-commutative 72.6%

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

      3. *-commutative 72.6%

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

   5. Simplified 72.6%

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

   6. Taylor expanded in y around inf 61.3%

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

      1. mul-1-neg 61.3%

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

      2. *-commutative 61.3%

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

      3. distribute-rgt-neg-in 61.3%

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

      4. distribute-rgt-neg-out 61.3%

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

   8. Simplified 61.3%

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

   if 1.65e238 < y

   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 z around inf 48.1%

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

      1. *-commutative 48.1%

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

   5. Simplified 48.1%

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

   6. Taylor expanded in x around inf 63.3%

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

      1. *-commutative 63.3%

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

   8. Simplified 63.3%

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

4. Final simplification 51.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 78000:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+52}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+171}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+238}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 29.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+125}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= a -7.5e+125)
   (* c (* a j))
   (if (<= a -1.05e-82)
     (* b (* t i))
     (if (<= a -4.8e-261)
       (* z (* x y))
       (if (<= a 6.5e-48) (* t (* b 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 (a <= -7.5e+125) {
		tmp = c * (a * j);
	} else if (a <= -1.05e-82) {
		tmp = b * (t * i);
	} else if (a <= -4.8e-261) {
		tmp = z * (x * y);
	} else if (a <= 6.5e-48) {
		tmp = t * (b * 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 (a <= (-7.5d+125)) then
        tmp = c * (a * j)
    else if (a <= (-1.05d-82)) then
        tmp = b * (t * i)
    else if (a <= (-4.8d-261)) then
        tmp = z * (x * y)
    else if (a <= 6.5d-48) then
        tmp = t * (b * 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 (a <= -7.5e+125) {
		tmp = c * (a * j);
	} else if (a <= -1.05e-82) {
		tmp = b * (t * i);
	} else if (a <= -4.8e-261) {
		tmp = z * (x * y);
	} else if (a <= 6.5e-48) {
		tmp = t * (b * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if a <= -7.5e+125:
		tmp = c * (a * j)
	elif a <= -1.05e-82:
		tmp = b * (t * i)
	elif a <= -4.8e-261:
		tmp = z * (x * y)
	elif a <= 6.5e-48:
		tmp = t * (b * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (a <= -7.5e+125)
		tmp = Float64(c * Float64(a * j));
	elseif (a <= -1.05e-82)
		tmp = Float64(b * Float64(t * i));
	elseif (a <= -4.8e-261)
		tmp = Float64(z * Float64(x * y));
	elseif (a <= 6.5e-48)
		tmp = Float64(t * Float64(b * 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 (a <= -7.5e+125)
		tmp = c * (a * j);
	elseif (a <= -1.05e-82)
		tmp = b * (t * i);
	elseif (a <= -4.8e-261)
		tmp = z * (x * y);
	elseif (a <= 6.5e-48)
		tmp = t * (b * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[a, -7.5e+125], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.05e-82], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -4.8e-261], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-48], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -7.5000000000000006e125

   1. Initial program 57.8%

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

   3. Taylor expanded in z around inf 63.3%

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

   4. Taylor expanded in c around inf 65.4%

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

   5. Taylor expanded in z around 0 48.7%

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

      1. *-commutative 48.7%

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

      2. associate-*l* 51.0%

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

      3. *-commutative 51.0%

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

   7. Simplified 51.0%

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

   if -7.5000000000000006e125 < a < -1.05e-82

   1. Initial program 82.6%

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

   3. Taylor expanded in j around 0 67.7%

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

   4. Taylor expanded in i around inf 33.5%

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

      1. *-commutative 33.5%

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

   6. Simplified 33.5%

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

   if -1.05e-82 < a < -4.80000000000000028e-261

   1. Initial program 77.9%

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

   3. Taylor expanded in z around inf 51.3%

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

      1. *-commutative 51.3%

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

   5. Simplified 51.3%

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

   6. Taylor expanded in x around inf 37.8%

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

      1. *-commutative 37.8%

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

   8. Simplified 37.8%

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

   if -4.80000000000000028e-261 < a < 6.5e-48

   1. Initial program 86.3%

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

   3. Taylor expanded in j around 0 70.2%

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

   4. Taylor expanded in i around inf 28.7%

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

      1. associate-*r* 36.0%

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

   6. Simplified 36.0%

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

   if 6.5e-48 < a

   1. Initial program 66.0%

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

   3. Taylor expanded in a around inf 64.9%

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

      1. +-commutative 64.9%

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

      2. mul-1-neg 64.9%

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

      3. unsub-neg 64.9%

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

      4. *-commutative 64.9%

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

      5. *-commutative 64.9%

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

   5. Simplified 64.9%

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

   6. Taylor expanded in j around inf 34.2%

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

      1. *-commutative 34.2%

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

   8. Simplified 34.2%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7.5 \cdot 10^{+125}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \mathbf{elif}\;a \leq -1.05 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-261}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-48}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 58.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+96} \lor \neg \left(i \leq 9.5 \cdot 10^{-50}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.25e+96) (not (<= i 9.5e-50)))
   (* i (- (* t b) (* y j)))
   (- (* x (- (* y z) (* t a))) (* 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 tmp;
	if ((i <= -1.25e+96) || !(i <= 9.5e-50)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.25d+96)) .or. (.not. (i <= 9.5d-50))) then
        tmp = i * ((t * b) - (y * j))
    else
        tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.25e+96) || !(i <= 9.5e-50)) {
		tmp = i * ((t * b) - (y * j));
	} else {
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.25e+96) or not (i <= 9.5e-50):
		tmp = i * ((t * b) - (y * j))
	else:
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.25e+96) || !(i <= 9.5e-50))
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	else
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(b * Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.25e+96) || ~((i <= 9.5e-50)))
		tmp = i * ((t * b) - (y * j));
	else
		tmp = (x * ((y * z) - (t * a))) - (b * (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.25e+96], N[Not[LessEqual[i, 9.5e-50]], $MachinePrecision]], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.2500000000000001e96 or 9.4999999999999993e-50 < i

   1. Initial program 64.1%

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

   3. Taylor expanded in i around inf 69.0%

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

      1. distribute-lft-out-- 69.0%

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

      2. *-commutative 69.0%

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

      3. *-commutative 69.0%

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

   5. Simplified 69.0%

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

   6. Taylor expanded in i around 0 69.0%

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

      1. mul-1-neg 69.0%

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

      2. *-commutative 69.0%

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

      3. *-commutative 69.0%

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

      4. *-commutative 69.0%

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

      5. distribute-rgt-neg-in 69.0%

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

      6. *-commutative 69.0%

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

   8. Simplified 69.0%

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

   if -1.2500000000000001e96 < i < 9.4999999999999993e-50

   1. Initial program 82.8%

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

   3. Taylor expanded in j around 0 64.6%

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

   4. Taylor expanded in c around inf 60.4%

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

      1. *-commutative 60.4%

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

   6. Simplified 60.4%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.25 \cdot 10^{+96} \lor \neg \left(i \leq 9.5 \cdot 10^{-50}\right):\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 47.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;j \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+88}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (- (* c j) (* x t)))))
   (if (<= j -2.5e-40)
     t_1
     (if (<= j 4.4e-105)
       (* b (- (* t i) (* z c)))
       (if (<= j 6e+88) 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 = a * ((c * j) - (x * t));
	double tmp;
	if (j <= -2.5e-40) {
		tmp = t_1;
	} else if (j <= 4.4e-105) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 6e+88) {
		tmp = t_1;
	} else {
		tmp = 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) :: tmp
    t_1 = a * ((c * j) - (x * t))
    if (j <= (-2.5d-40)) then
        tmp = t_1
    else if (j <= 4.4d-105) then
        tmp = b * ((t * i) - (z * c))
    else if (j <= 6d+88) then
        tmp = t_1
    else
        tmp = 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 = a * ((c * j) - (x * t));
	double tmp;
	if (j <= -2.5e-40) {
		tmp = t_1;
	} else if (j <= 4.4e-105) {
		tmp = b * ((t * i) - (z * c));
	} else if (j <= 6e+88) {
		tmp = t_1;
	} else {
		tmp = j * ((a * c) - (y * i));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * ((c * j) - (x * t))
	tmp = 0
	if j <= -2.5e-40:
		tmp = t_1
	elif j <= 4.4e-105:
		tmp = b * ((t * i) - (z * c))
	elif j <= 6e+88:
		tmp = t_1
	else:
		tmp = j * ((a * c) - (y * i))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (j <= -2.5e-40)
		tmp = t_1;
	elseif (j <= 4.4e-105)
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	elseif (j <= 6e+88)
		tmp = t_1;
	else
		tmp = 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 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (j <= -2.5e-40)
		tmp = t_1;
	elseif (j <= 4.4e-105)
		tmp = b * ((t * i) - (z * c));
	elseif (j <= 6e+88)
		tmp = t_1;
	else
		tmp = 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[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.5e-40], t$95$1, If[LessEqual[j, 4.4e-105], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 6e+88], t$95$1, N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.49999999999999982e-40 or 4.40000000000000008e-105 < j < 6.00000000000000011e88

   1. Initial program 72.5%

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

   3. Taylor expanded in a around inf 54.2%

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

      1. +-commutative 54.2%

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

      2. mul-1-neg 54.2%

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

      3. unsub-neg 54.2%

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

      4. *-commutative 54.2%

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

      5. *-commutative 54.2%

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

   5. Simplified 54.2%

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

   if -2.49999999999999982e-40 < j < 4.40000000000000008e-105

   1. Initial program 75.7%

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

   3. Taylor expanded in b around inf 48.9%

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

      1. *-commutative 48.9%

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

      2. *-commutative 48.9%

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

   5. Simplified 48.9%

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

   if 6.00000000000000011e88 < j

   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 b around inf 67.2%

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

      1. fma-define 72.4%

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

      2. associate-/l* 72.3%

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

      3. *-commutative 72.3%

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

      4. associate-/l* 74.9%

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

      5. *-commutative 74.9%

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

   5. Simplified 74.9%

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

   6. Taylor expanded in j around -inf 77.7%

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

      1. sub-neg 77.7%

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

      2. *-commutative 77.7%

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

      3. sub-neg 77.7%

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

   8. Simplified 77.7%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.5 \cdot 10^{-40}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;j \leq 4.4 \cdot 10^{-105}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 6 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-226}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= b -2.4e-60)
   (* b (* t i))
   (if (<= b 1.5e-226)
     (* a (* c j))
     (if (<= b 2.1e+103) (* i (* y (- j))) (* t (* b i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.4e-60) {
		tmp = b * (t * i);
	} else if (b <= 1.5e-226) {
		tmp = a * (c * j);
	} else if (b <= 2.1e+103) {
		tmp = i * (y * -j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (b <= (-2.4d-60)) then
        tmp = b * (t * i)
    else if (b <= 1.5d-226) then
        tmp = a * (c * j)
    else if (b <= 2.1d+103) then
        tmp = i * (y * -j)
    else
        tmp = t * (b * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (b <= -2.4e-60) {
		tmp = b * (t * i);
	} else if (b <= 1.5e-226) {
		tmp = a * (c * j);
	} else if (b <= 2.1e+103) {
		tmp = i * (y * -j);
	} else {
		tmp = t * (b * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if b <= -2.4e-60:
		tmp = b * (t * i)
	elif b <= 1.5e-226:
		tmp = a * (c * j)
	elif b <= 2.1e+103:
		tmp = i * (y * -j)
	else:
		tmp = t * (b * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (b <= -2.4e-60)
		tmp = Float64(b * Float64(t * i));
	elseif (b <= 1.5e-226)
		tmp = Float64(a * Float64(c * j));
	elseif (b <= 2.1e+103)
		tmp = Float64(i * Float64(y * Float64(-j)));
	else
		tmp = Float64(t * Float64(b * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (b <= -2.4e-60)
		tmp = b * (t * i);
	elseif (b <= 1.5e-226)
		tmp = a * (c * j);
	elseif (b <= 2.1e+103)
		tmp = i * (y * -j);
	else
		tmp = t * (b * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[b, -2.4e-60], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.5e-226], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+103], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.40000000000000009e-60

   1. Initial program 70.5%

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

   3. Taylor expanded in j around 0 70.4%

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

   4. Taylor expanded in i around inf 36.6%

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

      1. *-commutative 36.6%

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

   6. Simplified 36.6%

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

   if -2.40000000000000009e-60 < b < 1.49999999999999998e-226

   1. Initial program 78.3%

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

   3. Taylor expanded in a around inf 55.5%

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

      1. +-commutative 55.5%

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

      2. mul-1-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. *-commutative 55.5%

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

      5. *-commutative 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in j around inf 38.7%

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

      1. *-commutative 38.7%

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

   8. Simplified 38.7%

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

   if 1.49999999999999998e-226 < b < 2.1000000000000002e103

   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 i around inf 49.1%

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

      1. distribute-lft-out-- 49.1%

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

      2. *-commutative 49.1%

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

      3. *-commutative 49.1%

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

   5. Simplified 49.1%

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

   6. Taylor expanded in y around inf 38.5%

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

      1. mul-1-neg 38.5%

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

      2. *-commutative 38.5%

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

      3. distribute-rgt-neg-in 38.5%

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

      4. distribute-rgt-neg-out 38.5%

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

   8. Simplified 38.5%

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

   if 2.1000000000000002e103 < b

   1. Initial program 80.9%

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

   3. Taylor expanded in j around 0 78.5%

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

   4. Taylor expanded in i around inf 41.2%

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

      1. associate-*r* 46.1%

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

   6. Simplified 46.1%

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

4. Final simplification 39.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.4 \cdot 10^{-60}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;b \leq 1.5 \cdot 10^{-226}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+103}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -56000000000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= j -56000000000000.0)
   (* a (* c j))
   (if (<= j 2.65e-99)
     (* b (* t i))
     (if (<= j 1.15e+168) (* z (* x y)) (* c (* a j))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -56000000000000.0) {
		tmp = a * (c * j);
	} else if (j <= 2.65e-99) {
		tmp = b * (t * i);
	} else if (j <= 1.15e+168) {
		tmp = z * (x * y);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (j <= (-56000000000000.0d0)) then
        tmp = a * (c * j)
    else if (j <= 2.65d-99) then
        tmp = b * (t * i)
    else if (j <= 1.15d+168) then
        tmp = z * (x * y)
    else
        tmp = c * (a * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (j <= -56000000000000.0) {
		tmp = a * (c * j);
	} else if (j <= 2.65e-99) {
		tmp = b * (t * i);
	} else if (j <= 1.15e+168) {
		tmp = z * (x * y);
	} else {
		tmp = c * (a * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if j <= -56000000000000.0:
		tmp = a * (c * j)
	elif j <= 2.65e-99:
		tmp = b * (t * i)
	elif j <= 1.15e+168:
		tmp = z * (x * y)
	else:
		tmp = c * (a * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (j <= -56000000000000.0)
		tmp = Float64(a * Float64(c * j));
	elseif (j <= 2.65e-99)
		tmp = Float64(b * Float64(t * i));
	elseif (j <= 1.15e+168)
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(c * Float64(a * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (j <= -56000000000000.0)
		tmp = a * (c * j);
	elseif (j <= 2.65e-99)
		tmp = b * (t * i);
	elseif (j <= 1.15e+168)
		tmp = z * (x * y);
	else
		tmp = c * (a * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[j, -56000000000000.0], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.65e-99], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 1.15e+168], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(c * N[(a * j), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if j < -5.6e13

   1. Initial program 74.2%

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

   3. Taylor expanded in a around inf 55.7%

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

      1. +-commutative 55.7%

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

      2. mul-1-neg 55.7%

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

      3. unsub-neg 55.7%

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

      4. *-commutative 55.7%

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

      5. *-commutative 55.7%

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

   5. Simplified 55.7%

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

   6. Taylor expanded in j around inf 43.2%

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

      1. *-commutative 43.2%

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

   8. Simplified 43.2%

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

   if -5.6e13 < j < 2.6500000000000002e-99

   1. Initial program 76.9%

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

   3. Taylor expanded in j around 0 72.5%

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

   4. Taylor expanded in i around inf 32.6%

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

      1. *-commutative 32.6%

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

   6. Simplified 32.6%

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

   if 2.6500000000000002e-99 < j < 1.15e168

   1. Initial program 69.2%

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

   3. Taylor expanded in z around inf 36.4%

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

      1. *-commutative 36.4%

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

   5. Simplified 36.4%

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

   6. Taylor expanded in x around inf 23.5%

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

      1. *-commutative 23.5%

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

   8. Simplified 23.5%

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

   if 1.15e168 < j

   1. Initial program 71.3%

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

   3. Taylor expanded in z around inf 57.8%

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

   4. Taylor expanded in c around inf 58.1%

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

   5. Taylor expanded in z around 0 47.8%

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

      1. *-commutative 47.8%

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

      2. associate-*l* 51.0%

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

      3. *-commutative 51.0%

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

   7. Simplified 51.0%

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

4. Final simplification 35.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -56000000000000:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;j \leq 2.65 \cdot 10^{-99}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;j \leq 1.15 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;c \cdot \left(a \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 50.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+26} \lor \neg \left(a \leq 6.5 \cdot 10^{-53}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= a -1.8e+26) (not (<= a 6.5e-53)))
   (* a (- (* c j) (* x t)))
   (* b (- (* t i) (* z c)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.8e+26) || !(a <= 6.5e-53)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((a <= (-1.8d+26)) .or. (.not. (a <= 6.5d-53))) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * ((t * i) - (z * c))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((a <= -1.8e+26) || !(a <= 6.5e-53)) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * ((t * i) - (z * c));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (a <= -1.8e+26) or not (a <= 6.5e-53):
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * ((t * i) - (z * c))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((a <= -1.8e+26) || !(a <= 6.5e-53))
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(Float64(t * i) - Float64(z * c)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((a <= -1.8e+26) || ~((a <= 6.5e-53)))
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * ((t * i) - (z * c));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[a, -1.8e+26], N[Not[LessEqual[a, 6.5e-53]], $MachinePrecision]], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -1.80000000000000012e26 or 6.4999999999999997e-53 < a

   1. Initial program 67.3%

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

   3. Taylor expanded in a around inf 62.3%

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

      1. +-commutative 62.3%

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

      2. mul-1-neg 62.3%

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

      3. unsub-neg 62.3%

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

      4. *-commutative 62.3%

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

      5. *-commutative 62.3%

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

   5. Simplified 62.3%

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

   if -1.80000000000000012e26 < a < 6.4999999999999997e-53

   1. Initial program 82.4%

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

   3. Taylor expanded in b around inf 44.2%

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

      1. *-commutative 44.2%

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

      2. *-commutative 44.2%

         \[\leadsto b \cdot \left(t \cdot i - \color{blue}{z \cdot c}\right) \]

   5. Simplified 44.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i - z \cdot c\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.8 \cdot 10^{+26} \lor \neg \left(a \leq 6.5 \cdot 10^{-53}\right):\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 50.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+69} \lor \neg \left(j \leq 2.4 \cdot 10^{+103}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= j -1.4e+69) (not (<= j 2.4e+103)))
   (* j (- (* a c) (* y i)))
   (* x (- (* y z) (* t a)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.4e+69) || !(j <= 2.4e+103)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((j <= (-1.4d+69)) .or. (.not. (j <= 2.4d+103))) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = x * ((y * z) - (t * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((j <= -1.4e+69) || !(j <= 2.4e+103)) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = x * ((y * z) - (t * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (j <= -1.4e+69) or not (j <= 2.4e+103):
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = x * ((y * z) - (t * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((j <= -1.4e+69) || !(j <= 2.4e+103))
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = Float64(x * Float64(Float64(y * z) - Float64(t * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((j <= -1.4e+69) || ~((j <= 2.4e+103)))
		tmp = j * ((a * c) - (y * i));
	else
		tmp = x * ((y * z) - (t * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[j, -1.4e+69], N[Not[LessEqual[j, 2.4e+103]], $MachinePrecision]], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if j < -1.39999999999999991e69 or 2.3999999999999998e103 < j

   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 b around inf 70.6%

      \[\leadsto \color{blue}{b \cdot \left(\left(i \cdot t + \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{b} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right)\right) - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. fma-define 74.1%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(i, t, \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{b} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right)} - c \cdot z\right) \]

      2. associate-/l* 75.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(i, t, \color{blue}{j \cdot \frac{a \cdot c - i \cdot y}{b}} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right) - c \cdot z\right) \]

      3. *-commutative 75.2%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(i, t, j \cdot \frac{a \cdot c - \color{blue}{y \cdot i}}{b} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right) - c \cdot z\right) \]

      4. associate-/l* 77.6%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(i, t, j \cdot \frac{a \cdot c - y \cdot i}{b} + \color{blue}{x \cdot \frac{y \cdot z - a \cdot t}{b}}\right) - c \cdot z\right) \]

      5. *-commutative 77.6%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(i, t, j \cdot \frac{a \cdot c - y \cdot i}{b} + x \cdot \frac{y \cdot z - a \cdot t}{b}\right) - \color{blue}{z \cdot c}\right) \]

   5. Simplified 77.6%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(i, t, j \cdot \frac{a \cdot c - y \cdot i}{b} + x \cdot \frac{y \cdot z - a \cdot t}{b}\right) - z \cdot c\right)} \]

   6. Taylor expanded in j around -inf 72.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - i \cdot y\right)} \]
   7. Step-by-step derivation

      1. sub-neg 72.1%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c + \left(-i \cdot y\right)\right)} \]

      2. *-commutative 72.1%

         \[\leadsto j \cdot \left(a \cdot c + \left(-\color{blue}{y \cdot i}\right)\right) \]

      3. sub-neg 72.1%

         \[\leadsto j \cdot \color{blue}{\left(a \cdot c - y \cdot i\right)} \]

   8. Simplified 72.1%

      \[\leadsto \color{blue}{j \cdot \left(a \cdot c - y \cdot i\right)} \]

   if -1.39999999999999991e69 < j < 2.3999999999999998e103

   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 b around inf 68.4%

      \[\leadsto \color{blue}{b \cdot \left(\left(i \cdot t + \left(\frac{j \cdot \left(a \cdot c - i \cdot y\right)}{b} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right)\right) - c \cdot z\right)} \]
   4. Step-by-step derivation

      1. fma-define 70.7%

         \[\leadsto b \cdot \left(\color{blue}{\mathsf{fma}\left(i, t, \frac{j \cdot \left(a \cdot c - i \cdot y\right)}{b} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right)} - c \cdot z\right) \]

      2. associate-/l* 67.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(i, t, \color{blue}{j \cdot \frac{a \cdot c - i \cdot y}{b}} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right) - c \cdot z\right) \]

      3. *-commutative 67.4%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(i, t, j \cdot \frac{a \cdot c - \color{blue}{y \cdot i}}{b} + \frac{x \cdot \left(y \cdot z - a \cdot t\right)}{b}\right) - c \cdot z\right) \]

      4. associate-/l* 67.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(i, t, j \cdot \frac{a \cdot c - y \cdot i}{b} + \color{blue}{x \cdot \frac{y \cdot z - a \cdot t}{b}}\right) - c \cdot z\right) \]

      5. *-commutative 67.9%

         \[\leadsto b \cdot \left(\mathsf{fma}\left(i, t, j \cdot \frac{a \cdot c - y \cdot i}{b} + x \cdot \frac{y \cdot z - a \cdot t}{b}\right) - \color{blue}{z \cdot c}\right) \]

   5. Simplified 67.9%

      \[\leadsto \color{blue}{b \cdot \left(\mathsf{fma}\left(i, t, j \cdot \frac{a \cdot c - y \cdot i}{b} + x \cdot \frac{y \cdot z - a \cdot t}{b}\right) - z \cdot c\right)} \]

   6. Taylor expanded in x around -inf 47.2%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.4 \cdot 10^{+69} \lor \neg \left(j \leq 2.4 \cdot 10^{+103}\right):\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 30.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+63} \lor \neg \left(c \leq 8.5 \cdot 10^{+40}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= c -4.6e+63) (not (<= c 8.5e+40))) (* a (* c j)) (* b (* t i))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -4.6e+63) || !(c <= 8.5e+40)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((c <= (-4.6d+63)) .or. (.not. (c <= 8.5d+40))) then
        tmp = a * (c * j)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((c <= -4.6e+63) || !(c <= 8.5e+40)) {
		tmp = a * (c * j);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (c <= -4.6e+63) or not (c <= 8.5e+40):
		tmp = a * (c * j)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((c <= -4.6e+63) || !(c <= 8.5e+40))
		tmp = Float64(a * Float64(c * j));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((c <= -4.6e+63) || ~((c <= 8.5e+40)))
		tmp = a * (c * j);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[c, -4.6e+63], N[Not[LessEqual[c, 8.5e+40]], $MachinePrecision]], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if c < -4.59999999999999986e63 or 8.49999999999999996e40 < c

   1. Initial program 61.7%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 56.0%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 56.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 56.0%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 56.0%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 56.0%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

      5. *-commutative 56.0%

         \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

   5. Simplified 56.0%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

   6. Taylor expanded in j around inf 45.4%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   7. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

   8. Simplified 45.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

   if -4.59999999999999986e63 < c < 8.49999999999999996e40

   1. Initial program 81.0%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in j around 0 65.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z - a \cdot t\right) - b \cdot \left(c \cdot z - i \cdot t\right)} \]

   4. Taylor expanded in i around inf 27.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   5. Step-by-step derivation

      1. *-commutative 27.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   6. Simplified 27.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c \leq -4.6 \cdot 10^{+63} \lor \neg \left(c \leq 8.5 \cdot 10^{+40}\right):\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 22.7% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 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 a around inf 42.3%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 42.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 42.3%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 42.3%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 42.3%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. *-commutative 42.3%

      \[\leadsto a \cdot \left(j \cdot c - \color{blue}{x \cdot t}\right) \]

5. Simplified 42.3%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - x \cdot t\right)} \]

6. Taylor expanded in j around inf 22.9%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
7. Step-by-step derivation

   1. *-commutative 22.9%

      \[\leadsto a \cdot \color{blue}{\left(j \cdot c\right)} \]

8. Simplified 22.9%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c\right)} \]

9. Final simplification 22.9%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
10. Add Preprocessing

Developer target: 60.1% 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 2024077 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :alt
  (if (< x -1.469694296777705e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i)))))