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

Percentage Accurate: 73.2% → 81.7%

Time: 37.0s

Alternatives: 28

Speedup: 0.5×

• 58.2% 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: 73.2% 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 90.9%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in t around inf 58.4%

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

      1. distribute-lft-out-- 58.4%

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

      2. *-commutative 58.4%

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

   5. Simplified 58.4%

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

4. Final simplification 84.3%

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

Alternative 2: 51.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := b \cdot \left(c \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ t_3 := a \cdot \left(c \cdot j - x \cdot t\right)\\ t_4 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+70}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-11}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-122}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-195}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-249}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-75}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{+159}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* b (* c (- (* i (/ t c)) z))))
        (t_3 (* a (- (* c j) (* x t))))
        (t_4 (* y (- (* x z) (* i j)))))
   (if (<= y -2.6e+70)
     t_4
     (if (<= y -7e-11)
       t_2
       (if (<= y -1.3e-97)
         t_1
         (if (<= y -8e-122)
           t_3
           (if (<= y -6.2e-195)
             (* c (- (* a j) (* z b)))
             (if (<= y -1.7e-249)
               t_3
               (if (<= y 5.4e-75)
                 t_2
                 (if (<= y 1.55e+44)
                   (* i (- (* t b) (* y j)))
                   (if (<= y 3.45e+159) t_1 t_4)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * (c * ((i * (t / c)) - z));
	double t_3 = a * ((c * j) - (x * t));
	double t_4 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.6e+70) {
		tmp = t_4;
	} else if (y <= -7e-11) {
		tmp = t_2;
	} else if (y <= -1.3e-97) {
		tmp = t_1;
	} else if (y <= -8e-122) {
		tmp = t_3;
	} else if (y <= -6.2e-195) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= -1.7e-249) {
		tmp = t_3;
	} else if (y <= 5.4e-75) {
		tmp = t_2;
	} else if (y <= 1.55e+44) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= 3.45e+159) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = b * (c * ((i * (t / c)) - z))
    t_3 = a * ((c * j) - (x * t))
    t_4 = y * ((x * z) - (i * j))
    if (y <= (-2.6d+70)) then
        tmp = t_4
    else if (y <= (-7d-11)) then
        tmp = t_2
    else if (y <= (-1.3d-97)) then
        tmp = t_1
    else if (y <= (-8d-122)) then
        tmp = t_3
    else if (y <= (-6.2d-195)) then
        tmp = c * ((a * j) - (z * b))
    else if (y <= (-1.7d-249)) then
        tmp = t_3
    else if (y <= 5.4d-75) then
        tmp = t_2
    else if (y <= 1.55d+44) then
        tmp = i * ((t * b) - (y * j))
    else if (y <= 3.45d+159) then
        tmp = t_1
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = b * (c * ((i * (t / c)) - z));
	double t_3 = a * ((c * j) - (x * t));
	double t_4 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -2.6e+70) {
		tmp = t_4;
	} else if (y <= -7e-11) {
		tmp = t_2;
	} else if (y <= -1.3e-97) {
		tmp = t_1;
	} else if (y <= -8e-122) {
		tmp = t_3;
	} else if (y <= -6.2e-195) {
		tmp = c * ((a * j) - (z * b));
	} else if (y <= -1.7e-249) {
		tmp = t_3;
	} else if (y <= 5.4e-75) {
		tmp = t_2;
	} else if (y <= 1.55e+44) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= 3.45e+159) {
		tmp = t_1;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = b * (c * ((i * (t / c)) - z))
	t_3 = a * ((c * j) - (x * t))
	t_4 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -2.6e+70:
		tmp = t_4
	elif y <= -7e-11:
		tmp = t_2
	elif y <= -1.3e-97:
		tmp = t_1
	elif y <= -8e-122:
		tmp = t_3
	elif y <= -6.2e-195:
		tmp = c * ((a * j) - (z * b))
	elif y <= -1.7e-249:
		tmp = t_3
	elif y <= 5.4e-75:
		tmp = t_2
	elif y <= 1.55e+44:
		tmp = i * ((t * b) - (y * j))
	elif y <= 3.45e+159:
		tmp = t_1
	else:
		tmp = t_4
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(b * Float64(c * Float64(Float64(i * Float64(t / c)) - z)))
	t_3 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	t_4 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -2.6e+70)
		tmp = t_4;
	elseif (y <= -7e-11)
		tmp = t_2;
	elseif (y <= -1.3e-97)
		tmp = t_1;
	elseif (y <= -8e-122)
		tmp = t_3;
	elseif (y <= -6.2e-195)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	elseif (y <= -1.7e-249)
		tmp = t_3;
	elseif (y <= 5.4e-75)
		tmp = t_2;
	elseif (y <= 1.55e+44)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (y <= 3.45e+159)
		tmp = t_1;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = b * (c * ((i * (t / c)) - z));
	t_3 = a * ((c * j) - (x * t));
	t_4 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -2.6e+70)
		tmp = t_4;
	elseif (y <= -7e-11)
		tmp = t_2;
	elseif (y <= -1.3e-97)
		tmp = t_1;
	elseif (y <= -8e-122)
		tmp = t_3;
	elseif (y <= -6.2e-195)
		tmp = c * ((a * j) - (z * b));
	elseif (y <= -1.7e-249)
		tmp = t_3;
	elseif (y <= 5.4e-75)
		tmp = t_2;
	elseif (y <= 1.55e+44)
		tmp = i * ((t * b) - (y * j));
	elseif (y <= 3.45e+159)
		tmp = t_1;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(c * N[(N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+70], t$95$4, If[LessEqual[y, -7e-11], t$95$2, If[LessEqual[y, -1.3e-97], t$95$1, If[LessEqual[y, -8e-122], t$95$3, If[LessEqual[y, -6.2e-195], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e-249], t$95$3, If[LessEqual[y, 5.4e-75], t$95$2, If[LessEqual[y, 1.55e+44], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.45e+159], t$95$1, t$95$4]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.6e70 or 3.4500000000000001e159 < y

   1. Initial program 64.6%

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

   3. Taylor expanded in y around inf 73.3%

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

      1. +-commutative 73.3%

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

      2. mul-1-neg 73.3%

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

      3. unsub-neg 73.3%

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

      4. *-commutative 73.3%

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

      5. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -2.6e70 < y < -7.00000000000000038e-11 or -1.6999999999999999e-249 < y < 5.3999999999999996e-75

   1. Initial program 78.9%

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

   3. Taylor expanded in b around inf 57.3%

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

   4. Taylor expanded in c around inf 57.4%

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

      1. associate-/l* 60.1%

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

   6. Simplified 60.1%

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

   if -7.00000000000000038e-11 < y < -1.30000000000000003e-97 or 1.54999999999999998e44 < y < 3.4500000000000001e159

   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 t around 0 65.1%

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

   4. Taylor expanded in j around inf 55.5%

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

      1. *-commutative 55.5%

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

   6. Simplified 55.5%

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

   if -1.30000000000000003e-97 < y < -8.00000000000000047e-122 or -6.20000000000000005e-195 < y < -1.6999999999999999e-249

   1. Initial program 83.3%

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

   3. Taylor expanded in a around inf 75.3%

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

      1. +-commutative 75.3%

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

      2. mul-1-neg 75.3%

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

      3. unsub-neg 75.3%

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

      4. *-commutative 75.3%

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

   5. Simplified 75.3%

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

   if -8.00000000000000047e-122 < y < -6.20000000000000005e-195

   1. Initial program 84.0%

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

   3. Taylor expanded in c around inf 74.3%

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

      1. *-commutative 74.3%

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

   5. Simplified 74.3%

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

   if 5.3999999999999996e-75 < y < 1.54999999999999998e44

   1. Initial program 58.8%

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

   3. Taylor expanded in i around inf 63.7%

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

      1. distribute-lft-out-- 63.7%

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

   5. Simplified 63.7%

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

   6. Taylor expanded in i around 0 63.7%

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

      1. mul-1-neg 63.7%

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

      2. *-commutative 63.7%

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

      3. *-commutative 63.7%

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

      4. fma-neg 63.7%

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

      5. distribute-rgt-neg-out 63.7%

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

      6. fma-neg 63.7%

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

   8. Simplified 63.7%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-11}:\\ \;\;\;\;b \cdot \left(c \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-97}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq -8 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-195}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-75}:\\ \;\;\;\;b \cdot \left(c \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+44}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 3.45 \cdot 10^{+159}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+152}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;t \leq -25500:\\ \;\;\;\;b \cdot \left(c \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-220}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -1.9e+152)
     t_2
     (if (<= t -2.7e+45)
       (* x (* y (- z (/ (* t a) y))))
       (if (<= t -25500.0)
         (* b (* c (- (* i (/ t c)) z)))
         (if (<= t -2.7e-66)
           t_1
           (if (<= t -4.8e-186)
             (* i (- (* t b) (* y j)))
             (if (<= t -2.15e-220)
               (* z (- (* x y) (* b c)))
               (if (<= t 7.2e-200)
                 (- (* z (* x y)) (* i (* y j)))
                 (if (<= t 2.1e-22) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.9e+152) {
		tmp = t_2;
	} else if (t <= -2.7e+45) {
		tmp = x * (y * (z - ((t * a) / y)));
	} else if (t <= -25500.0) {
		tmp = b * (c * ((i * (t / c)) - z));
	} else if (t <= -2.7e-66) {
		tmp = t_1;
	} else if (t <= -4.8e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -2.15e-220) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 7.2e-200) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (t <= 2.1e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-1.9d+152)) then
        tmp = t_2
    else if (t <= (-2.7d+45)) then
        tmp = x * (y * (z - ((t * a) / y)))
    else if (t <= (-25500.0d0)) then
        tmp = b * (c * ((i * (t / c)) - z))
    else if (t <= (-2.7d-66)) then
        tmp = t_1
    else if (t <= (-4.8d-186)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= (-2.15d-220)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 7.2d-200) then
        tmp = (z * (x * y)) - (i * (y * j))
    else if (t <= 2.1d-22) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.9e+152) {
		tmp = t_2;
	} else if (t <= -2.7e+45) {
		tmp = x * (y * (z - ((t * a) / y)));
	} else if (t <= -25500.0) {
		tmp = b * (c * ((i * (t / c)) - z));
	} else if (t <= -2.7e-66) {
		tmp = t_1;
	} else if (t <= -4.8e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -2.15e-220) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 7.2e-200) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (t <= 2.1e-22) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.9e+152:
		tmp = t_2
	elif t <= -2.7e+45:
		tmp = x * (y * (z - ((t * a) / y)))
	elif t <= -25500.0:
		tmp = b * (c * ((i * (t / c)) - z))
	elif t <= -2.7e-66:
		tmp = t_1
	elif t <= -4.8e-186:
		tmp = i * ((t * b) - (y * j))
	elif t <= -2.15e-220:
		tmp = z * ((x * y) - (b * c))
	elif t <= 7.2e-200:
		tmp = (z * (x * y)) - (i * (y * j))
	elif t <= 2.1e-22:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.9e+152)
		tmp = t_2;
	elseif (t <= -2.7e+45)
		tmp = Float64(x * Float64(y * Float64(z - Float64(Float64(t * a) / y))));
	elseif (t <= -25500.0)
		tmp = Float64(b * Float64(c * Float64(Float64(i * Float64(t / c)) - z)));
	elseif (t <= -2.7e-66)
		tmp = t_1;
	elseif (t <= -4.8e-186)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= -2.15e-220)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 7.2e-200)
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(i * Float64(y * j)));
	elseif (t <= 2.1e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.9e+152)
		tmp = t_2;
	elseif (t <= -2.7e+45)
		tmp = x * (y * (z - ((t * a) / y)));
	elseif (t <= -25500.0)
		tmp = b * (c * ((i * (t / c)) - z));
	elseif (t <= -2.7e-66)
		tmp = t_1;
	elseif (t <= -4.8e-186)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= -2.15e-220)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 7.2e-200)
		tmp = (z * (x * y)) - (i * (y * j));
	elseif (t <= 2.1e-22)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.9e+152], t$95$2, If[LessEqual[t, -2.7e+45], N[(x * N[(y * N[(z - N[(N[(t * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -25500.0], N[(b * N[(c * N[(N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.7e-66], t$95$1, If[LessEqual[t, -4.8e-186], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.15e-220], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e-200], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.1e-22], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -1.9e152 or 2.10000000000000008e-22 < t

   1. Initial program 57.5%

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

   3. Taylor expanded in t around inf 72.2%

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

      1. distribute-lft-out-- 72.2%

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

      2. *-commutative 72.2%

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

   5. Simplified 72.2%

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

   if -1.9e152 < t < -2.69999999999999984e45

   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 y around -inf 73.4%

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

   5. Simplified 77.3%

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

   6. Taylor expanded in x around inf 73.8%

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

      1. mul-1-neg 73.8%

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

      2. *-commutative 73.8%

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

   8. Simplified 73.8%

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

   if -2.69999999999999984e45 < t < -25500

   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 b around inf 70.4%

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

   4. Taylor expanded in c around inf 80.0%

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

      1. associate-/l* 80.0%

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

   6. Simplified 80.0%

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

   if -25500 < t < -2.69999999999999996e-66 or 7.2000000000000003e-200 < t < 2.10000000000000008e-22

   1. Initial program 86.4%

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

   3. Taylor expanded in t around 0 76.8%

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

   4. Taylor expanded in j around inf 67.2%

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

      1. *-commutative 67.2%

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

   6. Simplified 67.2%

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

   if -2.69999999999999996e-66 < t < -4.80000000000000006e-186

   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 i around inf 57.9%

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

      1. distribute-lft-out-- 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in i around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. *-commutative 57.9%

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

      4. fma-neg 57.9%

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

      5. distribute-rgt-neg-out 57.9%

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

      6. fma-neg 57.9%

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

   8. Simplified 57.9%

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

   if -4.80000000000000006e-186 < t < -2.1499999999999999e-220

   1. Initial program 68.8%

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

   3. Taylor expanded in z around inf 95.3%

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

      1. *-commutative 95.3%

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

      2. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   if -2.1499999999999999e-220 < t < 7.2000000000000003e-200

   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 t around 0 69.3%

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

   4. Taylor expanded in c around inf 61.7%

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

   5. Taylor expanded in c around 0 55.5%

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

      1. +-commutative 55.5%

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

      2. *-commutative 55.5%

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

      3. mul-1-neg 55.5%

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

      4. unsub-neg 55.5%

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

      5. *-commutative 55.5%

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

      6. associate-*r* 61.4%

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

      7. *-commutative 61.4%

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

      8. *-commutative 61.4%

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

   7. Simplified 61.4%

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

4. Final simplification 69.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+152}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(y \cdot \left(z - \frac{t \cdot a}{y}\right)\right)\\ \mathbf{elif}\;t \leq -25500:\\ \;\;\;\;b \cdot \left(c \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ \mathbf{elif}\;t \leq -2.7 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -2.15 \cdot 10^{-220}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.3 \cdot 10^{-51}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -3.55 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-284}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+56}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* t i) (* z c))) (* a (- (* x t) (* c j)))))
        (t_2 (+ (* x (- (* y z) (* t a))) (* j (- (* a c) (* y i))))))
   (if (<= j -1.3e-51)
     t_2
     (if (<= j -1.45e-207)
       (* t (- (* b i) (* x a)))
       (if (<= j -3.55e-236)
         (- (* z (* x y)) (* i (* y j)))
         (if (<= j -1.45e-282)
           t_1
           (if (<= j 2e-284)
             (* (* x y) (- z (* a (/ t y))))
             (if (<= j 2.1e+56) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((t * i) - (z * c))) - (a * ((x * t) - (c * j)));
	double t_2 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (j <= -1.3e-51) {
		tmp = t_2;
	} else if (j <= -1.45e-207) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= -3.55e-236) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (j <= -1.45e-282) {
		tmp = t_1;
	} else if (j <= 2e-284) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (j <= 2.1e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * ((t * i) - (z * c))) - (a * ((x * t) - (c * j)))
    t_2 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
    if (j <= (-1.3d-51)) then
        tmp = t_2
    else if (j <= (-1.45d-207)) then
        tmp = t * ((b * i) - (x * a))
    else if (j <= (-3.55d-236)) then
        tmp = (z * (x * y)) - (i * (y * j))
    else if (j <= (-1.45d-282)) then
        tmp = t_1
    else if (j <= 2d-284) then
        tmp = (x * y) * (z - (a * (t / y)))
    else if (j <= 2.1d+56) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((t * i) - (z * c))) - (a * ((x * t) - (c * j)));
	double t_2 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	double tmp;
	if (j <= -1.3e-51) {
		tmp = t_2;
	} else if (j <= -1.45e-207) {
		tmp = t * ((b * i) - (x * a));
	} else if (j <= -3.55e-236) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (j <= -1.45e-282) {
		tmp = t_1;
	} else if (j <= 2e-284) {
		tmp = (x * y) * (z - (a * (t / y)));
	} else if (j <= 2.1e+56) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((t * i) - (z * c))) - (a * ((x * t) - (c * j)))
	t_2 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)))
	tmp = 0
	if j <= -1.3e-51:
		tmp = t_2
	elif j <= -1.45e-207:
		tmp = t * ((b * i) - (x * a))
	elif j <= -3.55e-236:
		tmp = (z * (x * y)) - (i * (y * j))
	elif j <= -1.45e-282:
		tmp = t_1
	elif j <= 2e-284:
		tmp = (x * y) * (z - (a * (t / y)))
	elif j <= 2.1e+56:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(a * Float64(Float64(x * t) - Float64(c * j))))
	t_2 = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (j <= -1.3e-51)
		tmp = t_2;
	elseif (j <= -1.45e-207)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (j <= -3.55e-236)
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(i * Float64(y * j)));
	elseif (j <= -1.45e-282)
		tmp = t_1;
	elseif (j <= 2e-284)
		tmp = Float64(Float64(x * y) * Float64(z - Float64(a * Float64(t / y))));
	elseif (j <= 2.1e+56)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * ((t * i) - (z * c))) - (a * ((x * t) - (c * j)));
	t_2 = (x * ((y * z) - (t * a))) + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (j <= -1.3e-51)
		tmp = t_2;
	elseif (j <= -1.45e-207)
		tmp = t * ((b * i) - (x * a));
	elseif (j <= -3.55e-236)
		tmp = (z * (x * y)) - (i * (y * j));
	elseif (j <= -1.45e-282)
		tmp = t_1;
	elseif (j <= 2e-284)
		tmp = (x * y) * (z - (a * (t / y)));
	elseif (j <= 2.1e+56)
		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[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.3e-51], t$95$2, If[LessEqual[j, -1.45e-207], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -3.55e-236], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, -1.45e-282], t$95$1, If[LessEqual[j, 2e-284], N[(N[(x * y), $MachinePrecision] * N[(z - N[(a * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 2.1e+56], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if j < -1.3e-51 or 2.10000000000000017e56 < j

   1. Initial program 75.9%

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

   3. Taylor expanded in b around 0 70.6%

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

   if -1.3e-51 < j < -1.45000000000000006e-207

   1. Initial program 55.4%

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

   3. Taylor expanded in t around inf 73.0%

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

      1. distribute-lft-out-- 73.0%

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

      2. *-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -1.45000000000000006e-207 < j < -3.55000000000000001e-236

   1. Initial program 51.5%

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

   3. Taylor expanded in t around 0 63.8%

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

   4. Taylor expanded in c around inf 63.5%

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

   5. Taylor expanded in c around 0 75.3%

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

      1. +-commutative 75.3%

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

      2. *-commutative 75.3%

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

      3. mul-1-neg 75.3%

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

      4. unsub-neg 75.3%

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

      5. *-commutative 75.3%

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

      6. associate-*r* 75.4%

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

      7. *-commutative 75.4%

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

      8. *-commutative 75.4%

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

   7. Simplified 75.4%

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

   if -3.55000000000000001e-236 < j < -1.44999999999999999e-282 or 2.00000000000000007e-284 < j < 2.10000000000000017e56

   1. Initial program 79.4%

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

   3. Taylor expanded in y around 0 79.5%

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

      1. cancel-sign-sub-inv 79.5%

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

      2. *-commutative 79.5%

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

      3. associate-*r* 79.5%

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

      4. *-commutative 79.5%

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

      5. distribute-rgt-in 79.5%

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

      6. +-commutative 79.5%

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

      7. mul-1-neg 79.5%

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

      8. unsub-neg 79.5%

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

      9. *-commutative 79.5%

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

      10. distribute-lft-neg-in 79.5%

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

      11. sub-neg 79.5%

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

      12. distribute-rgt-neg-out 79.5%

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

      13. distribute-lft-out 78.2%

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

      14. +-commutative 78.2%

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

      15. distribute-rgt-neg-out 78.2%

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

      16. distribute-rgt-neg-in 78.2%

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

      17. mul-1-neg 78.2%

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

   5. Simplified 79.5%

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

   if -1.44999999999999999e-282 < j < 2.00000000000000007e-284

   1. Initial program 59.1%

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

   3. Taylor expanded in y around -inf 70.4%

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

   5. Simplified 70.4%

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

   6. Taylor expanded in x around inf 88.8%

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

      1. associate-*r* 88.9%

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

      2. *-commutative 88.9%

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

      3. mul-1-neg 88.9%

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

      4. unsub-neg 88.9%

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

      5. associate-/l* 88.9%

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

   8. Simplified 88.9%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.3 \cdot 10^{-51}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-207}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;j \leq -3.55 \cdot 10^{-236}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-282}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;j \leq 2 \cdot 10^{-284}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \left(z - a \cdot \frac{t}{y}\right)\\ \mathbf{elif}\;j \leq 2.1 \cdot 10^{+56}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 30.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ t_2 := i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{if}\;t \leq -2.45 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+52}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-186}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-286}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-10}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))) (t_2 (* i (* y (- j)))))
   (if (<= t -2.45e+148)
     (* b (* t i))
     (if (<= t -1.75e+52)
       t_1
       (if (<= t -3.6e+18)
         (* t (* b i))
         (if (<= t -1.35e-88)
           (* a (* c j))
           (if (<= t -1.15e-186)
             t_2
             (if (<= t -6.8e-286)
               (* z (* c (- b)))
               (if (<= t 8.2e-200)
                 (* y (* x z))
                 (if (<= t 1.08e-10) t_2 t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double t_2 = i * (y * -j);
	double tmp;
	if (t <= -2.45e+148) {
		tmp = b * (t * i);
	} else if (t <= -1.75e+52) {
		tmp = t_1;
	} else if (t <= -3.6e+18) {
		tmp = t * (b * i);
	} else if (t <= -1.35e-88) {
		tmp = a * (c * j);
	} else if (t <= -1.15e-186) {
		tmp = t_2;
	} else if (t <= -6.8e-286) {
		tmp = z * (c * -b);
	} else if (t <= 8.2e-200) {
		tmp = y * (x * z);
	} else if (t <= 1.08e-10) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a * (x * -t)
    t_2 = i * (y * -j)
    if (t <= (-2.45d+148)) then
        tmp = b * (t * i)
    else if (t <= (-1.75d+52)) then
        tmp = t_1
    else if (t <= (-3.6d+18)) then
        tmp = t * (b * i)
    else if (t <= (-1.35d-88)) then
        tmp = a * (c * j)
    else if (t <= (-1.15d-186)) then
        tmp = t_2
    else if (t <= (-6.8d-286)) then
        tmp = z * (c * -b)
    else if (t <= 8.2d-200) then
        tmp = y * (x * z)
    else if (t <= 1.08d-10) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = a * (x * -t);
	double t_2 = i * (y * -j);
	double tmp;
	if (t <= -2.45e+148) {
		tmp = b * (t * i);
	} else if (t <= -1.75e+52) {
		tmp = t_1;
	} else if (t <= -3.6e+18) {
		tmp = t * (b * i);
	} else if (t <= -1.35e-88) {
		tmp = a * (c * j);
	} else if (t <= -1.15e-186) {
		tmp = t_2;
	} else if (t <= -6.8e-286) {
		tmp = z * (c * -b);
	} else if (t <= 8.2e-200) {
		tmp = y * (x * z);
	} else if (t <= 1.08e-10) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	t_2 = i * (y * -j)
	tmp = 0
	if t <= -2.45e+148:
		tmp = b * (t * i)
	elif t <= -1.75e+52:
		tmp = t_1
	elif t <= -3.6e+18:
		tmp = t * (b * i)
	elif t <= -1.35e-88:
		tmp = a * (c * j)
	elif t <= -1.15e-186:
		tmp = t_2
	elif t <= -6.8e-286:
		tmp = z * (c * -b)
	elif t <= 8.2e-200:
		tmp = y * (x * z)
	elif t <= 1.08e-10:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	t_2 = Float64(i * Float64(y * Float64(-j)))
	tmp = 0.0
	if (t <= -2.45e+148)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -1.75e+52)
		tmp = t_1;
	elseif (t <= -3.6e+18)
		tmp = Float64(t * Float64(b * i));
	elseif (t <= -1.35e-88)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= -1.15e-186)
		tmp = t_2;
	elseif (t <= -6.8e-286)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (t <= 8.2e-200)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 1.08e-10)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = a * (x * -t);
	t_2 = i * (y * -j);
	tmp = 0.0;
	if (t <= -2.45e+148)
		tmp = b * (t * i);
	elseif (t <= -1.75e+52)
		tmp = t_1;
	elseif (t <= -3.6e+18)
		tmp = t * (b * i);
	elseif (t <= -1.35e-88)
		tmp = a * (c * j);
	elseif (t <= -1.15e-186)
		tmp = t_2;
	elseif (t <= -6.8e-286)
		tmp = z * (c * -b);
	elseif (t <= 8.2e-200)
		tmp = y * (x * z);
	elseif (t <= 1.08e-10)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(a * N[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.45e+148], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.75e+52], t$95$1, If[LessEqual[t, -3.6e+18], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.35e-88], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.15e-186], t$95$2, If[LessEqual[t, -6.8e-286], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.2e-200], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.08e-10], t$95$2, t$95$1]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if t < -2.45e148

   1. Initial program 52.2%

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

   3. Taylor expanded in i around inf 50.7%

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

      1. distribute-lft-out-- 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around 0 46.5%

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

      1. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if -2.45e148 < t < -1.75e52 or 1.08000000000000002e-10 < t

   1. Initial program 66.7%

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

   3. Taylor expanded in a around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in j around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. distribute-lft-neg-out 45.3%

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

      3. *-commutative 45.3%

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

   8. Simplified 45.3%

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

   if -1.75e52 < t < -3.6e18

   1. Initial program 88.5%

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

   3. Taylor expanded in i around inf 67.1%

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

      1. distribute-lft-out-- 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in j around 0 56.3%

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

      1. *-commutative 56.3%

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

   8. Simplified 56.3%

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

   9. Taylor expanded in b around 0 56.3%

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

       1. associate-*r* 56.5%

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

       2. *-commutative 56.5%

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

   11. Simplified 56.5%

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

   if -3.6e18 < t < -1.34999999999999997e-88

   1. Initial program 87.3%

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

   3. Taylor expanded in a around inf 45.8%

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

      1. +-commutative 45.8%

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

      2. mul-1-neg 45.8%

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

      3. unsub-neg 45.8%

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

      4. *-commutative 45.8%

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

   5. Simplified 45.8%

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

   6. Taylor expanded in j around inf 37.1%

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

   if -1.34999999999999997e-88 < t < -1.15e-186 or 8.19999999999999974e-200 < t < 1.08000000000000002e-10

   1. Initial program 85.3%

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

   3. Taylor expanded in t around 0 72.3%

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

   4. Taylor expanded in c around inf 65.6%

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

   5. Taylor expanded in i around inf 41.8%

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

      1. associate-*r* 41.8%

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

      2. mul-1-neg 41.8%

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

      3. *-commutative 41.8%

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

   7. Simplified 41.8%

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

   if -1.15e-186 < t < -6.8000000000000002e-286

   1. Initial program 74.6%

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

   3. Taylor expanded in z around inf 78.2%

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

      1. *-commutative 78.2%

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

      2. *-commutative 78.2%

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

   5. Simplified 78.2%

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

   6. Taylor expanded in y around 0 54.4%

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

      1. mul-1-neg 54.4%

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

      2. *-commutative 54.4%

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

      3. distribute-rgt-neg-in 54.4%

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

   8. Simplified 54.4%

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

   if -6.8000000000000002e-286 < t < 8.19999999999999974e-200

   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 55.3%

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

      1. *-commutative 55.3%

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

      2. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in y around inf 43.9%

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

      1. *-commutative 43.9%

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

      2. associate-*r* 51.1%

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

   8. Simplified 51.1%

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

4. Final simplification 45.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{+52}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq -3.6 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-88}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;t \leq -6.8 \cdot 10^{-286}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-10}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -1.25 \cdot 10^{+19}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-228}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 10^{-199}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -1.25e+19)
     t_2
     (if (<= t -2.25e-66)
       t_1
       (if (<= t -5.6e-186)
         (* i (- (* t b) (* y j)))
         (if (<= t -5e-228)
           (* z (- (* x y) (* b c)))
           (if (<= t 1e-199)
             (* y (- (* x z) (* i j)))
             (if (<= t 5.4e-196)
               (* c (* z (- b)))
               (if (<= t 1.4e-21) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.25e+19) {
		tmp = t_2;
	} else if (t <= -2.25e-66) {
		tmp = t_1;
	} else if (t <= -5.6e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -5e-228) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1e-199) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 5.4e-196) {
		tmp = c * (z * -b);
	} else if (t <= 1.4e-21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-1.25d+19)) then
        tmp = t_2
    else if (t <= (-2.25d-66)) then
        tmp = t_1
    else if (t <= (-5.6d-186)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= (-5d-228)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 1d-199) then
        tmp = y * ((x * z) - (i * j))
    else if (t <= 5.4d-196) then
        tmp = c * (z * -b)
    else if (t <= 1.4d-21) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -1.25e+19) {
		tmp = t_2;
	} else if (t <= -2.25e-66) {
		tmp = t_1;
	} else if (t <= -5.6e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -5e-228) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 1e-199) {
		tmp = y * ((x * z) - (i * j));
	} else if (t <= 5.4e-196) {
		tmp = c * (z * -b);
	} else if (t <= 1.4e-21) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -1.25e+19:
		tmp = t_2
	elif t <= -2.25e-66:
		tmp = t_1
	elif t <= -5.6e-186:
		tmp = i * ((t * b) - (y * j))
	elif t <= -5e-228:
		tmp = z * ((x * y) - (b * c))
	elif t <= 1e-199:
		tmp = y * ((x * z) - (i * j))
	elif t <= 5.4e-196:
		tmp = c * (z * -b)
	elif t <= 1.4e-21:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -1.25e+19)
		tmp = t_2;
	elseif (t <= -2.25e-66)
		tmp = t_1;
	elseif (t <= -5.6e-186)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= -5e-228)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 1e-199)
		tmp = Float64(y * Float64(Float64(x * z) - Float64(i * j)));
	elseif (t <= 5.4e-196)
		tmp = Float64(c * Float64(z * Float64(-b)));
	elseif (t <= 1.4e-21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -1.25e+19)
		tmp = t_2;
	elseif (t <= -2.25e-66)
		tmp = t_1;
	elseif (t <= -5.6e-186)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= -5e-228)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 1e-199)
		tmp = y * ((x * z) - (i * j));
	elseif (t <= 5.4e-196)
		tmp = c * (z * -b);
	elseif (t <= 1.4e-21)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.25e+19], t$95$2, If[LessEqual[t, -2.25e-66], t$95$1, If[LessEqual[t, -5.6e-186], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5e-228], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-199], N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.4e-196], N[(c * N[(z * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e-21], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.25e19 or 1.40000000000000002e-21 < t

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 70.2%

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

      1. distribute-lft-out-- 70.2%

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

      2. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -1.25e19 < t < -2.2499999999999999e-66 or 5.39999999999999963e-196 < t < 1.40000000000000002e-21

   1. Initial program 86.9%

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

   3. Taylor expanded in t around 0 77.6%

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

   4. Taylor expanded in j around inf 66.6%

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

      1. *-commutative 66.6%

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

   6. Simplified 66.6%

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

   if -2.2499999999999999e-66 < t < -5.59999999999999966e-186

   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 i around inf 57.9%

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

      1. distribute-lft-out-- 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in i around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. *-commutative 57.9%

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

      4. fma-neg 57.9%

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

      5. distribute-rgt-neg-out 57.9%

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

      6. fma-neg 57.9%

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

   8. Simplified 57.9%

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

   if -5.59999999999999966e-186 < t < -4.99999999999999972e-228

   1. Initial program 68.8%

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

   3. Taylor expanded in z around inf 95.3%

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

      1. *-commutative 95.3%

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

      2. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   if -4.99999999999999972e-228 < t < 9.99999999999999982e-200

   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 y around inf 61.2%

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

      1. +-commutative 61.2%

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

      2. mul-1-neg 61.2%

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

      3. unsub-neg 61.2%

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

      4. *-commutative 61.2%

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

      5. *-commutative 61.2%

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

   5. Simplified 61.2%

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

   if 9.99999999999999982e-200 < t < 5.39999999999999963e-196

   1. Initial program 98.4%

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

   3. Taylor expanded in z around inf 98.4%

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

      1. *-commutative 98.4%

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

      2. *-commutative 98.4%

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

   5. Simplified 98.4%

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

   6. Taylor expanded in y around 0 98.4%

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

      1. mul-1-neg 98.4%

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

      2. *-commutative 98.4%

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

      3. associate-*r* 100.0%

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

      4. *-commutative 100.0%

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

      5. distribute-rgt-neg-out 100.0%

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

      6. *-commutative 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.25 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.25 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-228}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 10^{-199}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-196}:\\ \;\;\;\;c \cdot \left(z \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 51.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ t_3 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-209}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-21}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i))))
        (t_2 (* z (- (* x y) (* b c))))
        (t_3 (* t (- (* b i) (* x a)))))
   (if (<= t -5.8e+18)
     t_3
     (if (<= t -2.5e-66)
       t_1
       (if (<= t -5.8e-186)
         (* i (- (* t b) (* y j)))
         (if (<= t -8.6e-209)
           t_2
           (if (<= t 1.26e-207)
             (- (* x (* y z)) (* b (* z c)))
             (if (<= t 2.6e-184) t_2 (if (<= t 1.05e-21) t_1 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -5.8e+18) {
		tmp = t_3;
	} else if (t <= -2.5e-66) {
		tmp = t_1;
	} else if (t <= -5.8e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -8.6e-209) {
		tmp = t_2;
	} else if (t <= 1.26e-207) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (t <= 2.6e-184) {
		tmp = t_2;
	} else if (t <= 1.05e-21) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = z * ((x * y) - (b * c))
    t_3 = t * ((b * i) - (x * a))
    if (t <= (-5.8d+18)) then
        tmp = t_3
    else if (t <= (-2.5d-66)) then
        tmp = t_1
    else if (t <= (-5.8d-186)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= (-8.6d-209)) then
        tmp = t_2
    else if (t <= 1.26d-207) then
        tmp = (x * (y * z)) - (b * (z * c))
    else if (t <= 2.6d-184) then
        tmp = t_2
    else if (t <= 1.05d-21) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double t_3 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -5.8e+18) {
		tmp = t_3;
	} else if (t <= -2.5e-66) {
		tmp = t_1;
	} else if (t <= -5.8e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -8.6e-209) {
		tmp = t_2;
	} else if (t <= 1.26e-207) {
		tmp = (x * (y * z)) - (b * (z * c));
	} else if (t <= 2.6e-184) {
		tmp = t_2;
	} else if (t <= 1.05e-21) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = z * ((x * y) - (b * c))
	t_3 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -5.8e+18:
		tmp = t_3
	elif t <= -2.5e-66:
		tmp = t_1
	elif t <= -5.8e-186:
		tmp = i * ((t * b) - (y * j))
	elif t <= -8.6e-209:
		tmp = t_2
	elif t <= 1.26e-207:
		tmp = (x * (y * z)) - (b * (z * c))
	elif t <= 2.6e-184:
		tmp = t_2
	elif t <= 1.05e-21:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	t_3 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -5.8e+18)
		tmp = t_3;
	elseif (t <= -2.5e-66)
		tmp = t_1;
	elseif (t <= -5.8e-186)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= -8.6e-209)
		tmp = t_2;
	elseif (t <= 1.26e-207)
		tmp = Float64(Float64(x * Float64(y * z)) - Float64(b * Float64(z * c)));
	elseif (t <= 2.6e-184)
		tmp = t_2;
	elseif (t <= 1.05e-21)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = z * ((x * y) - (b * c));
	t_3 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -5.8e+18)
		tmp = t_3;
	elseif (t <= -2.5e-66)
		tmp = t_1;
	elseif (t <= -5.8e-186)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= -8.6e-209)
		tmp = t_2;
	elseif (t <= 1.26e-207)
		tmp = (x * (y * z)) - (b * (z * c));
	elseif (t <= 2.6e-184)
		tmp = t_2;
	elseif (t <= 1.05e-21)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.8e+18], t$95$3, If[LessEqual[t, -2.5e-66], t$95$1, If[LessEqual[t, -5.8e-186], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -8.6e-209], t$95$2, If[LessEqual[t, 1.26e-207], N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e-184], t$95$2, If[LessEqual[t, 1.05e-21], t$95$1, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -5.8e18 or 1.05000000000000006e-21 < t

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 70.2%

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

      1. distribute-lft-out-- 70.2%

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

      2. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -5.8e18 < t < -2.49999999999999981e-66 or 2.59999999999999978e-184 < t < 1.05000000000000006e-21

   1. Initial program 86.7%

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

   3. Taylor expanded in t around 0 78.8%

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

   4. Taylor expanded in j around inf 67.6%

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

      1. *-commutative 67.6%

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

   6. Simplified 67.6%

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

   if -2.49999999999999981e-66 < t < -5.80000000000000038e-186

   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 i around inf 57.9%

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

      1. distribute-lft-out-- 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in i around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. *-commutative 57.9%

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

      4. fma-neg 57.9%

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

      5. distribute-rgt-neg-out 57.9%

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

      6. fma-neg 57.9%

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

   8. Simplified 57.9%

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

   if -5.80000000000000038e-186 < t < -8.60000000000000011e-209 or 1.25999999999999999e-207 < t < 2.59999999999999978e-184

   1. Initial program 65.2%

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

   3. Taylor expanded in z around inf 79.8%

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

      1. *-commutative 79.8%

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

      2. *-commutative 79.8%

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

   5. Simplified 79.8%

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

   if -8.60000000000000011e-209 < t < 1.25999999999999999e-207

   1. Initial program 78.4%

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

   3. Taylor expanded in t around 0 75.5%

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

   4. Taylor expanded in j around 0 62.9%

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

      1. *-commutative 62.9%

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

   6. Simplified 62.9%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{-209}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.26 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-21}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{if}\;t \leq -2.85 \cdot 10^{+88}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(b \cdot \frac{i}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -0.2:\\ \;\;\;\;b \cdot \left(c \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-160}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-278}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-209}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-184}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-22}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* z (- (* x y) (* b c)))))
   (if (<= t -2.85e+88)
     (* (* y t) (- (* b (/ i y)) (* a (/ x y))))
     (if (<= t -0.2)
       (* b (* c (- (* i (/ t c)) z)))
       (if (<= t -9.8e-160)
         t_1
         (if (<= t -2.3e-278)
           t_2
           (if (<= t 4.6e-209)
             (- (* z (* x y)) (* i (* y j)))
             (if (<= t 1.02e-184)
               t_2
               (if (<= t 2.4e-22) t_1 (* t (- (* b i) (* x a))))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (t <= -2.85e+88) {
		tmp = (y * t) * ((b * (i / y)) - (a * (x / y)));
	} else if (t <= -0.2) {
		tmp = b * (c * ((i * (t / c)) - z));
	} else if (t <= -9.8e-160) {
		tmp = t_1;
	} else if (t <= -2.3e-278) {
		tmp = t_2;
	} else if (t <= 4.6e-209) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (t <= 1.02e-184) {
		tmp = t_2;
	} else if (t <= 2.4e-22) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = z * ((x * y) - (b * c))
    if (t <= (-2.85d+88)) then
        tmp = (y * t) * ((b * (i / y)) - (a * (x / y)))
    else if (t <= (-0.2d0)) then
        tmp = b * (c * ((i * (t / c)) - z))
    else if (t <= (-9.8d-160)) then
        tmp = t_1
    else if (t <= (-2.3d-278)) then
        tmp = t_2
    else if (t <= 4.6d-209) then
        tmp = (z * (x * y)) - (i * (y * j))
    else if (t <= 1.02d-184) then
        tmp = t_2
    else if (t <= 2.4d-22) then
        tmp = t_1
    else
        tmp = t * ((b * i) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = z * ((x * y) - (b * c));
	double tmp;
	if (t <= -2.85e+88) {
		tmp = (y * t) * ((b * (i / y)) - (a * (x / y)));
	} else if (t <= -0.2) {
		tmp = b * (c * ((i * (t / c)) - z));
	} else if (t <= -9.8e-160) {
		tmp = t_1;
	} else if (t <= -2.3e-278) {
		tmp = t_2;
	} else if (t <= 4.6e-209) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (t <= 1.02e-184) {
		tmp = t_2;
	} else if (t <= 2.4e-22) {
		tmp = t_1;
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = z * ((x * y) - (b * c))
	tmp = 0
	if t <= -2.85e+88:
		tmp = (y * t) * ((b * (i / y)) - (a * (x / y)))
	elif t <= -0.2:
		tmp = b * (c * ((i * (t / c)) - z))
	elif t <= -9.8e-160:
		tmp = t_1
	elif t <= -2.3e-278:
		tmp = t_2
	elif t <= 4.6e-209:
		tmp = (z * (x * y)) - (i * (y * j))
	elif t <= 1.02e-184:
		tmp = t_2
	elif t <= 2.4e-22:
		tmp = t_1
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(z * Float64(Float64(x * y) - Float64(b * c)))
	tmp = 0.0
	if (t <= -2.85e+88)
		tmp = Float64(Float64(y * t) * Float64(Float64(b * Float64(i / y)) - Float64(a * Float64(x / y))));
	elseif (t <= -0.2)
		tmp = Float64(b * Float64(c * Float64(Float64(i * Float64(t / c)) - z)));
	elseif (t <= -9.8e-160)
		tmp = t_1;
	elseif (t <= -2.3e-278)
		tmp = t_2;
	elseif (t <= 4.6e-209)
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(i * Float64(y * j)));
	elseif (t <= 1.02e-184)
		tmp = t_2;
	elseif (t <= 2.4e-22)
		tmp = t_1;
	else
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = z * ((x * y) - (b * c));
	tmp = 0.0;
	if (t <= -2.85e+88)
		tmp = (y * t) * ((b * (i / y)) - (a * (x / y)));
	elseif (t <= -0.2)
		tmp = b * (c * ((i * (t / c)) - z));
	elseif (t <= -9.8e-160)
		tmp = t_1;
	elseif (t <= -2.3e-278)
		tmp = t_2;
	elseif (t <= 4.6e-209)
		tmp = (z * (x * y)) - (i * (y * j));
	elseif (t <= 1.02e-184)
		tmp = t_2;
	elseif (t <= 2.4e-22)
		tmp = t_1;
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.85e+88], N[(N[(y * t), $MachinePrecision] * N[(N[(b * N[(i / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -0.2], N[(b * N[(c * N[(N[(i * N[(t / c), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -9.8e-160], t$95$1, If[LessEqual[t, -2.3e-278], t$95$2, If[LessEqual[t, 4.6e-209], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e-184], t$95$2, If[LessEqual[t, 2.4e-22], t$95$1, N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -2.85000000000000011e88

   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 y around -inf 55.6%

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

   5. Simplified 58.9%

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

   6. Taylor expanded in t around inf 65.4%

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

      1. associate-*r* 71.5%

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

      2. +-commutative 71.5%

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

      3. mul-1-neg 71.5%

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

      4. unsub-neg 71.5%

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

      5. associate-/l* 68.5%

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

      6. associate-/l* 68.5%

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

   8. Simplified 68.5%

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

   if -2.85000000000000011e88 < t < -0.20000000000000001

   1. Initial program 95.0%

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

   3. Taylor expanded in b around inf 62.9%

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

   4. Taylor expanded in c around inf 67.5%

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

      1. associate-/l* 72.2%

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

   6. Simplified 72.2%

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

   if -0.20000000000000001 < t < -9.7999999999999998e-160 or 1.0200000000000001e-184 < t < 2.40000000000000002e-22

   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 t around 0 75.3%

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

   4. Taylor expanded in j around inf 65.2%

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

      1. *-commutative 65.2%

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

   6. Simplified 65.2%

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

   if -9.7999999999999998e-160 < t < -2.30000000000000003e-278 or 4.5999999999999999e-209 < t < 1.0200000000000001e-184

   1. Initial program 80.0%

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

   3. Taylor expanded in z around inf 65.1%

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

      1. *-commutative 65.1%

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

      2. *-commutative 65.1%

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

   5. Simplified 65.1%

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

   if -2.30000000000000003e-278 < t < 4.5999999999999999e-209

   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 t around 0 70.0%

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

   4. Taylor expanded in c around inf 66.8%

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

   5. Taylor expanded in c around 0 65.9%

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

      1. +-commutative 65.9%

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

      2. *-commutative 65.9%

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

      3. mul-1-neg 65.9%

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

      4. unsub-neg 65.9%

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

      5. *-commutative 65.9%

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

      6. associate-*r* 70.8%

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

      7. *-commutative 70.8%

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

      8. *-commutative 70.8%

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

   7. Simplified 70.8%

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

   if 2.40000000000000002e-22 < t

   1. Initial program 60.7%

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

   3. Taylor expanded in t around inf 77.1%

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

      1. distribute-lft-out-- 77.1%

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

      2. *-commutative 77.1%

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

   5. Simplified 77.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{+88}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(b \cdot \frac{i}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -0.2:\\ \;\;\;\;b \cdot \left(c \cdot \left(i \cdot \frac{t}{c} - z\right)\right)\\ \mathbf{elif}\;t \leq -9.8 \cdot 10^{-160}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-278}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{-209}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-184}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 2.4 \cdot 10^{-22}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 29.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c\right)\\ t_2 := y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{if}\;i \leq -1 \cdot 10^{+233}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-246}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+127}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+160}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (* a c))) (t_2 (* y (* i (- j)))))
   (if (<= i -1e+233)
     t_2
     (if (<= i -2.9e-114)
       (* t (* b i))
       (if (<= i 1.9e-246)
         (* z (* x y))
         (if (<= i 3.9e-94)
           t_1
           (if (<= i 1.9e+40)
             (* x (* y z))
             (if (<= i 1.3e+127)
               t_1
               (if (<= i 1.05e+160) t_2 (* b (* t i)))))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double t_2 = y * (i * -j);
	double tmp;
	if (i <= -1e+233) {
		tmp = t_2;
	} else if (i <= -2.9e-114) {
		tmp = t * (b * i);
	} else if (i <= 1.9e-246) {
		tmp = z * (x * y);
	} else if (i <= 3.9e-94) {
		tmp = t_1;
	} else if (i <= 1.9e+40) {
		tmp = x * (y * z);
	} else if (i <= 1.3e+127) {
		tmp = t_1;
	} else if (i <= 1.05e+160) {
		tmp = t_2;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * (a * c)
    t_2 = y * (i * -j)
    if (i <= (-1d+233)) then
        tmp = t_2
    else if (i <= (-2.9d-114)) then
        tmp = t * (b * i)
    else if (i <= 1.9d-246) then
        tmp = z * (x * y)
    else if (i <= 3.9d-94) then
        tmp = t_1
    else if (i <= 1.9d+40) then
        tmp = x * (y * z)
    else if (i <= 1.3d+127) then
        tmp = t_1
    else if (i <= 1.05d+160) then
        tmp = t_2
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * (a * c);
	double t_2 = y * (i * -j);
	double tmp;
	if (i <= -1e+233) {
		tmp = t_2;
	} else if (i <= -2.9e-114) {
		tmp = t * (b * i);
	} else if (i <= 1.9e-246) {
		tmp = z * (x * y);
	} else if (i <= 3.9e-94) {
		tmp = t_1;
	} else if (i <= 1.9e+40) {
		tmp = x * (y * z);
	} else if (i <= 1.3e+127) {
		tmp = t_1;
	} else if (i <= 1.05e+160) {
		tmp = t_2;
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * (a * c)
	t_2 = y * (i * -j)
	tmp = 0
	if i <= -1e+233:
		tmp = t_2
	elif i <= -2.9e-114:
		tmp = t * (b * i)
	elif i <= 1.9e-246:
		tmp = z * (x * y)
	elif i <= 3.9e-94:
		tmp = t_1
	elif i <= 1.9e+40:
		tmp = x * (y * z)
	elif i <= 1.3e+127:
		tmp = t_1
	elif i <= 1.05e+160:
		tmp = t_2
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(a * c))
	t_2 = Float64(y * Float64(i * Float64(-j)))
	tmp = 0.0
	if (i <= -1e+233)
		tmp = t_2;
	elseif (i <= -2.9e-114)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 1.9e-246)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 3.9e-94)
		tmp = t_1;
	elseif (i <= 1.9e+40)
		tmp = Float64(x * Float64(y * z));
	elseif (i <= 1.3e+127)
		tmp = t_1;
	elseif (i <= 1.05e+160)
		tmp = t_2;
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * (a * c);
	t_2 = y * (i * -j);
	tmp = 0.0;
	if (i <= -1e+233)
		tmp = t_2;
	elseif (i <= -2.9e-114)
		tmp = t * (b * i);
	elseif (i <= 1.9e-246)
		tmp = z * (x * y);
	elseif (i <= 3.9e-94)
		tmp = t_1;
	elseif (i <= 1.9e+40)
		tmp = x * (y * z);
	elseif (i <= 1.3e+127)
		tmp = t_1;
	elseif (i <= 1.05e+160)
		tmp = t_2;
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1e+233], t$95$2, If[LessEqual[i, -2.9e-114], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.9e-246], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 3.9e-94], t$95$1, If[LessEqual[i, 1.9e+40], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.3e+127], t$95$1, If[LessEqual[i, 1.05e+160], t$95$2, N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if i < -9.99999999999999974e232 or 1.3000000000000001e127 < i < 1.04999999999999998e160

   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 i around inf 76.3%

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

      1. distribute-lft-out-- 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in j around inf 67.9%

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

      1. mul-1-neg 67.9%

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

      2. associate-*r* 67.9%

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

   8. Simplified 67.9%

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

   if -9.99999999999999974e232 < i < -2.89999999999999997e-114

   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 i around inf 56.6%

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

      1. distribute-lft-out-- 56.6%

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

   5. Simplified 56.6%

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

   6. Taylor expanded in j around 0 42.6%

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

      1. *-commutative 42.6%

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

   8. Simplified 42.6%

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

   9. Taylor expanded in b around 0 42.6%

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

       1. associate-*r* 42.7%

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

       2. *-commutative 42.7%

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

   11. Simplified 42.7%

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

   if -2.89999999999999997e-114 < i < 1.89999999999999988e-246

   1. Initial program 79.2%

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

   3. Taylor expanded in t around 0 55.5%

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

   4. Taylor expanded in j around 0 36.7%

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

      1. *-commutative 36.7%

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

   6. Simplified 36.7%

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

   7. Taylor expanded in x around inf 35.1%

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

      1. associate-*r* 39.6%

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

      2. *-commutative 39.6%

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

   9. Simplified 39.6%

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

   if 1.89999999999999988e-246 < i < 3.9000000000000002e-94 or 1.90000000000000002e40 < i < 1.3000000000000001e127

   1. Initial program 81.6%

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

   3. Taylor expanded in t around 0 68.9%

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

   4. Taylor expanded in c around inf 58.7%

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

   5. Taylor expanded in a around inf 26.9%

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

      1. associate-*r* 38.5%

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

      2. *-commutative 38.5%

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

   7. Simplified 38.5%

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

   if 3.9000000000000002e-94 < i < 1.90000000000000002e40

   1. Initial program 61.8%

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

   3. Taylor expanded in t around 0 55.0%

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

   4. Taylor expanded in j around 0 47.3%

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

      1. *-commutative 47.3%

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

   6. Simplified 47.3%

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

   7. Taylor expanded in x around inf 36.2%

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

      1. *-commutative 36.2%

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

   9. Simplified 36.2%

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

   if 1.04999999999999998e160 < i

   1. Initial program 48.5%

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

   3. Taylor expanded in i around inf 76.3%

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

      1. distribute-lft-out-- 76.3%

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

   5. Simplified 76.3%

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

   6. Taylor expanded in j around 0 53.2%

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

      1. *-commutative 53.2%

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

   8. Simplified 53.2%

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

4. Final simplification 43.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1 \cdot 10^{+233}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -2.9 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{-246}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 3.9 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.9 \cdot 10^{+40}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;i \leq 1.3 \cdot 10^{+127}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.05 \cdot 10^{+160}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+76}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-19}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-63}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;a \leq 5600000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+79}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* a (- (* c j) (* x t)))))
   (if (<= a -2.2e+76)
     t_2
     (if (<= a -8.2e-19)
       t_1
       (if (<= a -1.9e-63)
         (* i (* y (- j)))
         (if (<= a 5.8e-31)
           t_1
           (if (<= a 5600000000000.0)
             (* x (* y z))
             (if (<= a 2.5e+79) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.2e+76) {
		tmp = t_2;
	} else if (a <= -8.2e-19) {
		tmp = t_1;
	} else if (a <= -1.9e-63) {
		tmp = i * (y * -j);
	} else if (a <= 5.8e-31) {
		tmp = t_1;
	} else if (a <= 5600000000000.0) {
		tmp = x * (y * z);
	} else if (a <= 2.5e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = a * ((c * j) - (x * t))
    if (a <= (-2.2d+76)) then
        tmp = t_2
    else if (a <= (-8.2d-19)) then
        tmp = t_1
    else if (a <= (-1.9d-63)) then
        tmp = i * (y * -j)
    else if (a <= 5.8d-31) then
        tmp = t_1
    else if (a <= 5600000000000.0d0) then
        tmp = x * (y * z)
    else if (a <= 2.5d+79) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = a * ((c * j) - (x * t));
	double tmp;
	if (a <= -2.2e+76) {
		tmp = t_2;
	} else if (a <= -8.2e-19) {
		tmp = t_1;
	} else if (a <= -1.9e-63) {
		tmp = i * (y * -j);
	} else if (a <= 5.8e-31) {
		tmp = t_1;
	} else if (a <= 5600000000000.0) {
		tmp = x * (y * z);
	} else if (a <= 2.5e+79) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = a * ((c * j) - (x * t))
	tmp = 0
	if a <= -2.2e+76:
		tmp = t_2
	elif a <= -8.2e-19:
		tmp = t_1
	elif a <= -1.9e-63:
		tmp = i * (y * -j)
	elif a <= 5.8e-31:
		tmp = t_1
	elif a <= 5600000000000.0:
		tmp = x * (y * z)
	elif a <= 2.5e+79:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(a * Float64(Float64(c * j) - Float64(x * t)))
	tmp = 0.0
	if (a <= -2.2e+76)
		tmp = t_2;
	elseif (a <= -8.2e-19)
		tmp = t_1;
	elseif (a <= -1.9e-63)
		tmp = Float64(i * Float64(y * Float64(-j)));
	elseif (a <= 5.8e-31)
		tmp = t_1;
	elseif (a <= 5600000000000.0)
		tmp = Float64(x * Float64(y * z));
	elseif (a <= 2.5e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = a * ((c * j) - (x * t));
	tmp = 0.0;
	if (a <= -2.2e+76)
		tmp = t_2;
	elseif (a <= -8.2e-19)
		tmp = t_1;
	elseif (a <= -1.9e-63)
		tmp = i * (y * -j);
	elseif (a <= 5.8e-31)
		tmp = t_1;
	elseif (a <= 5600000000000.0)
		tmp = x * (y * z);
	elseif (a <= 2.5e+79)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2.2e+76], t$95$2, If[LessEqual[a, -8.2e-19], t$95$1, If[LessEqual[a, -1.9e-63], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.8e-31], t$95$1, If[LessEqual[a, 5600000000000.0], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 2.5e+79], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -2.2e76 or 2.5e79 < a

   1. Initial program 59.5%

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

   3. Taylor expanded in a around inf 68.4%

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

      1. +-commutative 68.4%

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

      2. mul-1-neg 68.4%

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

      3. unsub-neg 68.4%

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

      4. *-commutative 68.4%

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

   5. Simplified 68.4%

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

   if -2.2e76 < a < -8.1999999999999997e-19 or -1.90000000000000009e-63 < a < 5.8000000000000001e-31 or 5.6e12 < a < 2.5e79

   1. Initial program 79.9%

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

   3. Taylor expanded in b around inf 56.5%

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

   if -8.1999999999999997e-19 < a < -1.90000000000000009e-63

   1. Initial program 77.3%

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

   3. Taylor expanded in t around 0 55.4%

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

   4. Taylor expanded in c around inf 48.8%

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

   5. Taylor expanded in i around inf 48.1%

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

      1. associate-*r* 48.1%

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

      2. mul-1-neg 48.1%

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

      3. *-commutative 48.1%

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

   7. Simplified 48.1%

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

   if 5.8000000000000001e-31 < a < 5.6e12

   1. Initial program 66.5%

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

   3. Taylor expanded in t around 0 66.5%

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

   4. Taylor expanded in j around 0 66.5%

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

      1. *-commutative 66.5%

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

   6. Simplified 66.5%

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

   7. Taylor expanded in x around inf 89.0%

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

      1. *-commutative 89.0%

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

   9. Simplified 89.0%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.2 \cdot 10^{+76}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;a \leq -8.2 \cdot 10^{-19}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-63}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \mathbf{elif}\;a \leq 5.8 \cdot 10^{-31}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;a \leq 5600000000000:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+79}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 52.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-75}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+43}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.55e+77)
     t_2
     (if (<= y -1.45e-75)
       t_1
       (if (<= y -1.02e-249)
         (* a (- (* c j) (* x t)))
         (if (<= y 9.8e+43)
           t_1
           (if (<= y 5.5e+99)
             (* j (- (* a c) (* y i)))
             (if (<= y 2.95e+107) (* c (- (* a j) (* z b))) 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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.55e+77) {
		tmp = t_2;
	} else if (y <= -1.45e-75) {
		tmp = t_1;
	} else if (y <= -1.02e-249) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 9.8e+43) {
		tmp = t_1;
	} else if (y <= 5.5e+99) {
		tmp = j * ((a * c) - (y * i));
	} else if (y <= 2.95e+107) {
		tmp = c * ((a * j) - (z * b));
	} 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 = y * ((x * z) - (i * j))
    if (y <= (-1.55d+77)) then
        tmp = t_2
    else if (y <= (-1.45d-75)) then
        tmp = t_1
    else if (y <= (-1.02d-249)) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 9.8d+43) then
        tmp = t_1
    else if (y <= 5.5d+99) then
        tmp = j * ((a * c) - (y * i))
    else if (y <= 2.95d+107) then
        tmp = c * ((a * j) - (z * b))
    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 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.55e+77) {
		tmp = t_2;
	} else if (y <= -1.45e-75) {
		tmp = t_1;
	} else if (y <= -1.02e-249) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 9.8e+43) {
		tmp = t_1;
	} else if (y <= 5.5e+99) {
		tmp = j * ((a * c) - (y * i));
	} else if (y <= 2.95e+107) {
		tmp = c * ((a * j) - (z * b));
	} 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 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.55e+77:
		tmp = t_2
	elif y <= -1.45e-75:
		tmp = t_1
	elif y <= -1.02e-249:
		tmp = a * ((c * j) - (x * t))
	elif y <= 9.8e+43:
		tmp = t_1
	elif y <= 5.5e+99:
		tmp = j * ((a * c) - (y * i))
	elif y <= 2.95e+107:
		tmp = c * ((a * j) - (z * b))
	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(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.55e+77)
		tmp = t_2;
	elseif (y <= -1.45e-75)
		tmp = t_1;
	elseif (y <= -1.02e-249)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 9.8e+43)
		tmp = t_1;
	elseif (y <= 5.5e+99)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	elseif (y <= 2.95e+107)
		tmp = Float64(c * Float64(Float64(a * j) - Float64(z * b)));
	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 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.55e+77)
		tmp = t_2;
	elseif (y <= -1.45e-75)
		tmp = t_1;
	elseif (y <= -1.02e-249)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 9.8e+43)
		tmp = t_1;
	elseif (y <= 5.5e+99)
		tmp = j * ((a * c) - (y * i));
	elseif (y <= 2.95e+107)
		tmp = c * ((a * j) - (z * b));
	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[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+77], t$95$2, If[LessEqual[y, -1.45e-75], t$95$1, If[LessEqual[y, -1.02e-249], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+43], t$95$1, If[LessEqual[y, 5.5e+99], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e+107], N[(c * N[(N[(a * j), $MachinePrecision] - N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.54999999999999999e77 or 2.9500000000000002e107 < y

   1. Initial program 63.3%

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

   3. Taylor expanded in y around inf 71.3%

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

      1. +-commutative 71.3%

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

      2. mul-1-neg 71.3%

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

      3. unsub-neg 71.3%

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

      4. *-commutative 71.3%

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

      5. *-commutative 71.3%

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

   5. Simplified 71.3%

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

   if -1.54999999999999999e77 < y < -1.4500000000000001e-75 or -1.02e-249 < y < 9.7999999999999999e43

   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 b around inf 52.2%

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

   if -1.4500000000000001e-75 < y < -1.02e-249

   1. Initial program 82.2%

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

   3. Taylor expanded in a around inf 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if 9.7999999999999999e43 < y < 5.5000000000000002e99

   1. Initial program 80.0%

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

   3. Taylor expanded in t around 0 67.0%

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

   4. Taylor expanded in j around inf 73.8%

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

      1. *-commutative 73.8%

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

   6. Simplified 73.8%

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

   if 5.5000000000000002e99 < y < 2.9500000000000002e107

   1. Initial program 74.6%

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

   3. Taylor expanded in c around inf 75.8%

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

      1. *-commutative 75.8%

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

   5. Simplified 75.8%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+77}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-75}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+99}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+107}:\\ \;\;\;\;c \cdot \left(a \cdot j - z \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 52.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+70}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-80}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-56}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+153}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -6.8e+70)
     t_2
     (if (<= y -8.2e-80)
       t_1
       (if (<= y -5.6e-249)
         (* a (- (* c j) (* x t)))
         (if (<= y 3.2e-56)
           t_1
           (if (<= y 2.05e+43)
             (* i (- (* t b) (* y j)))
             (if (<= y 3.3e+153) (* j (- (* a c) (* y i))) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.8e+70) {
		tmp = t_2;
	} else if (y <= -8.2e-80) {
		tmp = t_1;
	} else if (y <= -5.6e-249) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 3.2e-56) {
		tmp = t_1;
	} else if (y <= 2.05e+43) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= 3.3e+153) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-6.8d+70)) then
        tmp = t_2
    else if (y <= (-8.2d-80)) then
        tmp = t_1
    else if (y <= (-5.6d-249)) then
        tmp = a * ((c * j) - (x * t))
    else if (y <= 3.2d-56) then
        tmp = t_1
    else if (y <= 2.05d+43) then
        tmp = i * ((t * b) - (y * j))
    else if (y <= 3.3d+153) then
        tmp = j * ((a * c) - (y * i))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -6.8e+70) {
		tmp = t_2;
	} else if (y <= -8.2e-80) {
		tmp = t_1;
	} else if (y <= -5.6e-249) {
		tmp = a * ((c * j) - (x * t));
	} else if (y <= 3.2e-56) {
		tmp = t_1;
	} else if (y <= 2.05e+43) {
		tmp = i * ((t * b) - (y * j));
	} else if (y <= 3.3e+153) {
		tmp = j * ((a * c) - (y * i));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -6.8e+70:
		tmp = t_2
	elif y <= -8.2e-80:
		tmp = t_1
	elif y <= -5.6e-249:
		tmp = a * ((c * j) - (x * t))
	elif y <= 3.2e-56:
		tmp = t_1
	elif y <= 2.05e+43:
		tmp = i * ((t * b) - (y * j))
	elif y <= 3.3e+153:
		tmp = j * ((a * c) - (y * i))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -6.8e+70)
		tmp = t_2;
	elseif (y <= -8.2e-80)
		tmp = t_1;
	elseif (y <= -5.6e-249)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	elseif (y <= 3.2e-56)
		tmp = t_1;
	elseif (y <= 2.05e+43)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (y <= 3.3e+153)
		tmp = Float64(j * Float64(Float64(a * c) - Float64(y * i)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -6.8e+70)
		tmp = t_2;
	elseif (y <= -8.2e-80)
		tmp = t_1;
	elseif (y <= -5.6e-249)
		tmp = a * ((c * j) - (x * t));
	elseif (y <= 3.2e-56)
		tmp = t_1;
	elseif (y <= 2.05e+43)
		tmp = i * ((t * b) - (y * j));
	elseif (y <= 3.3e+153)
		tmp = j * ((a * c) - (y * i));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e+70], t$95$2, If[LessEqual[y, -8.2e-80], t$95$1, If[LessEqual[y, -5.6e-249], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-56], t$95$1, If[LessEqual[y, 2.05e+43], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+153], N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.8000000000000002e70 or 3.29999999999999994e153 < y

   1. Initial program 64.6%

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

   3. Taylor expanded in y around inf 73.3%

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

      1. +-commutative 73.3%

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

      2. mul-1-neg 73.3%

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

      3. unsub-neg 73.3%

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

      4. *-commutative 73.3%

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

      5. *-commutative 73.3%

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

   5. Simplified 73.3%

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

   if -6.8000000000000002e70 < y < -8.1999999999999999e-80 or -5.5999999999999998e-249 < y < 3.19999999999999986e-56

   1. Initial program 79.6%

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

   3. Taylor expanded in b around inf 54.0%

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

   if -8.1999999999999999e-80 < y < -5.5999999999999998e-249

   1. Initial program 82.2%

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

   3. Taylor expanded in a around inf 65.7%

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

      1. +-commutative 65.7%

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

      2. mul-1-neg 65.7%

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

      3. unsub-neg 65.7%

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

      4. *-commutative 65.7%

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

   5. Simplified 65.7%

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

   if 3.19999999999999986e-56 < y < 2.05e43

   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 i around inf 67.3%

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

      1. distribute-lft-out-- 67.3%

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

   5. Simplified 67.3%

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

   6. Taylor expanded in i around 0 67.3%

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

      1. mul-1-neg 67.3%

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

      2. *-commutative 67.3%

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

      3. *-commutative 67.3%

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

      4. fma-neg 67.3%

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

      5. distribute-rgt-neg-out 67.3%

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

      6. fma-neg 67.3%

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

   8. Simplified 67.3%

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

   if 2.05e43 < y < 3.29999999999999994e153

   1. Initial program 70.3%

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

   3. Taylor expanded in t around 0 55.8%

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

   4. Taylor expanded in j around inf 59.7%

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

      1. *-commutative 59.7%

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

   6. Simplified 59.7%

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

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+70}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-249}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-56}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{+43}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+153}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 51.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(a \cdot c - y \cdot i\right)\\ t_2 := t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{if}\;t \leq -6.4 \cdot 10^{+18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-23}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* a c) (* y i)))) (t_2 (* t (- (* b i) (* x a)))))
   (if (<= t -6.4e+18)
     t_2
     (if (<= t -3.2e-66)
       t_1
       (if (<= t -5.5e-186)
         (* i (- (* t b) (* y j)))
         (if (<= t -3.35e-233)
           (* z (- (* x y) (* b c)))
           (if (<= t 9e-200)
             (- (* z (* x y)) (* i (* y j)))
             (if (<= t 6.8e-23) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -6.4e+18) {
		tmp = t_2;
	} else if (t <= -3.2e-66) {
		tmp = t_1;
	} else if (t <= -5.5e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -3.35e-233) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 9e-200) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (t <= 6.8e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((a * c) - (y * i))
    t_2 = t * ((b * i) - (x * a))
    if (t <= (-6.4d+18)) then
        tmp = t_2
    else if (t <= (-3.2d-66)) then
        tmp = t_1
    else if (t <= (-5.5d-186)) then
        tmp = i * ((t * b) - (y * j))
    else if (t <= (-3.35d-233)) then
        tmp = z * ((x * y) - (b * c))
    else if (t <= 9d-200) then
        tmp = (z * (x * y)) - (i * (y * j))
    else if (t <= 6.8d-23) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((a * c) - (y * i));
	double t_2 = t * ((b * i) - (x * a));
	double tmp;
	if (t <= -6.4e+18) {
		tmp = t_2;
	} else if (t <= -3.2e-66) {
		tmp = t_1;
	} else if (t <= -5.5e-186) {
		tmp = i * ((t * b) - (y * j));
	} else if (t <= -3.35e-233) {
		tmp = z * ((x * y) - (b * c));
	} else if (t <= 9e-200) {
		tmp = (z * (x * y)) - (i * (y * j));
	} else if (t <= 6.8e-23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((a * c) - (y * i))
	t_2 = t * ((b * i) - (x * a))
	tmp = 0
	if t <= -6.4e+18:
		tmp = t_2
	elif t <= -3.2e-66:
		tmp = t_1
	elif t <= -5.5e-186:
		tmp = i * ((t * b) - (y * j))
	elif t <= -3.35e-233:
		tmp = z * ((x * y) - (b * c))
	elif t <= 9e-200:
		tmp = (z * (x * y)) - (i * (y * j))
	elif t <= 6.8e-23:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(a * c) - Float64(y * i)))
	t_2 = Float64(t * Float64(Float64(b * i) - Float64(x * a)))
	tmp = 0.0
	if (t <= -6.4e+18)
		tmp = t_2;
	elseif (t <= -3.2e-66)
		tmp = t_1;
	elseif (t <= -5.5e-186)
		tmp = Float64(i * Float64(Float64(t * b) - Float64(y * j)));
	elseif (t <= -3.35e-233)
		tmp = Float64(z * Float64(Float64(x * y) - Float64(b * c)));
	elseif (t <= 9e-200)
		tmp = Float64(Float64(z * Float64(x * y)) - Float64(i * Float64(y * j)));
	elseif (t <= 6.8e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((a * c) - (y * i));
	t_2 = t * ((b * i) - (x * a));
	tmp = 0.0;
	if (t <= -6.4e+18)
		tmp = t_2;
	elseif (t <= -3.2e-66)
		tmp = t_1;
	elseif (t <= -5.5e-186)
		tmp = i * ((t * b) - (y * j));
	elseif (t <= -3.35e-233)
		tmp = z * ((x * y) - (b * c));
	elseif (t <= 9e-200)
		tmp = (z * (x * y)) - (i * (y * j));
	elseif (t <= 6.8e-23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.4e+18], t$95$2, If[LessEqual[t, -3.2e-66], t$95$1, If[LessEqual[t, -5.5e-186], N[(i * N[(N[(t * b), $MachinePrecision] - N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.35e-233], N[(z * N[(N[(x * y), $MachinePrecision] - N[(b * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9e-200], N[(N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision] - N[(i * N[(y * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-23], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -6.4e18 or 6.8000000000000001e-23 < t

   1. Initial program 63.6%

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

   3. Taylor expanded in t around inf 70.2%

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

      1. distribute-lft-out-- 70.2%

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

      2. *-commutative 70.2%

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

   5. Simplified 70.2%

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

   if -6.4e18 < t < -3.19999999999999982e-66 or 9.0000000000000004e-200 < t < 6.8000000000000001e-23

   1. Initial program 87.1%

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

   3. Taylor expanded in t around 0 77.9%

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

   4. Taylor expanded in j around inf 65.6%

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

      1. *-commutative 65.6%

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

   6. Simplified 65.6%

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

   if -3.19999999999999982e-66 < t < -5.5000000000000001e-186

   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 i around inf 57.9%

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

      1. distribute-lft-out-- 57.9%

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

   5. Simplified 57.9%

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

   6. Taylor expanded in i around 0 57.9%

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

      1. mul-1-neg 57.9%

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

      2. *-commutative 57.9%

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

      3. *-commutative 57.9%

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

      4. fma-neg 57.9%

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

      5. distribute-rgt-neg-out 57.9%

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

      6. fma-neg 57.9%

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

   8. Simplified 57.9%

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

   if -5.5000000000000001e-186 < t < -3.35000000000000011e-233

   1. Initial program 68.8%

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

   3. Taylor expanded in z around inf 95.3%

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

      1. *-commutative 95.3%

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

      2. *-commutative 95.3%

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

   5. Simplified 95.3%

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

   if -3.35000000000000011e-233 < t < 9.0000000000000004e-200

   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 t around 0 69.3%

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

   4. Taylor expanded in c around inf 61.7%

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

   5. Taylor expanded in c around 0 55.5%

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

      1. +-commutative 55.5%

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

      2. *-commutative 55.5%

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

      3. mul-1-neg 55.5%

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

      4. unsub-neg 55.5%

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

      5. *-commutative 55.5%

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

      6. associate-*r* 61.4%

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

      7. *-commutative 61.4%

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

      8. *-commutative 61.4%

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

   7. Simplified 61.4%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.4 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-66}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-186}:\\ \;\;\;\;i \cdot \left(t \cdot b - y \cdot j\right)\\ \mathbf{elif}\;t \leq -3.35 \cdot 10^{-233}:\\ \;\;\;\;z \cdot \left(x \cdot y - b \cdot c\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \left(x \cdot y\right) - i \cdot \left(y \cdot j\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-23}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ t_2 := y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-49}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 10^{+163}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (- (* b (- (* t i) (* z c))) (* a (- (* x t) (* c j)))))
        (t_2 (* y (- (* x z) (* i j)))))
   (if (<= y -1.15e+78)
     t_2
     (if (<= y 1.02e-49)
       t_1
       (if (<= y 1.85e+39)
         (* t (- (* b i) (* x a)))
         (if (<= y 1e+163) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((t * i) - (z * c))) - (a * ((x * t) - (c * j)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.15e+78) {
		tmp = t_2;
	} else if (y <= 1.02e-49) {
		tmp = t_1;
	} else if (y <= 1.85e+39) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1e+163) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (b * ((t * i) - (z * c))) - (a * ((x * t) - (c * j)))
    t_2 = y * ((x * z) - (i * j))
    if (y <= (-1.15d+78)) then
        tmp = t_2
    else if (y <= 1.02d-49) then
        tmp = t_1
    else if (y <= 1.85d+39) then
        tmp = t * ((b * i) - (x * a))
    else if (y <= 1d+163) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = (b * ((t * i) - (z * c))) - (a * ((x * t) - (c * j)));
	double t_2 = y * ((x * z) - (i * j));
	double tmp;
	if (y <= -1.15e+78) {
		tmp = t_2;
	} else if (y <= 1.02e-49) {
		tmp = t_1;
	} else if (y <= 1.85e+39) {
		tmp = t * ((b * i) - (x * a));
	} else if (y <= 1e+163) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = (b * ((t * i) - (z * c))) - (a * ((x * t) - (c * j)))
	t_2 = y * ((x * z) - (i * j))
	tmp = 0
	if y <= -1.15e+78:
		tmp = t_2
	elif y <= 1.02e-49:
		tmp = t_1
	elif y <= 1.85e+39:
		tmp = t * ((b * i) - (x * a))
	elif y <= 1e+163:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(Float64(b * Float64(Float64(t * i) - Float64(z * c))) - Float64(a * Float64(Float64(x * t) - Float64(c * j))))
	t_2 = Float64(y * Float64(Float64(x * z) - Float64(i * j)))
	tmp = 0.0
	if (y <= -1.15e+78)
		tmp = t_2;
	elseif (y <= 1.02e-49)
		tmp = t_1;
	elseif (y <= 1.85e+39)
		tmp = Float64(t * Float64(Float64(b * i) - Float64(x * a)));
	elseif (y <= 1e+163)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = (b * ((t * i) - (z * c))) - (a * ((x * t) - (c * j)));
	t_2 = y * ((x * z) - (i * j));
	tmp = 0.0;
	if (y <= -1.15e+78)
		tmp = t_2;
	elseif (y <= 1.02e-49)
		tmp = t_1;
	elseif (y <= 1.85e+39)
		tmp = t * ((b * i) - (x * a));
	elseif (y <= 1e+163)
		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[(N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(N[(x * z), $MachinePrecision] - N[(i * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.15e+78], t$95$2, If[LessEqual[y, 1.02e-49], t$95$1, If[LessEqual[y, 1.85e+39], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+163], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1500000000000001e78 or 9.9999999999999994e162 < y

   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 y around inf 74.2%

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

      1. +-commutative 74.2%

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

      2. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. *-commutative 74.2%

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

      5. *-commutative 74.2%

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

   5. Simplified 74.2%

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

   if -1.1500000000000001e78 < y < 1.02000000000000009e-49 or 1.85000000000000006e39 < y < 9.9999999999999994e162

   1. Initial program 79.1%

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

   3. Taylor expanded in y around 0 69.8%

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

      1. cancel-sign-sub-inv 69.8%

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

      2. *-commutative 69.8%

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

      3. associate-*r* 69.8%

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

      4. *-commutative 69.8%

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

      5. distribute-rgt-in 70.4%

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

      6. +-commutative 70.4%

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

      7. mul-1-neg 70.4%

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

      8. unsub-neg 70.4%

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

      9. *-commutative 70.4%

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

      10. distribute-lft-neg-in 70.4%

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

      11. sub-neg 70.4%

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

      12. distribute-rgt-neg-out 70.4%

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

      13. distribute-lft-out 69.8%

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

      14. +-commutative 69.8%

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

      15. distribute-rgt-neg-out 69.8%

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

      16. distribute-rgt-neg-in 69.8%

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

      17. mul-1-neg 69.8%

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

   5. Simplified 70.4%

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

   if 1.02000000000000009e-49 < y < 1.85000000000000006e39

   1. Initial program 50.8%

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

   3. Taylor expanded in t around inf 72.6%

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

      1. distribute-lft-out-- 72.6%

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

      2. *-commutative 72.6%

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

   5. Simplified 72.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+78}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-49}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{+39}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \mathbf{elif}\;y \leq 10^{+163}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z - i \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;t \leq -1.22 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{+51}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= t -1.22e+148)
     (* b (* t i))
     (if (<= t -5.3e+51)
       t_1
       (if (<= t -1.25e+19)
         (* t (* b i))
         (if (<= t -3.5e-161)
           (* a (* c j))
           (if (<= t 5.1e-200)
             (* y (* x z))
             (if (<= t 5.2e-12) (* y (* i (- 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 * (x * -t);
	double tmp;
	if (t <= -1.22e+148) {
		tmp = b * (t * i);
	} else if (t <= -5.3e+51) {
		tmp = t_1;
	} else if (t <= -1.25e+19) {
		tmp = t * (b * i);
	} else if (t <= -3.5e-161) {
		tmp = a * (c * j);
	} else if (t <= 5.1e-200) {
		tmp = y * (x * z);
	} else if (t <= 5.2e-12) {
		tmp = y * (i * -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 * (x * -t)
    if (t <= (-1.22d+148)) then
        tmp = b * (t * i)
    else if (t <= (-5.3d+51)) then
        tmp = t_1
    else if (t <= (-1.25d+19)) then
        tmp = t * (b * i)
    else if (t <= (-3.5d-161)) then
        tmp = a * (c * j)
    else if (t <= 5.1d-200) then
        tmp = y * (x * z)
    else if (t <= 5.2d-12) then
        tmp = y * (i * -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 * (x * -t);
	double tmp;
	if (t <= -1.22e+148) {
		tmp = b * (t * i);
	} else if (t <= -5.3e+51) {
		tmp = t_1;
	} else if (t <= -1.25e+19) {
		tmp = t * (b * i);
	} else if (t <= -3.5e-161) {
		tmp = a * (c * j);
	} else if (t <= 5.1e-200) {
		tmp = y * (x * z);
	} else if (t <= 5.2e-12) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	tmp = 0
	if t <= -1.22e+148:
		tmp = b * (t * i)
	elif t <= -5.3e+51:
		tmp = t_1
	elif t <= -1.25e+19:
		tmp = t * (b * i)
	elif t <= -3.5e-161:
		tmp = a * (c * j)
	elif t <= 5.1e-200:
		tmp = y * (x * z)
	elif t <= 5.2e-12:
		tmp = y * (i * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (t <= -1.22e+148)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -5.3e+51)
		tmp = t_1;
	elseif (t <= -1.25e+19)
		tmp = Float64(t * Float64(b * i));
	elseif (t <= -3.5e-161)
		tmp = Float64(a * Float64(c * j));
	elseif (t <= 5.1e-200)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 5.2e-12)
		tmp = Float64(y * Float64(i * Float64(-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 * (x * -t);
	tmp = 0.0;
	if (t <= -1.22e+148)
		tmp = b * (t * i);
	elseif (t <= -5.3e+51)
		tmp = t_1;
	elseif (t <= -1.25e+19)
		tmp = t * (b * i);
	elseif (t <= -3.5e-161)
		tmp = a * (c * j);
	elseif (t <= 5.1e-200)
		tmp = y * (x * z);
	elseif (t <= 5.2e-12)
		tmp = y * (i * -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[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.22e+148], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.3e+51], t$95$1, If[LessEqual[t, -1.25e+19], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.5e-161], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e-200], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.2e-12], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.22000000000000007e148

   1. Initial program 52.2%

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

   3. Taylor expanded in i around inf 50.7%

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

      1. distribute-lft-out-- 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around 0 46.5%

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

      1. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if -1.22000000000000007e148 < t < -5.2999999999999997e51 or 5.19999999999999965e-12 < t

   1. Initial program 66.7%

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

   3. Taylor expanded in a around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in j around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. distribute-lft-neg-out 45.3%

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

      3. *-commutative 45.3%

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

   8. Simplified 45.3%

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

   if -5.2999999999999997e51 < t < -1.25e19

   1. Initial program 88.5%

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

   3. Taylor expanded in i around inf 67.1%

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

      1. distribute-lft-out-- 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in j around 0 56.3%

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

      1. *-commutative 56.3%

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

   8. Simplified 56.3%

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

   9. Taylor expanded in b around 0 56.3%

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

       1. associate-*r* 56.5%

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

       2. *-commutative 56.5%

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

   11. Simplified 56.5%

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

   if -1.25e19 < t < -3.5000000000000002e-161

   1. Initial program 85.4%

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

   3. Taylor expanded in a around inf 41.0%

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

      1. +-commutative 41.0%

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

      2. mul-1-neg 41.0%

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

      3. unsub-neg 41.0%

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

      4. *-commutative 41.0%

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

   5. Simplified 41.0%

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

   6. Taylor expanded in j around inf 34.2%

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

   if -3.5000000000000002e-161 < t < 5.0999999999999999e-200

   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 z around inf 59.5%

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

      1. *-commutative 59.5%

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

      2. *-commutative 59.5%

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

   5. Simplified 59.5%

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

   6. Taylor expanded in y around inf 34.2%

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

      1. *-commutative 34.2%

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

      2. associate-*r* 39.4%

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

   8. Simplified 39.4%

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

   if 5.0999999999999999e-200 < t < 5.19999999999999965e-12

   1. Initial program 86.5%

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

   3. Taylor expanded in i around inf 50.4%

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

      1. distribute-lft-out-- 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in j around inf 42.5%

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

      1. mul-1-neg 42.5%

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

      2. associate-*r* 40.1%

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

   8. Simplified 40.1%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{+51}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{+19}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-161}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{+54}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-285}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* a (* x (- t)))))
   (if (<= t -1.85e+148)
     (* b (* t i))
     (if (<= t -7.4e+54)
       t_1
       (if (<= t -6e+18)
         (* t (* b i))
         (if (<= t -6.4e-285)
           (* z (* c (- b)))
           (if (<= t 5.1e-200)
             (* y (* x z))
             (if (<= t 7.6e-10) (* y (* i (- 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 * (x * -t);
	double tmp;
	if (t <= -1.85e+148) {
		tmp = b * (t * i);
	} else if (t <= -7.4e+54) {
		tmp = t_1;
	} else if (t <= -6e+18) {
		tmp = t * (b * i);
	} else if (t <= -6.4e-285) {
		tmp = z * (c * -b);
	} else if (t <= 5.1e-200) {
		tmp = y * (x * z);
	} else if (t <= 7.6e-10) {
		tmp = y * (i * -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 * (x * -t)
    if (t <= (-1.85d+148)) then
        tmp = b * (t * i)
    else if (t <= (-7.4d+54)) then
        tmp = t_1
    else if (t <= (-6d+18)) then
        tmp = t * (b * i)
    else if (t <= (-6.4d-285)) then
        tmp = z * (c * -b)
    else if (t <= 5.1d-200) then
        tmp = y * (x * z)
    else if (t <= 7.6d-10) then
        tmp = y * (i * -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 * (x * -t);
	double tmp;
	if (t <= -1.85e+148) {
		tmp = b * (t * i);
	} else if (t <= -7.4e+54) {
		tmp = t_1;
	} else if (t <= -6e+18) {
		tmp = t * (b * i);
	} else if (t <= -6.4e-285) {
		tmp = z * (c * -b);
	} else if (t <= 5.1e-200) {
		tmp = y * (x * z);
	} else if (t <= 7.6e-10) {
		tmp = y * (i * -j);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = a * (x * -t)
	tmp = 0
	if t <= -1.85e+148:
		tmp = b * (t * i)
	elif t <= -7.4e+54:
		tmp = t_1
	elif t <= -6e+18:
		tmp = t * (b * i)
	elif t <= -6.4e-285:
		tmp = z * (c * -b)
	elif t <= 5.1e-200:
		tmp = y * (x * z)
	elif t <= 7.6e-10:
		tmp = y * (i * -j)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(a * Float64(x * Float64(-t)))
	tmp = 0.0
	if (t <= -1.85e+148)
		tmp = Float64(b * Float64(t * i));
	elseif (t <= -7.4e+54)
		tmp = t_1;
	elseif (t <= -6e+18)
		tmp = Float64(t * Float64(b * i));
	elseif (t <= -6.4e-285)
		tmp = Float64(z * Float64(c * Float64(-b)));
	elseif (t <= 5.1e-200)
		tmp = Float64(y * Float64(x * z));
	elseif (t <= 7.6e-10)
		tmp = Float64(y * Float64(i * Float64(-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 * (x * -t);
	tmp = 0.0;
	if (t <= -1.85e+148)
		tmp = b * (t * i);
	elseif (t <= -7.4e+54)
		tmp = t_1;
	elseif (t <= -6e+18)
		tmp = t * (b * i);
	elseif (t <= -6.4e-285)
		tmp = z * (c * -b);
	elseif (t <= 5.1e-200)
		tmp = y * (x * z);
	elseif (t <= 7.6e-10)
		tmp = y * (i * -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[(x * (-t)), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.85e+148], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -7.4e+54], t$95$1, If[LessEqual[t, -6e+18], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -6.4e-285], N[(z * N[(c * (-b)), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.1e-200], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.6e-10], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.8500000000000001e148

   1. Initial program 52.2%

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

   3. Taylor expanded in i around inf 50.7%

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

      1. distribute-lft-out-- 50.7%

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

   5. Simplified 50.7%

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

   6. Taylor expanded in j around 0 46.5%

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

      1. *-commutative 46.5%

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

   8. Simplified 46.5%

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

   if -1.8500000000000001e148 < t < -7.4000000000000004e54 or 7.5999999999999996e-10 < t

   1. Initial program 66.7%

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

   3. Taylor expanded in a around inf 52.9%

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

      1. +-commutative 52.9%

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

      2. mul-1-neg 52.9%

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

      3. unsub-neg 52.9%

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

      4. *-commutative 52.9%

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

   5. Simplified 52.9%

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

   6. Taylor expanded in j around 0 45.3%

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

      1. mul-1-neg 45.3%

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

      2. distribute-lft-neg-out 45.3%

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

      3. *-commutative 45.3%

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

   8. Simplified 45.3%

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

   if -7.4000000000000004e54 < t < -6e18

   1. Initial program 88.5%

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

   3. Taylor expanded in i around inf 67.1%

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

      1. distribute-lft-out-- 67.1%

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

   5. Simplified 67.1%

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

   6. Taylor expanded in j around 0 56.3%

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

      1. *-commutative 56.3%

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

   8. Simplified 56.3%

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

   9. Taylor expanded in b around 0 56.3%

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

       1. associate-*r* 56.5%

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

       2. *-commutative 56.5%

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

   11. Simplified 56.5%

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

   if -6e18 < t < -6.40000000000000032e-285

   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 z around inf 48.3%

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

      1. *-commutative 48.3%

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

      2. *-commutative 48.3%

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

   5. Simplified 48.3%

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

   6. Taylor expanded in y around 0 31.8%

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

      1. mul-1-neg 31.8%

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

      2. *-commutative 31.8%

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

      3. distribute-rgt-neg-in 31.8%

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

   8. Simplified 31.8%

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

   if -6.40000000000000032e-285 < t < 5.0999999999999999e-200

   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 55.3%

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

      1. *-commutative 55.3%

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

      2. *-commutative 55.3%

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

   5. Simplified 55.3%

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

   6. Taylor expanded in y around inf 43.9%

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

      1. *-commutative 43.9%

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

      2. associate-*r* 51.1%

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

   8. Simplified 51.1%

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

   if 5.0999999999999999e-200 < t < 7.5999999999999996e-10

   1. Initial program 86.5%

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

   3. Taylor expanded in i around inf 50.4%

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

      1. distribute-lft-out-- 50.4%

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

   5. Simplified 50.4%

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

   6. Taylor expanded in j around inf 42.5%

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

      1. mul-1-neg 42.5%

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

      2. associate-*r* 40.1%

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

   8. Simplified 40.1%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+148}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{+54}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \mathbf{elif}\;t \leq -6 \cdot 10^{+18}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-285}:\\ \;\;\;\;z \cdot \left(c \cdot \left(-b\right)\right)\\ \mathbf{elif}\;t \leq 5.1 \cdot 10^{-200}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(x \cdot \left(-t\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 65.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+267}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(b \cdot \frac{i}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= t -5.2e+267)
   (* (* y t) (- (* b (/ i y)) (* a (/ x y))))
   (if (<= t -3.9e+18)
     (+ (* x (- (* y z) (* t a))) (* b (- (* t i) (* z c))))
     (if (<= t 1.02e-5)
       (- (- (* x (* y z)) (* j (- (* y i) (* a c)))) (* b (* z c)))
       (* 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 tmp;
	if (t <= -5.2e+267) {
		tmp = (y * t) * ((b * (i / y)) - (a * (x / y)));
	} else if (t <= -3.9e+18) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (t <= 1.02e-5) {
		tmp = ((x * (y * z)) - (j * ((y * i) - (a * c)))) - (b * (z * c));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (t <= (-5.2d+267)) then
        tmp = (y * t) * ((b * (i / y)) - (a * (x / y)))
    else if (t <= (-3.9d+18)) then
        tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
    else if (t <= 1.02d-5) then
        tmp = ((x * (y * z)) - (j * ((y * i) - (a * c)))) - (b * (z * c))
    else
        tmp = t * ((b * i) - (x * a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (t <= -5.2e+267) {
		tmp = (y * t) * ((b * (i / y)) - (a * (x / y)));
	} else if (t <= -3.9e+18) {
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	} else if (t <= 1.02e-5) {
		tmp = ((x * (y * z)) - (j * ((y * i) - (a * c)))) - (b * (z * c));
	} else {
		tmp = t * ((b * i) - (x * a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if t <= -5.2e+267:
		tmp = (y * t) * ((b * (i / y)) - (a * (x / y)))
	elif t <= -3.9e+18:
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)))
	elif t <= 1.02e-5:
		tmp = ((x * (y * z)) - (j * ((y * i) - (a * c)))) - (b * (z * c))
	else:
		tmp = t * ((b * i) - (x * a))
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (t <= -5.2e+267)
		tmp = Float64(Float64(y * t) * Float64(Float64(b * Float64(i / y)) - Float64(a * Float64(x / y))));
	elseif (t <= -3.9e+18)
		tmp = Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) + Float64(b * Float64(Float64(t * i) - Float64(z * c))));
	elseif (t <= 1.02e-5)
		tmp = Float64(Float64(Float64(x * Float64(y * z)) - Float64(j * Float64(Float64(y * i) - Float64(a * c)))) - Float64(b * Float64(z * c)));
	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)
	tmp = 0.0;
	if (t <= -5.2e+267)
		tmp = (y * t) * ((b * (i / y)) - (a * (x / y)));
	elseif (t <= -3.9e+18)
		tmp = (x * ((y * z) - (t * a))) + (b * ((t * i) - (z * c)));
	elseif (t <= 1.02e-5)
		tmp = ((x * (y * z)) - (j * ((y * i) - (a * c)))) - (b * (z * c));
	else
		tmp = t * ((b * i) - (x * a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[t, -5.2e+267], N[(N[(y * t), $MachinePrecision] * N[(N[(b * N[(i / y), $MachinePrecision]), $MachinePrecision] - N[(a * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -3.9e+18], 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], If[LessEqual[t, 1.02e-5], N[(N[(N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision] - N[(j * N[(N[(y * i), $MachinePrecision] - N[(a * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(b * N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.20000000000000005e267

   1. Initial program 9.4%

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

   3. Taylor expanded in y around -inf 18.5%

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

   5. Simplified 27.6%

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

   6. Taylor expanded in t around inf 82.5%

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

      1. associate-*r* 90.9%

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

      2. +-commutative 90.9%

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

      3. mul-1-neg 90.9%

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

      4. unsub-neg 90.9%

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

      5. associate-/l* 90.9%

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

      6. associate-/l* 90.9%

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

   8. Simplified 90.9%

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

   if -5.20000000000000005e267 < t < -3.9e18

   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 j around 0 78.8%

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

   if -3.9e18 < t < 1.0200000000000001e-5

   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 t around 0 72.7%

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

   if 1.0200000000000001e-5 < t

   1. Initial program 59.2%

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

   3. Taylor expanded in t around inf 78.1%

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

      1. distribute-lft-out-- 78.1%

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

      2. *-commutative 78.1%

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

   5. Simplified 78.1%

      \[\leadsto \color{blue}{t \cdot \left(-1 \cdot \left(a \cdot x - i \cdot b\right)\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+267}:\\ \;\;\;\;\left(y \cdot t\right) \cdot \left(b \cdot \frac{i}{y} - a \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{+18}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-5}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z\right) - j \cdot \left(y \cdot i - a \cdot c\right)\right) - b \cdot \left(z \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b \cdot i - x \cdot a\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -1.1 \cdot 10^{-36}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-282}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-74}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c)))) (t_2 (* j (- (* a c) (* y i)))))
   (if (<= j -1.1e-36)
     t_2
     (if (<= j -1.45e-282)
       t_1
       (if (<= j 4.8e-300)
         (* y (* x z))
         (if (<= j 7.5e-74)
           t_1
           (if (<= j 5.6e+31) (* a (- (* c j) (* x t))) 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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.1e-36) {
		tmp = t_2;
	} else if (j <= -1.45e-282) {
		tmp = t_1;
	} else if (j <= 4.8e-300) {
		tmp = y * (x * z);
	} else if (j <= 7.5e-74) {
		tmp = t_1;
	} else if (j <= 5.6e+31) {
		tmp = a * ((c * j) - (x * t));
	} 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 = j * ((a * c) - (y * i))
    if (j <= (-1.1d-36)) then
        tmp = t_2
    else if (j <= (-1.45d-282)) then
        tmp = t_1
    else if (j <= 4.8d-300) then
        tmp = y * (x * z)
    else if (j <= 7.5d-74) then
        tmp = t_1
    else if (j <= 5.6d+31) then
        tmp = a * ((c * j) - (x * t))
    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 = j * ((a * c) - (y * i));
	double tmp;
	if (j <= -1.1e-36) {
		tmp = t_2;
	} else if (j <= -1.45e-282) {
		tmp = t_1;
	} else if (j <= 4.8e-300) {
		tmp = y * (x * z);
	} else if (j <= 7.5e-74) {
		tmp = t_1;
	} else if (j <= 5.6e+31) {
		tmp = a * ((c * j) - (x * t));
	} 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 = j * ((a * c) - (y * i))
	tmp = 0
	if j <= -1.1e-36:
		tmp = t_2
	elif j <= -1.45e-282:
		tmp = t_1
	elif j <= 4.8e-300:
		tmp = y * (x * z)
	elif j <= 7.5e-74:
		tmp = t_1
	elif j <= 5.6e+31:
		tmp = a * ((c * j) - (x * t))
	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(j * Float64(Float64(a * c) - Float64(y * i)))
	tmp = 0.0
	if (j <= -1.1e-36)
		tmp = t_2;
	elseif (j <= -1.45e-282)
		tmp = t_1;
	elseif (j <= 4.8e-300)
		tmp = Float64(y * Float64(x * z));
	elseif (j <= 7.5e-74)
		tmp = t_1;
	elseif (j <= 5.6e+31)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	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 = j * ((a * c) - (y * i));
	tmp = 0.0;
	if (j <= -1.1e-36)
		tmp = t_2;
	elseif (j <= -1.45e-282)
		tmp = t_1;
	elseif (j <= 4.8e-300)
		tmp = y * (x * z);
	elseif (j <= 7.5e-74)
		tmp = t_1;
	elseif (j <= 5.6e+31)
		tmp = a * ((c * j) - (x * t));
	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[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -1.1e-36], t$95$2, If[LessEqual[j, -1.45e-282], t$95$1, If[LessEqual[j, 4.8e-300], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[j, 7.5e-74], t$95$1, If[LessEqual[j, 5.6e+31], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if j < -1.1e-36 or 5.60000000000000034e31 < j

   1. Initial program 75.9%

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

   3. Taylor expanded in t around 0 66.5%

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

   4. Taylor expanded in j around inf 59.0%

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

      1. *-commutative 59.0%

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

   6. Simplified 59.0%

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

   if -1.1e-36 < j < -1.44999999999999999e-282 or 4.79999999999999999e-300 < j < 7.5e-74

   1. Initial program 69.9%

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

   3. Taylor expanded in b around inf 58.3%

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

   if -1.44999999999999999e-282 < j < 4.79999999999999999e-300

   1. Initial program 61.9%

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

   3. Taylor expanded in z around inf 69.8%

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

      1. *-commutative 69.8%

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

      2. *-commutative 69.8%

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

   5. Simplified 69.8%

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

   6. Taylor expanded in y around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. associate-*r* 76.7%

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

   8. Simplified 76.7%

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

   if 7.5e-74 < j < 5.60000000000000034e31

   1. Initial program 70.8%

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

   3. Taylor expanded in 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. Simplified 55.5%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -1.1 \cdot 10^{-36}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq -1.45 \cdot 10^{-282}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.8 \cdot 10^{-300}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;j \leq 7.5 \cdot 10^{-74}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 5.6 \cdot 10^{+31}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 69.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i - z \cdot c\right)\\ t_2 := x \cdot \left(y \cdot z - t \cdot a\right)\\ t_3 := t\_2 + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{if}\;j \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-123}:\\ \;\;\;\;t\_2 + t\_1\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+53}:\\ \;\;\;\;t\_1 - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (- (* t i) (* z c))))
        (t_2 (* x (- (* y z) (* t a))))
        (t_3 (+ t_2 (* j (- (* a c) (* y i))))))
   (if (<= j -2.8e-52)
     t_3
     (if (<= j 2.6e-123)
       (+ t_2 t_1)
       (if (<= j 4.5e+53) (- t_1 (* a (- (* x t) (* c j)))) t_3)))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (j * ((a * c) - (y * i)));
	double tmp;
	if (j <= -2.8e-52) {
		tmp = t_3;
	} else if (j <= 2.6e-123) {
		tmp = t_2 + t_1;
	} else if (j <= 4.5e+53) {
		tmp = t_1 - (a * ((x * t) - (c * j)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = b * ((t * i) - (z * c))
    t_2 = x * ((y * z) - (t * a))
    t_3 = t_2 + (j * ((a * c) - (y * i)))
    if (j <= (-2.8d-52)) then
        tmp = t_3
    else if (j <= 2.6d-123) then
        tmp = t_2 + t_1
    else if (j <= 4.5d+53) then
        tmp = t_1 - (a * ((x * t) - (c * j)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * ((t * i) - (z * c));
	double t_2 = x * ((y * z) - (t * a));
	double t_3 = t_2 + (j * ((a * c) - (y * i)));
	double tmp;
	if (j <= -2.8e-52) {
		tmp = t_3;
	} else if (j <= 2.6e-123) {
		tmp = t_2 + t_1;
	} else if (j <= 4.5e+53) {
		tmp = t_1 - (a * ((x * t) - (c * j)));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * ((t * i) - (z * c))
	t_2 = x * ((y * z) - (t * a))
	t_3 = t_2 + (j * ((a * c) - (y * i)))
	tmp = 0
	if j <= -2.8e-52:
		tmp = t_3
	elif j <= 2.6e-123:
		tmp = t_2 + t_1
	elif j <= 4.5e+53:
		tmp = t_1 - (a * ((x * t) - (c * j)))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(Float64(t * i) - Float64(z * c)))
	t_2 = Float64(x * Float64(Float64(y * z) - Float64(t * a)))
	t_3 = Float64(t_2 + Float64(j * Float64(Float64(a * c) - Float64(y * i))))
	tmp = 0.0
	if (j <= -2.8e-52)
		tmp = t_3;
	elseif (j <= 2.6e-123)
		tmp = Float64(t_2 + t_1);
	elseif (j <= 4.5e+53)
		tmp = Float64(t_1 - Float64(a * Float64(Float64(x * t) - Float64(c * j))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * ((t * i) - (z * c));
	t_2 = x * ((y * z) - (t * a));
	t_3 = t_2 + (j * ((a * c) - (y * i)));
	tmp = 0.0;
	if (j <= -2.8e-52)
		tmp = t_3;
	elseif (j <= 2.6e-123)
		tmp = t_2 + t_1;
	elseif (j <= 4.5e+53)
		tmp = t_1 - (a * ((x * t) - (c * j)));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(N[(t * i), $MachinePrecision] - N[(z * c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(j * N[(N[(a * c), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[j, -2.8e-52], t$95$3, If[LessEqual[j, 2.6e-123], N[(t$95$2 + t$95$1), $MachinePrecision], If[LessEqual[j, 4.5e+53], N[(t$95$1 - N[(a * N[(N[(x * t), $MachinePrecision] - N[(c * j), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]

Derivation

1. Split input into 3 regimes

2. if j < -2.79999999999999995e-52 or 4.5000000000000002e53 < j

   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 b around 0 70.8%

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

   if -2.79999999999999995e-52 < j < 2.59999999999999995e-123

   1. Initial program 68.8%

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

   3. Taylor expanded in j around 0 75.6%

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

   if 2.59999999999999995e-123 < j < 4.5000000000000002e53

   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 y around 0 78.7%

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

      1. cancel-sign-sub-inv 78.7%

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

      2. *-commutative 78.7%

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

      3. associate-*r* 78.7%

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

      4. *-commutative 78.7%

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

      5. distribute-rgt-in 78.7%

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

      6. +-commutative 78.7%

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

      7. mul-1-neg 78.7%

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

      8. unsub-neg 78.7%

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

      9. *-commutative 78.7%

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

      10. distribute-lft-neg-in 78.7%

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

      11. sub-neg 78.7%

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

      12. distribute-rgt-neg-out 78.7%

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

      13. distribute-lft-out 75.6%

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

      14. +-commutative 75.6%

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

      15. distribute-rgt-neg-out 75.6%

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

      16. distribute-rgt-neg-in 75.6%

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

      17. mul-1-neg 75.6%

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

   5. Simplified 78.7%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;j \leq -2.8 \cdot 10^{-52}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \mathbf{elif}\;j \leq 2.6 \cdot 10^{-123}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + b \cdot \left(t \cdot i - z \cdot c\right)\\ \mathbf{elif}\;j \leq 4.5 \cdot 10^{+53}:\\ \;\;\;\;b \cdot \left(t \cdot i - z \cdot c\right) - a \cdot \left(x \cdot t - c \cdot j\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z - t \cdot a\right) + j \cdot \left(a \cdot c - y \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 30.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+34}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-259}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{+106}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* x (* y z))))
   (if (<= y -1.85e+65)
     t_2
     (if (<= y -6e+40)
       t_1
       (if (<= y -4.5e+34)
         t_2
         (if (<= y -2.35e-259) (* a (* c j)) (if (<= y 7.1e+106) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -1.85e+65) {
		tmp = t_2;
	} else if (y <= -6e+40) {
		tmp = t_1;
	} else if (y <= -4.5e+34) {
		tmp = t_2;
	} else if (y <= -2.35e-259) {
		tmp = a * (c * j);
	} else if (y <= 7.1e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = x * (y * z)
    if (y <= (-1.85d+65)) then
        tmp = t_2
    else if (y <= (-6d+40)) then
        tmp = t_1
    else if (y <= (-4.5d+34)) then
        tmp = t_2
    else if (y <= (-2.35d-259)) then
        tmp = a * (c * j)
    else if (y <= 7.1d+106) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = x * (y * z);
	double tmp;
	if (y <= -1.85e+65) {
		tmp = t_2;
	} else if (y <= -6e+40) {
		tmp = t_1;
	} else if (y <= -4.5e+34) {
		tmp = t_2;
	} else if (y <= -2.35e-259) {
		tmp = a * (c * j);
	} else if (y <= 7.1e+106) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = x * (y * z)
	tmp = 0
	if y <= -1.85e+65:
		tmp = t_2
	elif y <= -6e+40:
		tmp = t_1
	elif y <= -4.5e+34:
		tmp = t_2
	elif y <= -2.35e-259:
		tmp = a * (c * j)
	elif y <= 7.1e+106:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (y <= -1.85e+65)
		tmp = t_2;
	elseif (y <= -6e+40)
		tmp = t_1;
	elseif (y <= -4.5e+34)
		tmp = t_2;
	elseif (y <= -2.35e-259)
		tmp = Float64(a * Float64(c * j));
	elseif (y <= 7.1e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = x * (y * z);
	tmp = 0.0;
	if (y <= -1.85e+65)
		tmp = t_2;
	elseif (y <= -6e+40)
		tmp = t_1;
	elseif (y <= -4.5e+34)
		tmp = t_2;
	elseif (y <= -2.35e-259)
		tmp = a * (c * j);
	elseif (y <= 7.1e+106)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.85e+65], t$95$2, If[LessEqual[y, -6e+40], t$95$1, If[LessEqual[y, -4.5e+34], t$95$2, If[LessEqual[y, -2.35e-259], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.1e+106], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.84999999999999997e65 or -6.0000000000000004e40 < y < -4.5e34 or 7.1000000000000003e106 < y

   1. Initial program 62.4%

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

   3. Taylor expanded in t around 0 59.6%

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

   4. Taylor expanded in j around 0 44.0%

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

      1. *-commutative 44.0%

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

   6. Simplified 44.0%

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

   7. Taylor expanded in x around inf 44.1%

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

      1. *-commutative 44.1%

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

   9. Simplified 44.1%

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

   if -1.84999999999999997e65 < y < -6.0000000000000004e40 or -2.34999999999999999e-259 < y < 7.1000000000000003e106

   1. Initial program 75.1%

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

   3. Taylor expanded in i around inf 48.5%

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

      1. distribute-lft-out-- 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in j around 0 41.0%

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

      1. *-commutative 41.0%

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

   8. Simplified 41.0%

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

   if -4.5e34 < y < -2.34999999999999999e-259

   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 a around inf 49.3%

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

      1. +-commutative 49.3%

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

      2. mul-1-neg 49.3%

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

      3. unsub-neg 49.3%

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

      4. *-commutative 49.3%

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

   5. Simplified 49.3%

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

   6. Taylor expanded in j around inf 28.7%

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

4. Final simplification 39.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+65}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{+40}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -2.35 \cdot 10^{-259}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;y \leq 7.1 \cdot 10^{+106}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 29.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-199}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+163}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= y -2.8e+73)
   (* z (* x y))
   (if (<= y 9e-199)
     (* (* z c) (- b))
     (if (<= y 2.2e+43)
       (* b (* t i))
       (if (<= y 1.12e+163) (* j (* a c)) (* i (* y (- j))))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.8e+73) {
		tmp = z * (x * y);
	} else if (y <= 9e-199) {
		tmp = (z * c) * -b;
	} else if (y <= 2.2e+43) {
		tmp = b * (t * i);
	} else if (y <= 1.12e+163) {
		tmp = j * (a * c);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (y <= (-2.8d+73)) then
        tmp = z * (x * y)
    else if (y <= 9d-199) then
        tmp = (z * c) * -b
    else if (y <= 2.2d+43) then
        tmp = b * (t * i)
    else if (y <= 1.12d+163) then
        tmp = j * (a * c)
    else
        tmp = i * (y * -j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (y <= -2.8e+73) {
		tmp = z * (x * y);
	} else if (y <= 9e-199) {
		tmp = (z * c) * -b;
	} else if (y <= 2.2e+43) {
		tmp = b * (t * i);
	} else if (y <= 1.12e+163) {
		tmp = j * (a * c);
	} else {
		tmp = i * (y * -j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if y <= -2.8e+73:
		tmp = z * (x * y)
	elif y <= 9e-199:
		tmp = (z * c) * -b
	elif y <= 2.2e+43:
		tmp = b * (t * i)
	elif y <= 1.12e+163:
		tmp = j * (a * c)
	else:
		tmp = i * (y * -j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (y <= -2.8e+73)
		tmp = Float64(z * Float64(x * y));
	elseif (y <= 9e-199)
		tmp = Float64(Float64(z * c) * Float64(-b));
	elseif (y <= 2.2e+43)
		tmp = Float64(b * Float64(t * i));
	elseif (y <= 1.12e+163)
		tmp = Float64(j * Float64(a * c));
	else
		tmp = Float64(i * Float64(y * Float64(-j)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (y <= -2.8e+73)
		tmp = z * (x * y);
	elseif (y <= 9e-199)
		tmp = (z * c) * -b;
	elseif (y <= 2.2e+43)
		tmp = b * (t * i);
	elseif (y <= 1.12e+163)
		tmp = j * (a * c);
	else
		tmp = i * (y * -j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[y, -2.8e+73], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-199], N[(N[(z * c), $MachinePrecision] * (-b)), $MachinePrecision], If[LessEqual[y, 2.2e+43], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.12e+163], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], N[(i * N[(y * (-j)), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -2.80000000000000008e73

   1. Initial program 65.9%

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

   3. Taylor expanded in t around 0 62.5%

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

   4. Taylor expanded in j around 0 47.1%

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

      1. *-commutative 47.1%

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

   6. Simplified 47.1%

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

   7. Taylor expanded in x around inf 45.4%

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

      1. associate-*r* 47.1%

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

      2. *-commutative 47.1%

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

   9. Simplified 47.1%

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

   if -2.80000000000000008e73 < y < 8.99999999999999995e-199

   1. Initial program 79.2%

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

   3. Taylor expanded in t around 0 58.3%

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

   4. Taylor expanded in b around inf 34.2%

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

      1. associate-*r* 34.2%

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

      2. neg-mul-1 34.2%

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

      3. *-commutative 34.2%

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

      4. *-commutative 34.2%

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

   6. Simplified 34.2%

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

   if 8.99999999999999995e-199 < y < 2.20000000000000001e43

   1. Initial program 71.6%

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

   3. Taylor expanded in i around inf 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%

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

   5. Simplified 54.1%

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

   6. Taylor expanded in j around 0 47.1%

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

      1. *-commutative 47.1%

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

   8. Simplified 47.1%

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

   if 2.20000000000000001e43 < y < 1.11999999999999996e163

   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 0 53.9%

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

   4. Taylor expanded in c around inf 46.8%

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

   5. Taylor expanded in a around inf 34.9%

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

      1. associate-*r* 41.7%

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

      2. *-commutative 41.7%

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

   7. Simplified 41.7%

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

   if 1.11999999999999996e163 < y

   1. Initial program 60.9%

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

   3. Taylor expanded in t around 0 61.1%

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

   4. Taylor expanded in c around inf 40.1%

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

   5. Taylor expanded in i around inf 54.3%

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

      1. associate-*r* 54.3%

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

      2. mul-1-neg 54.3%

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

      3. *-commutative 54.3%

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

   7. Simplified 54.3%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{+73}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-199}:\\ \;\;\;\;\left(z \cdot c\right) \cdot \left(-b\right)\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+43}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+163}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{else}:\\ \;\;\;\;i \cdot \left(y \cdot \left(-j\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 28.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ t_2 := y \cdot \left(x \cdot z\right)\\ \mathbf{if}\;x \leq -2.05 \cdot 10^{+53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-256}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+201}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))) (t_2 (* y (* x z))))
   (if (<= x -2.05e+53)
     t_2
     (if (<= x -3.3e-27)
       t_1
       (if (<= x 1.22e-256) (* a (* c j)) (if (<= x 2.9e+201) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = y * (x * z);
	double tmp;
	if (x <= -2.05e+53) {
		tmp = t_2;
	} else if (x <= -3.3e-27) {
		tmp = t_1;
	} else if (x <= 1.22e-256) {
		tmp = a * (c * j);
	} else if (x <= 2.9e+201) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = b * (t * i)
    t_2 = y * (x * z)
    if (x <= (-2.05d+53)) then
        tmp = t_2
    else if (x <= (-3.3d-27)) then
        tmp = t_1
    else if (x <= 1.22d-256) then
        tmp = a * (c * j)
    else if (x <= 2.9d+201) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double t_2 = y * (x * z);
	double tmp;
	if (x <= -2.05e+53) {
		tmp = t_2;
	} else if (x <= -3.3e-27) {
		tmp = t_1;
	} else if (x <= 1.22e-256) {
		tmp = a * (c * j);
	} else if (x <= 2.9e+201) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	t_2 = y * (x * z)
	tmp = 0
	if x <= -2.05e+53:
		tmp = t_2
	elif x <= -3.3e-27:
		tmp = t_1
	elif x <= 1.22e-256:
		tmp = a * (c * j)
	elif x <= 2.9e+201:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	t_2 = Float64(y * Float64(x * z))
	tmp = 0.0
	if (x <= -2.05e+53)
		tmp = t_2;
	elseif (x <= -3.3e-27)
		tmp = t_1;
	elseif (x <= 1.22e-256)
		tmp = Float64(a * Float64(c * j));
	elseif (x <= 2.9e+201)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	t_2 = y * (x * z);
	tmp = 0.0;
	if (x <= -2.05e+53)
		tmp = t_2;
	elseif (x <= -3.3e-27)
		tmp = t_1;
	elseif (x <= 1.22e-256)
		tmp = a * (c * j);
	elseif (x <= 2.9e+201)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.05e+53], t$95$2, If[LessEqual[x, -3.3e-27], t$95$1, If[LessEqual[x, 1.22e-256], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+201], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.05000000000000009e53 or 2.9000000000000002e201 < x

   1. Initial program 68.3%

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

   3. Taylor expanded in z around inf 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

   5. Simplified 49.9%

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

   6. Taylor expanded in y around inf 43.3%

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

      1. *-commutative 43.3%

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

      2. associate-*r* 48.3%

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

   8. Simplified 48.3%

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

   if -2.05000000000000009e53 < x < -3.29999999999999998e-27 or 1.2199999999999999e-256 < x < 2.9000000000000002e201

   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 49.2%

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

      1. distribute-lft-out-- 49.2%

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

   5. Simplified 49.2%

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

   6. Taylor expanded in j around 0 34.0%

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

      1. *-commutative 34.0%

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

   8. Simplified 34.0%

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

   if -3.29999999999999998e-27 < x < 1.2199999999999999e-256

   1. Initial program 72.2%

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

   3. Taylor expanded in a around inf 34.8%

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

      1. +-commutative 34.8%

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

      2. mul-1-neg 34.8%

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

      3. unsub-neg 34.8%

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

      4. *-commutative 34.8%

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

   5. Simplified 34.8%

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

   6. Taylor expanded in j around inf 33.2%

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

4. Final simplification 37.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+53}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-27}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-256}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+201}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 30.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t \cdot i\right)\\ \mathbf{if}\;i \leq -1.05 \cdot 10^{-114}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* b (* t i))))
   (if (<= i -1.05e-114)
     t_1
     (if (<= i 2.25e-246)
       (* y (* x z))
       (if (<= i 1.35e-94)
         (* j (* a c))
         (if (<= i 1.6e+49) (* x (* y z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (i <= -1.05e-114) {
		tmp = t_1;
	} else if (i <= 2.25e-246) {
		tmp = y * (x * z);
	} else if (i <= 1.35e-94) {
		tmp = j * (a * c);
	} else if (i <= 1.6e+49) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: tmp
    t_1 = b * (t * i)
    if (i <= (-1.05d-114)) then
        tmp = t_1
    else if (i <= 2.25d-246) then
        tmp = y * (x * z)
    else if (i <= 1.35d-94) then
        tmp = j * (a * c)
    else if (i <= 1.6d+49) then
        tmp = x * (y * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = b * (t * i);
	double tmp;
	if (i <= -1.05e-114) {
		tmp = t_1;
	} else if (i <= 2.25e-246) {
		tmp = y * (x * z);
	} else if (i <= 1.35e-94) {
		tmp = j * (a * c);
	} else if (i <= 1.6e+49) {
		tmp = x * (y * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = b * (t * i)
	tmp = 0
	if i <= -1.05e-114:
		tmp = t_1
	elif i <= 2.25e-246:
		tmp = y * (x * z)
	elif i <= 1.35e-94:
		tmp = j * (a * c)
	elif i <= 1.6e+49:
		tmp = x * (y * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(b * Float64(t * i))
	tmp = 0.0
	if (i <= -1.05e-114)
		tmp = t_1;
	elseif (i <= 2.25e-246)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 1.35e-94)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 1.6e+49)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = b * (t * i);
	tmp = 0.0;
	if (i <= -1.05e-114)
		tmp = t_1;
	elseif (i <= 2.25e-246)
		tmp = y * (x * z);
	elseif (i <= 1.35e-94)
		tmp = j * (a * c);
	elseif (i <= 1.6e+49)
		tmp = x * (y * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[i, -1.05e-114], t$95$1, If[LessEqual[i, 2.25e-246], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.35e-94], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.6e+49], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if i < -1.04999999999999996e-114 or 1.60000000000000007e49 < i

   1. Initial program 69.0%

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

   3. Taylor expanded in i around inf 61.7%

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

      1. distribute-lft-out-- 61.7%

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

   5. Simplified 61.7%

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

   6. Taylor expanded in j around 0 39.9%

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

      1. *-commutative 39.9%

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

   8. Simplified 39.9%

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

   if -1.04999999999999996e-114 < i < 2.25e-246

   1. Initial program 79.2%

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

   3. Taylor expanded in z around inf 48.2%

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

      1. *-commutative 48.2%

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

      2. *-commutative 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in y around inf 35.1%

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

      1. *-commutative 35.1%

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

      2. associate-*r* 39.6%

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

   8. Simplified 39.6%

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

   if 2.25e-246 < i < 1.3500000000000001e-94

   1. Initial program 80.5%

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

   3. Taylor expanded in t around 0 69.5%

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

   4. Taylor expanded in c around inf 56.9%

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

   5. Taylor expanded in a around inf 25.0%

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

      1. associate-*r* 40.3%

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

      2. *-commutative 40.3%

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

   7. Simplified 40.3%

      \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

   if 1.3500000000000001e-94 < i < 1.60000000000000007e49

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 61.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in j around 0 47.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto x \cdot \left(y \cdot z\right) - b \cdot \color{blue}{\left(z \cdot c\right)} \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)} \]

   7. Taylor expanded in x around inf 34.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 34.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 39.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.05 \cdot 10^{-114}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{elif}\;i \leq 2.25 \cdot 10^{-246}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 1.35 \cdot 10^{-94}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.6 \cdot 10^{+49}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 30.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -5.4 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 4.6 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -5.4e-114)
   (* t (* b i))
   (if (<= i 1.8e-247)
     (* y (* x z))
     (if (<= i 4.6e-95)
       (* j (* a c))
       (if (<= i 1.65e+58) (* x (* y z)) (* b (* t i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -5.4e-114) {
		tmp = t * (b * i);
	} else if (i <= 1.8e-247) {
		tmp = y * (x * z);
	} else if (i <= 4.6e-95) {
		tmp = j * (a * c);
	} else if (i <= 1.65e+58) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-5.4d-114)) then
        tmp = t * (b * i)
    else if (i <= 1.8d-247) then
        tmp = y * (x * z)
    else if (i <= 4.6d-95) then
        tmp = j * (a * c)
    else if (i <= 1.65d+58) then
        tmp = x * (y * z)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -5.4e-114) {
		tmp = t * (b * i);
	} else if (i <= 1.8e-247) {
		tmp = y * (x * z);
	} else if (i <= 4.6e-95) {
		tmp = j * (a * c);
	} else if (i <= 1.65e+58) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -5.4e-114:
		tmp = t * (b * i)
	elif i <= 1.8e-247:
		tmp = y * (x * z)
	elif i <= 4.6e-95:
		tmp = j * (a * c)
	elif i <= 1.65e+58:
		tmp = x * (y * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -5.4e-114)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 1.8e-247)
		tmp = Float64(y * Float64(x * z));
	elseif (i <= 4.6e-95)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 1.65e+58)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -5.4e-114)
		tmp = t * (b * i);
	elseif (i <= 1.8e-247)
		tmp = y * (x * z);
	elseif (i <= 4.6e-95)
		tmp = j * (a * c);
	elseif (i <= 1.65e+58)
		tmp = x * (y * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -5.4e-114], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.8e-247], N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 4.6e-95], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.65e+58], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -5.3999999999999999e-114

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 61.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 61.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 61.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 39.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.8%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 39.8%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 39.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 40.7%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 40.7%

          \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

   11. Simplified 40.7%

       \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} \]

   if -5.3999999999999999e-114 < i < 1.7999999999999998e-247

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in z around inf 48.2%

      \[\leadsto \color{blue}{z \cdot \left(x \cdot y - b \cdot c\right)} \]
   4. Step-by-step derivation

      1. *-commutative 48.2%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - b \cdot c\right) \]

      2. *-commutative 48.2%

         \[\leadsto z \cdot \left(y \cdot x - \color{blue}{c \cdot b}\right) \]

   5. Simplified 48.2%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - c \cdot b\right)} \]

   6. Taylor expanded in y around inf 35.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   7. Step-by-step derivation

      1. *-commutative 35.1%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. associate-*r* 39.6%

         \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   8. Simplified 39.6%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]

   if 1.7999999999999998e-247 < i < 4.59999999999999998e-95

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 69.5%

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around inf 56.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c} + \left(a \cdot j + \frac{x \cdot \left(y \cdot z\right)}{c}\right)\right) - b \cdot z\right)} \]

   5. Taylor expanded in a around inf 25.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.3%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

      2. *-commutative 40.3%

         \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   7. Simplified 40.3%

      \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

   if 4.59999999999999998e-95 < i < 1.64999999999999991e58

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 61.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in j around 0 47.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto x \cdot \left(y \cdot z\right) - b \cdot \color{blue}{\left(z \cdot c\right)} \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)} \]

   7. Taylor expanded in x around inf 34.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 34.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if 1.64999999999999991e58 < i

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 63.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 40.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -5.4 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.8 \cdot 10^{-247}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;i \leq 4.6 \cdot 10^{-95}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 29.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -2.55 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{-246}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 10^{-94}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -2.55e-114)
   (* t (* b i))
   (if (<= i 1.12e-246)
     (* z (* x y))
     (if (<= i 1e-94)
       (* j (* a c))
       (if (<= i 2.2e+54) (* x (* y z)) (* b (* t i)))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -2.55e-114) {
		tmp = t * (b * i);
	} else if (i <= 1.12e-246) {
		tmp = z * (x * y);
	} else if (i <= 1e-94) {
		tmp = j * (a * c);
	} else if (i <= 2.2e+54) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-2.55d-114)) then
        tmp = t * (b * i)
    else if (i <= 1.12d-246) then
        tmp = z * (x * y)
    else if (i <= 1d-94) then
        tmp = j * (a * c)
    else if (i <= 2.2d+54) then
        tmp = x * (y * z)
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -2.55e-114) {
		tmp = t * (b * i);
	} else if (i <= 1.12e-246) {
		tmp = z * (x * y);
	} else if (i <= 1e-94) {
		tmp = j * (a * c);
	} else if (i <= 2.2e+54) {
		tmp = x * (y * z);
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -2.55e-114:
		tmp = t * (b * i)
	elif i <= 1.12e-246:
		tmp = z * (x * y)
	elif i <= 1e-94:
		tmp = j * (a * c)
	elif i <= 2.2e+54:
		tmp = x * (y * z)
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -2.55e-114)
		tmp = Float64(t * Float64(b * i));
	elseif (i <= 1.12e-246)
		tmp = Float64(z * Float64(x * y));
	elseif (i <= 1e-94)
		tmp = Float64(j * Float64(a * c));
	elseif (i <= 2.2e+54)
		tmp = Float64(x * Float64(y * z));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -2.55e-114)
		tmp = t * (b * i);
	elseif (i <= 1.12e-246)
		tmp = z * (x * y);
	elseif (i <= 1e-94)
		tmp = j * (a * c);
	elseif (i <= 2.2e+54)
		tmp = x * (y * z);
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -2.55e-114], N[(t * N[(b * i), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1.12e-246], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 1e-94], N[(j * N[(a * c), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.2e+54], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if i < -2.55e-114

   1. Initial program 71.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 61.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 61.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 61.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 39.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 39.8%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 39.8%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   9. Taylor expanded in b around 0 39.8%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   10. Step-by-step derivation

       1. associate-*r* 40.7%

          \[\leadsto \color{blue}{\left(b \cdot i\right) \cdot t} \]

       2. *-commutative 40.7%

          \[\leadsto \color{blue}{\left(i \cdot b\right)} \cdot t \]

   11. Simplified 40.7%

       \[\leadsto \color{blue}{\left(i \cdot b\right) \cdot t} \]

   if -2.55e-114 < i < 1.11999999999999995e-246

   1. Initial program 79.2%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 55.5%

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in j around 0 36.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 36.7%

         \[\leadsto x \cdot \left(y \cdot z\right) - b \cdot \color{blue}{\left(z \cdot c\right)} \]

   6. Simplified 36.7%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)} \]

   7. Taylor expanded in x around inf 35.1%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. associate-*r* 39.6%

         \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot z} \]

      2. *-commutative 39.6%

         \[\leadsto \color{blue}{\left(y \cdot x\right)} \cdot z \]

   9. Simplified 39.6%

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot z} \]

   if 1.11999999999999995e-246 < i < 9.9999999999999996e-95

   1. Initial program 80.5%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 69.5%

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in c around inf 56.9%

      \[\leadsto \color{blue}{c \cdot \left(\left(-1 \cdot \frac{i \cdot \left(j \cdot y\right)}{c} + \left(a \cdot j + \frac{x \cdot \left(y \cdot z\right)}{c}\right)\right) - b \cdot z\right)} \]

   5. Taylor expanded in a around inf 25.0%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 40.3%

         \[\leadsto \color{blue}{\left(a \cdot c\right) \cdot j} \]

      2. *-commutative 40.3%

         \[\leadsto \color{blue}{\left(c \cdot a\right)} \cdot j \]

   7. Simplified 40.3%

      \[\leadsto \color{blue}{\left(c \cdot a\right) \cdot j} \]

   if 9.9999999999999996e-95 < i < 2.1999999999999999e54

   1. Initial program 66.9%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 61.0%

      \[\leadsto \color{blue}{\left(j \cdot \left(a \cdot c - i \cdot y\right) + x \cdot \left(y \cdot z\right)\right) - b \cdot \left(c \cdot z\right)} \]

   4. Taylor expanded in j around 0 47.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right) - b \cdot \left(c \cdot z\right)} \]
   5. Step-by-step derivation

      1. *-commutative 47.8%

         \[\leadsto x \cdot \left(y \cdot z\right) - b \cdot \color{blue}{\left(z \cdot c\right)} \]

   6. Simplified 47.8%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right) - b \cdot \left(z \cdot c\right)} \]

   7. Taylor expanded in x around inf 34.9%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot z\right)} \]
   8. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   9. Simplified 34.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot y\right)} \]

   if 2.1999999999999999e54 < i

   1. Initial program 63.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 63.2%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 63.2%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 40.2%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 40.2%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 40.2%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -2.55 \cdot 10^{-114}:\\ \;\;\;\;t \cdot \left(b \cdot i\right)\\ \mathbf{elif}\;i \leq 1.12 \cdot 10^{-246}:\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;i \leq 10^{-94}:\\ \;\;\;\;j \cdot \left(a \cdot c\right)\\ \mathbf{elif}\;i \leq 2.2 \cdot 10^{+54}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 39.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -3.9 \cdot 10^{+231}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-114}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq 2.55 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (<= i -3.9e+231)
   (* y (* i (- j)))
   (if (<= i -5.4e-114)
     (* i (* t b))
     (if (<= i 2.55e+156) (* a (- (* c j) (* x t))) (* b (* t i))))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.9e+231) {
		tmp = y * (i * -j);
	} else if (i <= -5.4e-114) {
		tmp = i * (t * b);
	} else if (i <= 2.55e+156) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if (i <= (-3.9d+231)) then
        tmp = y * (i * -j)
    else if (i <= (-5.4d-114)) then
        tmp = i * (t * b)
    else if (i <= 2.55d+156) then
        tmp = a * ((c * j) - (x * t))
    else
        tmp = b * (t * i)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if (i <= -3.9e+231) {
		tmp = y * (i * -j);
	} else if (i <= -5.4e-114) {
		tmp = i * (t * b);
	} else if (i <= 2.55e+156) {
		tmp = a * ((c * j) - (x * t));
	} else {
		tmp = b * (t * i);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if i <= -3.9e+231:
		tmp = y * (i * -j)
	elif i <= -5.4e-114:
		tmp = i * (t * b)
	elif i <= 2.55e+156:
		tmp = a * ((c * j) - (x * t))
	else:
		tmp = b * (t * i)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if (i <= -3.9e+231)
		tmp = Float64(y * Float64(i * Float64(-j)));
	elseif (i <= -5.4e-114)
		tmp = Float64(i * Float64(t * b));
	elseif (i <= 2.55e+156)
		tmp = Float64(a * Float64(Float64(c * j) - Float64(x * t)));
	else
		tmp = Float64(b * Float64(t * i));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if (i <= -3.9e+231)
		tmp = y * (i * -j);
	elseif (i <= -5.4e-114)
		tmp = i * (t * b);
	elseif (i <= 2.55e+156)
		tmp = a * ((c * j) - (x * t));
	else
		tmp = b * (t * i);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[LessEqual[i, -3.9e+231], N[(y * N[(i * (-j)), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, -5.4e-114], N[(i * N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[i, 2.55e+156], N[(a * N[(N[(c * j), $MachinePrecision] - N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if i < -3.9000000000000002e231

   1. Initial program 58.1%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 85.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 85.8%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 85.8%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around inf 72.7%

      \[\leadsto \color{blue}{-1 \cdot \left(i \cdot \left(j \cdot y\right)\right)} \]
   7. Step-by-step derivation

      1. mul-1-neg 72.7%

         \[\leadsto \color{blue}{-i \cdot \left(j \cdot y\right)} \]

      2. associate-*r* 72.7%

         \[\leadsto -\color{blue}{\left(i \cdot j\right) \cdot y} \]

   8. Simplified 72.7%

      \[\leadsto \color{blue}{-\left(i \cdot j\right) \cdot y} \]

   if -3.9000000000000002e231 < i < -5.3999999999999999e-114

   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 i around inf 56.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 56.6%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 56.6%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 43.9%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-1 \cdot \left(b \cdot t\right)\right)}\right) \]
   7. Step-by-step derivation

      1. mul-1-neg 43.9%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(-b \cdot t\right)}\right) \]

      2. distribute-lft-neg-out 43.9%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(\left(-b\right) \cdot t\right)}\right) \]

      3. *-commutative 43.9%

         \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(t \cdot \left(-b\right)\right)}\right) \]

   8. Simplified 43.9%

      \[\leadsto i \cdot \left(-1 \cdot \color{blue}{\left(t \cdot \left(-b\right)\right)}\right) \]

   if -5.3999999999999999e-114 < i < 2.55000000000000007e156

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 45.4%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 45.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 45.4%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 45.4%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 45.4%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 45.4%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   if 2.55000000000000007e156 < i

   1. Initial program 52.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 78.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 78.0%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 78.0%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 49.4%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 49.4%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 49.4%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 46.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -3.9 \cdot 10^{+231}:\\ \;\;\;\;y \cdot \left(i \cdot \left(-j\right)\right)\\ \mathbf{elif}\;i \leq -5.4 \cdot 10^{-114}:\\ \;\;\;\;i \cdot \left(t \cdot b\right)\\ \mathbf{elif}\;i \leq 2.55 \cdot 10^{+156}:\\ \;\;\;\;a \cdot \left(c \cdot j - x \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 29.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{-155} \lor \neg \left(i \leq 1.62 \cdot 10^{+59}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (if (or (<= i -1.55e-155) (not (<= i 1.62e+59))) (* b (* t i)) (* a (* c j))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.55e-155) || !(i <= 1.62e+59)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: tmp
    if ((i <= (-1.55d-155)) .or. (.not. (i <= 1.62d+59))) then
        tmp = b * (t * i)
    else
        tmp = a * (c * j)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double tmp;
	if ((i <= -1.55e-155) || !(i <= 1.62e+59)) {
		tmp = b * (t * i);
	} else {
		tmp = a * (c * j);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	tmp = 0
	if (i <= -1.55e-155) or not (i <= 1.62e+59):
		tmp = b * (t * i)
	else:
		tmp = a * (c * j)
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0
	if ((i <= -1.55e-155) || !(i <= 1.62e+59))
		tmp = Float64(b * Float64(t * i));
	else
		tmp = Float64(a * Float64(c * j));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	tmp = 0.0;
	if ((i <= -1.55e-155) || ~((i <= 1.62e+59)))
		tmp = b * (t * i);
	else
		tmp = a * (c * j);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := If[Or[LessEqual[i, -1.55e-155], N[Not[LessEqual[i, 1.62e+59]], $MachinePrecision]], N[(b * N[(t * i), $MachinePrecision]), $MachinePrecision], N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if i < -1.55e-155 or 1.6200000000000001e59 < i

   1. Initial program 69.3%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in i around inf 58.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y\right) - -1 \cdot \left(b \cdot t\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft-out-- 58.3%

         \[\leadsto i \cdot \color{blue}{\left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   5. Simplified 58.3%

      \[\leadsto \color{blue}{i \cdot \left(-1 \cdot \left(j \cdot y - b \cdot t\right)\right)} \]

   6. Taylor expanded in j around 0 38.0%

      \[\leadsto \color{blue}{b \cdot \left(i \cdot t\right)} \]
   7. Step-by-step derivation

      1. *-commutative 38.0%

         \[\leadsto b \cdot \color{blue}{\left(t \cdot i\right)} \]

   8. Simplified 38.0%

      \[\leadsto \color{blue}{b \cdot \left(t \cdot i\right)} \]

   if -1.55e-155 < i < 1.6200000000000001e59

   1. Initial program 76.8%

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
   2. Add Preprocessing

   3. Taylor expanded in a around inf 46.5%

      \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
   4. Step-by-step derivation

      1. +-commutative 46.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

      2. mul-1-neg 46.5%

         \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

      3. unsub-neg 46.5%

         \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

      4. *-commutative 46.5%

         \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

   5. Simplified 46.5%

      \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

   6. Taylor expanded in j around inf 26.2%

      \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;i \leq -1.55 \cdot 10^{-155} \lor \neg \left(i \leq 1.62 \cdot 10^{+59}\right):\\ \;\;\;\;b \cdot \left(t \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(c \cdot j\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 28: 21.8% accurate, 5.8× speedup

Math

\[\begin{array}{l} \\ a \cdot \left(c \cdot j\right) \end{array} \]

FPCore

(FPCore (x y z t a b c i j) :precision binary64 (* a (* c j)))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    code = a * (c * j)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	return a * (c * j);
}

Python

def code(x, y, z, t, a, b, c, i, j):
	return a * (c * j)

Julia

function code(x, y, z, t, a, b, c, i, j)
	return Float64(a * Float64(c * j))
end

MATLAB

function tmp = code(x, y, z, t, a, b, c, i, j)
	tmp = a * (c * j);
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := N[(a * N[(c * j), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.4%

   \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right) \]
2. Add Preprocessing

3. Taylor expanded in a around inf 36.5%

   \[\leadsto \color{blue}{a \cdot \left(-1 \cdot \left(t \cdot x\right) + c \cdot j\right)} \]
4. Step-by-step derivation

   1. +-commutative 36.5%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j + -1 \cdot \left(t \cdot x\right)\right)} \]

   2. mul-1-neg 36.5%

      \[\leadsto a \cdot \left(c \cdot j + \color{blue}{\left(-t \cdot x\right)}\right) \]

   3. unsub-neg 36.5%

      \[\leadsto a \cdot \color{blue}{\left(c \cdot j - t \cdot x\right)} \]

   4. *-commutative 36.5%

      \[\leadsto a \cdot \left(\color{blue}{j \cdot c} - t \cdot x\right) \]

5. Simplified 36.5%

   \[\leadsto \color{blue}{a \cdot \left(j \cdot c - t \cdot x\right)} \]

6. Taylor expanded in j around inf 17.8%

   \[\leadsto \color{blue}{a \cdot \left(c \cdot j\right)} \]

7. Final simplification 17.8%

   \[\leadsto a \cdot \left(c \cdot j\right) \]
8. Add Preprocessing

Developer target: 59.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := j \cdot \left(c \cdot a - y \cdot i\right)\\ t_2 := \left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + t\_1\\ \mathbf{if}\;x < -1.469694296777705 \cdot 10^{-64}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;x < 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - t\_1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b c i j)
 :precision binary64
 (let* ((t_1 (* j (- (* c a) (* y i))))
        (t_2
         (+
          (-
           (* x (- (* y z) (* t a)))
           (/
            (* b (- (pow (* c z) 2.0) (pow (* t i) 2.0)))
            (+ (* c z) (* t i))))
          t_1)))
   (if (< x -1.469694296777705e-64)
     t_2
     (if (< x 3.2113527362226803e-147)
       (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) t_1))
       t_2))))

C

double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (pow((c * z), 2.0) - pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b, c, i, j)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: i
    real(8), intent (in) :: j
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = j * ((c * a) - (y * i))
    t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ** 2.0d0) - ((t * i) ** 2.0d0))) / ((c * z) + (t * i)))) + t_1
    if (x < (-1.469694296777705d-64)) then
        tmp = t_2
    else if (x < 3.2113527362226803d-147) then
        tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
	double t_1 = j * ((c * a) - (y * i));
	double t_2 = ((x * ((y * z) - (t * a))) - ((b * (Math.pow((c * z), 2.0) - Math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1;
	double tmp;
	if (x < -1.469694296777705e-64) {
		tmp = t_2;
	} else if (x < 3.2113527362226803e-147) {
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b, c, i, j):
	t_1 = j * ((c * a) - (y * i))
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (math.pow((c * z), 2.0) - math.pow((t * i), 2.0))) / ((c * z) + (t * i)))) + t_1
	tmp = 0
	if x < -1.469694296777705e-64:
		tmp = t_2
	elif x < 3.2113527362226803e-147:
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b, c, i, j)
	t_1 = Float64(j * Float64(Float64(c * a) - Float64(y * i)))
	t_2 = Float64(Float64(Float64(x * Float64(Float64(y * z) - Float64(t * a))) - Float64(Float64(b * Float64((Float64(c * z) ^ 2.0) - (Float64(t * i) ^ 2.0))) / Float64(Float64(c * z) + Float64(t * i)))) + t_1)
	tmp = 0.0
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = Float64(Float64(Float64(Float64(b * i) - Float64(x * a)) * t) - Float64(Float64(z * Float64(c * b)) - t_1));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b, c, i, j)
	t_1 = j * ((c * a) - (y * i));
	t_2 = ((x * ((y * z) - (t * a))) - ((b * (((c * z) ^ 2.0) - ((t * i) ^ 2.0))) / ((c * z) + (t * i)))) + t_1;
	tmp = 0.0;
	if (x < -1.469694296777705e-64)
		tmp = t_2;
	elseif (x < 3.2113527362226803e-147)
		tmp = (((b * i) - (x * a)) * t) - ((z * (c * b)) - t_1);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_, c_, i_, j_] := Block[{t$95$1 = N[(j * N[(N[(c * a), $MachinePrecision] - N[(y * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(x * N[(N[(y * z), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(b * N[(N[Power[N[(c * z), $MachinePrecision], 2.0], $MachinePrecision] - N[Power[N[(t * i), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(c * z), $MachinePrecision] + N[(t * i), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[Less[x, -1.469694296777705e-64], t$95$2, If[Less[x, 3.2113527362226803e-147], N[(N[(N[(N[(b * i), $MachinePrecision] - N[(x * a), $MachinePrecision]), $MachinePrecision] * t), $MachinePrecision] - N[(N[(z * N[(c * b), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Reproduce

herbie shell --seed 2024055 
(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)))))